PDE: Partial Differentiable Equation

Neural Operators: Learning nonlinear mappings between function spaces.

Contributed by Chunyang Zhang.

1. Physics-informed machine learning. Nature Reviews Physics, 2021. paper

   George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

2. Neural operator: Learning maps between function spaces. arXiv, 2021. paper

   Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

3. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Physical Review Fluids, 2018. paper

   Jinlong Wu, Heng Xiao, and Eric Paterson.

4. Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Computing Surveys, 2023. paper

   Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar.

5. Physical laws meet machine intelligence: Current developments and future directions. Artificial Intelligence Review, 2022. paper

   Temoor Muther, Amirmasoud Kalantari Dahaghi, Fahad Iqbal Syed, and Vuong Van Pham.

6. A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis.

7. Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Beyond Traditional AI: The Impact of Machine Learning on Scientific Computing, 2022. book

   MingyuanYang and John T.Foster

8. When physics meets machine learning: A survey of physics-informed machine learning. arXiv, 2022. paper

   Chuizheng Meng, Sungyong Seo, Defu Cao, Sam Griesemer, and Yan Liu.

9. Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper

   Salah A. Faroughi, Nikhil M. Pawar, C´elio Fernandes, Subasish Das, Nima K. Kalantari, and Seyed Kourosh Mahjour.

10. Physics-informed machine learning: A survey on problems, methods and applications. arXiv, 2022. paper

    Zhongkai Hao, Songming Liu, Yichi Zhang, Chengyang Ying, Yao Feng, Hang Su, and Jun Zhu.

11. An overview on deep learning-based approximation methods for partial differential equations. arXiv, 2020. paper

    Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, and Benno Kuckuck.

12. Three ways to solve partial differential equations with neural networks—A review. GAMM‐Mitteilungen, 2021. paper

    Jan Blechschmidt and Oliver G. Ernst.

13. Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review. GAMM‐Mitteilungen, 2021. paper

    Alexander Heinlein, Axel Klawonn, Martin Lanser, and Janine Weber.

14. Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing. arXiv, 2022. paper

    Salah A Faroughi, Nikhil Pawar, Celio Fernandes, Subasish Das, Nima K. Kalantari, and Seyed Kourosh Mahjour.

15. Partial differential equations meet deep neural networks: A survey. arXiv, 2022. paper

    Shudong Huang, Wentao Feng, Chenwei Tang, and Jiancheng Lv.

16. Solving differential equations with Deep Learning: A beginner's guide. arXiv, 2023. paper

    Luis Medrano Navarro, Luis Martín Moreno, and Sergio G Rodrigo.

17. Deep learning algorithms for solving differential equations: a survey. Journal of Experimental & Theoretical Artificial Intelligence, 2023. paper

    Harender Kumara and Neha Yadav.

18. An expert's guide to training physics-informed neural networks. arXiv, 2023. paper

    Sifan Wang, Shyam Sankaran, Hanwen Wang, and Paris Perdikaris.

19. A survey on physics informed reinforcement learning: Review and open problems. arXiv, 2023. paper

    Chayan Banerjee, Kien Nguyen, Clinton Fookes, and Maziar Raissi.

20. Neural operators for accelerating scientific simulations and design. arXiv, 2023. paper

    Kamyar Azzizadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar.

21. Machine learning and domain decomposition methods -- A survey. arXiv, 2023. paper

    Axel Klawonn, Martin Lanser, and Janine Weber.

22. The transformative potential of machine learning for experiments in fluid mechanics. Nature Reviews Physics, 2023. paper

    Ricardo Vinuesa, Steven L. Brunton, and Beverley J. McKeon.

23. Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges. Reliability Engineering & System Safety, 2023. paper

    Yanwen Xu, Sara Kohtz, Jessica Boakye, Paolo Gardoni, and Pingfeng Wang.

24. Neural operators for accelerating scientific simulations and design. arXiv, 2024. paper

    Operator learning: Algorithms and analysis.

1. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020. paper

   Raissi Maziar, Alireza Yazdani, and George Em Karniadakis.

2. Deep hidden physics models: Deep learning of nonlinear partial differential equations. JMLR, 2018. paper

   Maziar Raissi.

3. A universal PINNs method for solving partial differential equations with a point source. IJCAI, 2022. paper

   Xiang Huang, Hongsheng Liu, Beiji Shi, Zidong Wang, Kang Yang, Yang Li, Min Wang, Haotian Chu, Jing Zhou, Fan Yu, Bei Hua, Bin Dong, and Lei Chen.

4. Parallel physics-informed neural networks via domain decomposition. JCP, 2021. paper

   Khemraj Shukla, Ameya D.Jagtap, and George Em Karniadakis.

5. Kolmogorov n–width and Lagrangian physics-informed neural networks: A causality-conforming manifold for convection-dominated PDEs. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.

6. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   N.Sukumar and Ankit Srivastava.

7. Physics-informed multi-LSTM networks for meta-modeling of nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 2020. paper

   Ruiyang Zhang, Yang Liu, and Hao Sun.

8. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.

9. Multi-output physics-informed neural networks for forward and inverse PDE problems with uncertainties. Computer Methods in Applied Mechanics and Engineering, 2022. paper

   MingyuanYang and John T.Foster

10. PPINN: Parareal physics-informed neural network for time-dependent PDEs. Computer Methods in Applied Mechanics and Engineering, 2020. paper

    Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis.

11. CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, and Yew-Soon Ong.

12. Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Thomas O’Leary-Roseberry, Umberto Villa, Peng Chen, and Omar Ghattas.

13. Physics-augmented learning: A new paradigm beyond physics-informed learning. NIPS, 2021. paper

    Ziming Liu, Yuanqi Du, Yunyue Chen, and Max Tegmark.

14. Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm. Physics Letters A, 2021. paper

    Yifan Mo, Liming Ling, and Delu Zeng.

15. Solving Benjamin–Ono equation via gradient balanced PINNs approach. The European Physical Journal Plus, 2022. paper

    Xiangyu Yang and Zhen Wang.

16. Robust learning of physics informed neural networks. arXiv, 2021. paper

    Chandrajit Bajaj, Luke McLennan, Timothy Andeen, and Avik Roy.

17. Learning physics-informed neural networks without stacked back-propagation. AISTATS, 2023. paper

    Di He, Wenlei Shi, Shanda Li, Xiaotian Gao, Jia Zhang, Jiang Bian, Liwei Wang, and Tieyan Liu.

18. NeuralPDE: Automating physics-informed neural networks (PINNs) with error approximations. arXiv, 2021. paper

    Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, Nand Vinchhi, Kaushik Balakrishnan, Devesh Upadhyay, and Chris Rackauckas.

19. Physics informed RNN-DCT networks for time-dependent partial differential equations. ICCS, 2022. paper

    Benjamin Wu, Oliver Hennigh, Jan Kautz, Sanjay Choudhry, and Wonmin Byeon.

20. Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation. JCP, 2022. paper

    Amirhossein Arzani, Kevin W.Cassel, and Roshan M.D'Souza.

21. A-PINN: Auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. JCP, 2022. paper

    Lei Yuan, Yiqing Ni, Xiangyun Deng, and Shuo Hao.

22. A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: Comparison with finite element method. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Shahed Rezaei, Ali Harandi, Ahmad Moeineddin, Baixiang Xua, and Stefanie Reese.

23. Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations. Computers & Mathematics with Applications, 2023. paper

    Siping Tang, Xinlong Feng, Wei Wu, and Hui Xu.

24. A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    Revanth Mattey and Susanta Ghosh.

25. RPINNs: Rectified-physics informed neural networks for solving stationary partial differential equations. Computers and Fluids, 2022. paper

    Pai Peng, Jiangong Pan, Hui Xu, and Xinlong Feng.

26. A-WPINN algorithm for the data-driven vector-soliton solutions and parameter discovery of general coupled nonlinear equations. Physica D: Nonlinear Phenomena, 2022. paper

    Shumei Qin, Min Li, Tao Xu, and Shaoqun Dong.

27. Physics-informed neural networks with adaptive localized artificial viscosity. arXiv, 2022. paper

    E.J.R. Coutinho, M. Dall'Aqua, L. McClenny, M. Zhong, U. Braga-Neto, and E. Gildin.

28. Physics-informed neural operator for learning partial differential equations. arXiv, 2021. paper

    Zongyi Li, Hongkai Zheng, Nikola Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, and Anima Anandkumar.

29. Anisotropic, sparse and interpretable physics-informed neural networks for PDEs. arXiv, 2022. paper

    Amuthan A. Ramabathiran and Prabhu Ramachandran.

30. Fast neural network based solving of partial differential equations. arXiv, 2022. paper

    Jaroslaw Rzepecki, Daniel Bates, and Chris Doran.

31. Discontinuity computing using physics-informed neural network. arXiv, 2022. paper

    Li Liu, Shengping Liu, Hui Xie, Fansheng Xiong, Tengchao Yu, Mengjuan Xiao, Lufeng Liu, and Heng Yong.

32. Learning differentiable solvers for systems with hard constraints. arXiv, 2022. paper

    Geoffrey Négiar, Michael W. Mahoney, and Aditi S. Krishnapriyan.

33. Momentum diminishes the effect of spectral bias in physics-informed neural networks. arXiv, 2022. paper

    Ghazal Farhani, Alexander Kazachek, and Boyu Wang.

34. Δ-PINNs: Physics-informed neural networks on complex geometries. arXiv, 2022. paper

    Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris.

35. Replacing automatic differentiation by Sobolev Cubatures fastens physics informed neural nets and strengthens their approximation power. arXiv, 2022. paper

    Juan Esteban Suarez Cardona and Michael Hecht.

36. FO-PINNs: A first-order formulation for physics informed neural networks. arXiv, 2022. paper

    Rini J. Gladstone, Mohammad A. Nabian, and Hadi Meidani.

37. Augmented physics-informed neural networks (APINNs): A gating network-based soft domain decomposition methodology. arXiv, 2022. paper

    Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, and Kenji Kawaguchi.

38. Physics-informed neural networks for operator equations with stochastic data. arXiv, 2022. paper

    Paul Escapil-Inchauspé and Gonzalo A. Ruz.

39. Physics-informed neural networks with unknown measurement noise. arXiv, 2022. paper

    Philipp Pilar and Niklas Wahlstrom.

40. On the compatibility between a neural network and a partial differential equation for physics-informed learning. arXiv, 2022. paper

    Kuangdai Leng and Jeyan Thiyagalingam.

41. Pre-training strategy for solving evolution equations based on physics-informed neural networks. arXiv, 2022. paper

    Jiawei Guo, Yanzhong Yao, Han Wang, and Tongxiang Gu.

42. L-HYDRA: Multi-head physics-informed neural networks. arXiv, 2023. paper

    Zongren Zou and George Em Karniadakis.

43. PINN for dynamical partial differential equations is not training deeper networks rather learning advection and time variance. arXiv, 2023. paper

    Siddharth Rout.

44. Wavelets based physics informed neural networks to solve non-linear differential equations. Scientific Reports, 2023. paper

    Ziya Uddin, Sai Ganga, Rishi Asthana, and Wubshet Ibrahim.

45. Improved training of physics-informed neural networks using energy-based priors: A study on electrical impedance tomography. ICLR, 2023. paper

    Akarsh Pokkunuru, Pedram Rooshenas, Thilo Strauss, Anuj Abhishek, and Taufiquar Khan.

46. Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems. arXiv, 2023. paper

    Sarah Perez, Suryanarayana Maddu, Ivo F. Sbalzarini, and Philippe Poncet.

47. Efficient physics-informed neural networks using hash encoding. arXiv, 2023. paper

    Xinquan Huang and Tariq Alkhalifah.

48. Ensemble learning for physics informed neural networks: A gradient boosting approach. arXiv, 2023. paper

    Zhiwei Fang, Sifan Wang, and Paris Perdikaris.

49. On the limitations of physics-informed deep learning: Illustrations using first order hyperbolic conservation law-based traffic flow models. arXiv, 2023. paper

    Archie J. Huang and Shaurya Agarwal.

50. Achieving high accuracy with PINNs via energy natural gradients. arXiv, 2023. paper

    Johannes Müller and Marius Zeinhofer.

51. Implicit stochastic gradient descent for training physics-informed neural networks. arXiv, 2023. paper

    Ye Li, Songcan Chen, and Shengjun Huang.

52. NSGA-PINN: A multi-objective optimization method for physics-informed neural network training. arXiv, 2023. paper

    Binghang Lu, Christian B. Moya, and Guang Lin.

53. Improving physics-informed neural networks with meta-learned optimization. arXiv, 2023. paper

    Alex Bihlo.

54. MetaPhysiCa: OOD robustness in physics-informed machine learning. arXiv, 2023. paper

    S Chandra Mouli, Muhammad Ashraful Alam, and Bruno Ribeiro.

55. HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions. arXiv, 2023. paper

    Haoyang Zheng, Yao Huang, Ziyang Huang, Wenrui Hao, and Guang Lin.

56. iPINNs: Incremental learning for physics-informed neural networks. arXiv, 2023. paper

    Aleksandr Dekhovich, Marcel H.F. Sluiter, David M.J. Tax, and Miguel A. Bessa.

57. Global convergence of deep Galerkin and PINNs methods for solving partial differential equations. arXiv, 2023. paper

    Francisco Eiras, Adel Bibi, Rudy Bunel, Krishnamurthy Dj Dvijotham, Philip Torr, and M. Pawan Kumar.

58. Provably correct physics-informed neural networks. arXiv, 2023. paper

    Deqing Jiang, Justin Sirignano, and Samuel N. Cohen.

59. Predictive limitations of physics-informed neural networks in vortex shedding. arXiv, 2023. paper

    Pi-Yueh Chuang and Lorena A. Barba.

60. Residual-based error bound for physics-informed neural networks. arXiv, 2023. paper

    Shuheng Liu, Xiyue Huang, and Pavlos Protopapas.

61. Automatic boundary fitting framework of boundary dependent physics-informed neural network solving partial differential equation with complex boundary conditions. Computer Methods in Applied Mechanics and Engineering, 2023. paper

    Yuchen Xie, Yu Ma, and Yahui Wang.

62. Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics informed neural networks. arXiv, 2023. paper

    Xi'an Li, Jinran Wu, Zhi-Qin John Xu, and You-Gan Wang.

63. Separable physics informed neural networks. arXiv, 2023. paper

    Junwoo Cho, Seungtae Nam, Hyunmo Yang, Seok-Bae Yun, Youngjoon Hong, and Eunbyung Park.

64. Achieving high accuracy with PINNs via energy natural gradient descent. ICML, 2023. paper

    Johannes Müller and Marius Zeinhofer.

65. Gradient descent finds the global optima of two-layer physics-informed neural networks. ICML, 2023. paper

    Yihang Gao, Yiqi Gu, and Michael Ng.

66. Residual-based attention in physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2024. paper

    Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, and George Em Karniadakis.

67. Auxiliary-tasks learning for physics-informed neural network-based partial differential equations solving. arXiv, 2023. paper

    Junjun Yan, Xinhai Chen, Zhichao Wang, Enqiang Zhou, and Jie Liu.

68. Tackling the curse of dimensionality with physics-informed neural networks. arXiv, 2023. paper

    Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, and Kenji Kawaguchi.

69. Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper

    Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.

70. Solving PDEs on spheres with physics-informed convolutional neural networks. arXiv, 2023. paper

    Guanhang Lei, Zhen Lei, Lei Shi, Chenyu Zeng, and Dingxuan Zhou.

71. Tensor-compressed back-propagation-free training for (physics-informed) neural networks. arXiv, 2023. paper

    Yequan Zhao, Xinling Yu, Zhixiong Chen, Ziyue Liu, Sijia Liu, and Zheng Zhang.

72. How to select physics-informed neural networks in the absence of ground truth: A pareto front-based strategy. ICML, 2023. paper

    Zhao Wei, Jian Cheng Wong, Nicholas Wei Yong Sung, Abhishek Gupta, Chin Chun Ooi, Pao-Hsiung Chiu, My Ha Dao, and Yew-Soon Ong.

73. A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gPINN structure. EAAI, 2023. paper

    Katayoun Eshkofti and Seyed Mahmoud Hosseini.

74. Learning only on boundaries: A physics-informed neural operator for solving parametric partial differential equations in complex geometries. arXiv, 2023. paper

    Zhiwei Fang, Sifan Wang, and Paris Perdikaris.

75. Exact and soft boundary conditions in physics-informed neural networks for the variable coefficient poisson equation. arXiv, 2023. paper

    Sebastian Barschkis.

76. Investigating the ability of PINNs to solve burgers’ PDE near finite-time blowup. arXiv, 2023. paper

    Dibyakanti Kumar and Anirbit Mukherjee.

77. Correcting model misspecification in physics-informed neural networks (PINNs). arXiv, 2023. paper

    Zongren Zou, Xuhui Meng, and George Em Karniadakis.

78. On residual minimization for PDEs: Failure of PINN, modified equation, and implicit bias. arXiv, 2023. paper

    Tao Luo and Qixuan Zhou.

79. Operator learning enhanced physics-informed neural networks for solving partial differential equations characterized by sharp solutions. arXiv, 2023. paper

    Bin Lin, Zhiping Mao, Zhicheng Wang, and George Em Karniadakis.

80. PINNs-TF2: Fast and user-friendly physics-informed neural networks in TensorFlow V2. NIPS, 2023. paper

    Reza Akbarian Bafghi and Maziar Raissi.

81. Filtered partial differential equations: A robust surrogate constraint in physics-informed deep learning framework. arXiv, 2023. paper

    Dashan Zhang, Yuntian Chen, and Shiyi Chen.

82. Enhanced physics-informed neural networks with domain scaling and residual correction methods for multi-frequency elliptic problems. arXiv, 2023. paper

    Deok-Kyu Jang, Hyea Hyun Kim, and Kyungsoo Kim.

83. Physics-informed neural networks for transformed geometries and manifolds. arXiv, 2023. paper

    Samuel Burbulla.

    Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, and Kenji Kawaguchi.

84. Neuro-PINN: A hybrid framework for efficient nonlinear projection equation solutions. The International Journal for Numerical Methods in Engineering, 2023. paper

    Dawen Wu and Abdel Lisser.

85. Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems. arXiv, 2023. paper

    Elsa Cardoso-Bihlo and Alex Bihlo.

86. Semi-analytic PINN methods for boundary layer problems in a rectangular domain. arXiv, 2023. paper

    Gungmin Gie, Youngjoon Hong, Chang-Yeol Jung, and Tselmuun Munkhjin.

87. PICL: Physics informed contrastive learning for partial differential equations. arXiv, 2024. paper

    Cooper Lorsung and Amir Barati Farimani.

88. Fourier warm start for physics-informed neural networks. EAAI, 2024. paper

    Ge Jin, Jian Cheng Wong, Abhishek Gupta, Shipeng Li, and Yew-Soon Ong.

89. Preconditioning for physics-informed neural networks. ICML, 2024. paper

    Songming Liu, Chang Su, Jiachen Yao, Zhongkai Hao, Hang Su, Youjia Wu, and Jun Zhu.

90. RBF-PINN: Non-Fourier positional embedding in physics-informed neural networks. arXiv, 2024. paper

    Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.

91. Training dynamics in physics-informed neural networks with feature mapping. arXiv, 2024. paper

    Chengxi Zeng, Tilo Burghardt, and Alberto M Gambaruto.

92. Score-based physics-informed neural networks for high-dimensional Fokker-Planck equations. arXiv, 2024. paper

    Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, and Kenji Kawaguchi.

93. Investigation of compressor cascade flow using physics-informed neural networks with adaptive learning strategy. AIAA Journal, 2024. paper

    Zhihui Li, Francesco Montomoli, and Sanjiv Sharma.

94. Exact enforcement of temporal continuity in sequential physics-informed neural networks. arXiv, 2024. paper

    Pratanu Roy and Stephen Castonguay.

95. Multiple scattering simulation via physics-informed neural networks. arXiv, 2024. paper

    Siddharth Nair, Timothy F. Walsh, Greg Pickrell, and Fabio Semperlotti.

96. Toward a better understanding of Fourier neural operators: Analysis and improvement from a spectral perspective. arXiv, 2024. paper

    Shaoxiang Qin, Fuyuan Lyu, Wenhui Peng, Dingyang Geng, Ju Wang, Naiping Gao, Xue Liu, and Liangzhu Leon Wang.

1. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. NMI, 2021. paper

   Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis.

2. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. SA, 2021. paper

   Wang Sifan, Hanwen Wang, and Paris Perdikaris.

3. Deep transfer operator learning for partial differential equations under conditional shift. NMI, 2022. paper

   Somdatta Goswami, Katiana Kontolati, Michael D. Shields, and George Em Karniadakis.

4. Variable-input deep operator networks. arXiv, 2022. paper

   Michael Prasthofer, Tim De Ryck, and Siddhartha Mishra.

5. MIONet: Learning multiple-input operators via tensor product. arXiv, 2022. paper

   Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis.

6. Long-time integration of parametric evolution equations with physics-informed DeepONets. arXiv, 2021. paper

   Sifan Wang and Paris Perdikaris.

7. Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing, 2022. paper

   Sifan Wang, Hanwen Wang, and Paris Perdikaris.

8. SVD perspectives for augmenting DeepONet flexibility and interpretability. arXiv, 2022. paper

   Simone Venturi and Tiernan Casey.

9. Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs. arXiv, 2021. paper

   Guang Lin, Christian Moya, and Zecheng Zhang.

10. Bi-fidelity modeling of uncertain and partially unknown systems using DeepONet. arXiv, 2022. paper

    Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan N. King, and Alireza Doostan.

11. MultiAuto-DeepONet: A multi-resolution autoencoder DeepONet for nonlinear dimension reduction, uncertainty quantification and operator learning of forward and inverse stochastic problems. arXiv, 2022. paper

    Jiahao Zhang, Shiqi Zhang, and Guang Lin.

12. Transfer learning enhanced DeepONet for long-time prediction of evolution equations. AAAI, 2023. paper

    Wuzhe Xu, Yulong Lu, and Li Wang.

13. B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD. JCP, 2023. paper

    Guang Lin, Christian Moy, and Zecheng Zhang.

14. VB-DeepONet: A Bayesian operator learning framework for uncertainty quantification. EAAI, 2023. paper

    Shailesh Garg and Souvik Chakraborty.

15. Sequential deep learning operator network (S-DeepONet) for time-dependent loads. arXiv, 2023. paper

    Jaewan Park, Shashank Kushwaha, Junyan He, Seid Koric, Diab Abueidda, and Iwona Jasiuk.

16. Asymptotic-preserving convolutional DeepONets capture the diffusive behavior of the multiscale linear transport equations. arXiv, 2023. paper

    Keke Wu, Xiong-bin Yan, Shi Jin, and Zheng Ma.

17. A hybrid decoder-DeepONet operator regression framework for unaligned observation data. arXiv, 2023. paper

    Bo Chen, Chenyu Wang, Weipeng Li, and Haiyang Fu.

18. Improving physics-informed DeepONets with hard constraints. arXiv, 2023. paper

    Rüdiger Brecht, Dmytro R. Popovych, Alex Bihlo, and Roman O. Popovych.

19. Capturing the diffusive behavior of the multiscale linear transport equations by asymptotic-preserving convolutional DeepONets. Computer Methods in Applied Mechanics and Engineering, 2023. paper

    Keke Wu, Xiong-Bin Yan, Shi Jin, and Zheng Ma.

20. DON-LSTM: Multi-resolution learning with DeepONets and long short-term memory neural networks. arXiv, 2023. paper

    Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, and Signe Riemer-Sørensen.

21. DeepOnet based preconditioning strategies for solving parametric linear systems of equations. arXiv, 2024. paper

    Alena Kopaničáková and George Em Karniadakis.

22. Derivative-enhanced deep operator network. arXiv, 2024. paper

    Yuan Qiu, Nolan Bridges, and Peng Chen.

1. Fourier neural operator for parametric partial differential equations. ICLR, 2021. paper

   Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

2. On universal approximation and error bounds for Fourier neural operators. JMLR, 2021. paper

   Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra.

3. HyperFNO: Improving the generalization behavior of Fourier neural operators. NIPS, 2022. paper

   Francesco Alesiani, Makoto Takamoto, and Mathias Niepert.

4. Neural operator: Graph kernel network for partial Differential equations. arXiv, 2020. paper

   Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

5. Fourier neural operator with learned deformations for PDEs on general geometries. arXiv, 2022. paper

   Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar.

6. Multipole graph neural operator for parametric partial differential equations. NIPS, 2020. paper

   Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar.

7. Fast sampling of diffusion models via operator learning. ICML, 2023. paper

   Hongkai Zheng, Weili Nie, Arash Vahdat, Kamyar Azizzadenesheli, and Anima Anandkumar.

8. Factorized Fourier neural operators. ICLR, 2023. paper

   Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong.

9. Model inversion for spatio-temporal processes using the Fourier neural operator. NIPS, 2023. paper

   Dan MacKinlay, Dan Pagendam, Petra M. Kuhnert, Tao Cui, David Robertson, and Sreekanth Janardhanan.

10. Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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11. On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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12. Semi-supervised learning of partial differential operators and dynamical flows. arXiv, 2022. paper

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13. Non-equispaced Fourier neural solvers for PDEs. arXiv, 2022. paper

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14. Incremental spectral learning Fourier neural operator. arXiv, 2022. paper

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15. Fourier continuation for exact derivative computation in physics-informed neural operators. arXiv, 2022. paper

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16. Non-equispaced Fourier neural solvers for PDEs. arXiv, 2023. paper

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17. Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errors. arXiv, 2023. paper

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18. Domain agnostic Fourier neural operators. arXiv, 2023. paper

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19. Spherical Fourier neural operators: Learning stable dynamics on the sphere. ICML, 2023. paper

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20. Group equivariant Fourier neural operators for partial differential equations. ICML, 2023. paper

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21. Speeding up Fourier neural operators via mixed precision. arXiv, 2023. paper

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22. Geometry-informed neural operator for large-scale 3D PDEs. arXiv, 2023. paper

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23. Deep equilibrium based neural operators for steady-state PDEs. NIPS, 2023. paper

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25. Approximating numerical flux by Fourier neural operators for the hyperbolic conservation laws. arXiv, 2024. paper

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26. Invertible Fourier neural operators for tackling both forward and inverse problems. arXiv, 2024. paper

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27. An operator learning perspective on parameter-to-observable maps. arXiv, 2024. paper

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28. Gabor-filtered Fourier neural operator for solving partial differential equations. Computers & Fluids, 2024. paper

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1. Message passing neural PDE solvers. ICLR, 2022. paper

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2. Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper

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3. Learning mesh-based simulation with graph networks. ICLR, 2021. paper

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4. Learning large-scale subsurface simulations with a hybrid graph network simulator. KDD, 2022. paper

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5. Unravelling the performance of physics-informed graph neural networks for dynamical systems. NIPS, 2022. paper

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6. Learning the solution operator of boundary value problems using graph neural networks. ICML, 2022. paper

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7. Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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8. Modular flows: Differential molecular generation. NIPS, 2022. paper

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9. Learning to solve PDE-constrained inverse problems with graph networks. ICML, 2022. paper

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10. Physics-embedded neural networks: E(n)-equivariant graph neural PDE solvers. NIPS, 2022. paper

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11. PDE-GCN: Novel architectures for graph neural networks motivated by partial differential equations. ICLR, 2021. paper

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12. Physics-aware difference graph networks for sparsely-observed dynamics. ICLR, 2020. paper

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13. Combining differentiable PDE solvers and graph neural networks for fluid flow prediction. ICML, 2022. paper

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14. Learning continuous-time PDEs from sparse data with graph neural networks. ICLR, 2021. paper

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15. Learning to simulate complex physics with graph networks. ICML, 2020. paper

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16. Multi-scale physical representations for approximating PDE solutions with graph neural operators. ICLR, 2022. paper

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17. DS-GPS: A deep statistical graph Poisson solver (for faster CFD simulations). NIPS, 2022. paper

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18. PF-GNN: Differentiable particle filtering based approximation of universal graph representations. ICLR, 2022. paper

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19. GRAND: Graph neural diffusion. ICML, 2021. paper

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20. GRAND++: Graph neural diffusion with a source term. ICML, 2022. paper

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21. Neural networks trained to solve differential equations learn general representations. NIPS, 2018. paper

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22. Graph element networks: Adaptive, structured computation and memory. ICML, 2019. paper

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23. Physics-constrained unsupervised learning of partial differential equations using meshes. arXiv, 2022. paper

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24. Neural PDE solvers for irregular domains. arXiv, 2022. paper

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25. Bi-stride multi-scale graph neural network for mesh-based physical simulation. arXiv, 2022. paper

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26. Learning time-dependent PDE solver using message passing graph neural networks. arXiv, 2022. paper

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27. On the robustness of graph neural diffusion to topology perturbations. arXiv, 2022. paper

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28. STONet: A neural-operator-driven spatio-temporal network. arXiv, 2022. paper

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29. PhyGNNet: Solving spatiotemporal PDEs with physics-informed graph neural network. arXiv, 2022. paper

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30. Differentiable physics-informed graph networks. arXiv, 2019. paper

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31. MG-GNN: Multigrid graph neural networks for learning multilevel domain decomposition methods. ICML, 2023. paper

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32. Multi-scale message passing neural PDE solvers. arXiv, 2023. paper

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33. An implicit GNN solver for Poisson-like problems. arXiv, 2023. paper

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34. GNN-based physics solver for time-independent PDEs. arXiv, 2023. paper

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35. E(3) equivariant graph neural networks for particle-based fluid mechanics. ICLR, 2023. paper

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36. Long-short-range message-passing: A physics-informed framework to capture non-local interaction for scalable molecular dynamics simulation. arXiv, 2023. paper

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37. A graph convolutional autoencoder approach to model order reduction for parametrized PDEs. arXiv, 2023. paper

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38. GAD-NR: Graph anomaly detection via neighborhood reconstruction. arXiv, 2023. paper

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39. GPINN: Physics-informed neural network with graph embedding. arXiv, 2023. paper

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40. GNRK: Graph Neural Runge-Kutta method for solving partial differential equations. arXiv, 2023. paper

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41. Equivariant graph neural operator for modeling 3D dynamics. arXiv, 2024. paper

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42. HAMLET: Graph transformer neural operator for partial differential equations. arXiv, 2024. paper

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43. Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids. arXiv, 2024. paper

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1. Learning Green's functions associated with time-dependent partial differential equations. JMLR, 2022. paper

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2. BI-GreenNet: Learning Green's functions by boundary integral network. arXiv, 2022. paper

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3. DeepGreen: Deep learning of Green’s functions for nonlinear boundary value problems. Scientific Reports, 2021. paper

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4. Data-driven discovery of Green’s functions with human-understandable deep learning. Scientific Reports, 2022. paper

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5. Data-driven discovery of Green's functions. Doctoral Dissertation, 2022. Ph.D.

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6. Principled interpolation of Green's functions learned from data. arXiv, 2022. paper

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7. Deep generalized Green's functions. arXiv, 2023. paper

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8. Operator approximation of the wave equation based on deep learning of Green’s function. arXiv, 2023. paper

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9. Deep surrogate model for learning Green's function associated with linear reaction-diffusion operator. arXiv, 2023. paper

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1. Composing partial differential equations with physics-aware neural networks. ICML, 2022. paper

   Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, and Wolfgang Nowak.

2. Learning the dynamics of physical systems from sparse observations with finite element networks. ICLR, 2022. paper

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3. A unified hard-constraint framework for solving geometrically complex PDEs. NIPS, 2022. paper

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4. LSH-SMILE: Locality sensitive Hashing accelerated simulation and learning. NIPS, 2021. paper

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5. Amortized finite element analysis for fast PDE-constrained optimization. ICML, 2020. paper

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6. Learning neural PDE solvers with convergence guarantees. ICLR, 2019. paper

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7. Hybrid finite difference with the physics-informed neural network for solving PDE in complex geometries. arXiv, 2022. paper

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8. Multilayer perceptron-based surrogate models for finite element analysis. arXiv, 2022. paper

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9. Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations. arXiv, 2024. paper

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10. Error assessment of an adaptive finite elements—neural networks method for an elliptic parametric PDE. Computer Methods in Applied Mechanics and Engineering, 2024. paper

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11. Predicting unsteady incompressible fluid dynamics with finite volume informed neural network. Physics of Fluids, 2024. paper

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12. Unified finite-volume physics informed neural networks to solve the heterogeneous partial differential equations. KBS, 2024. paper

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1. PDE-Net: Learning PDEs from data. ICML, 2018. paper

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2. PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network. JCP, 2019. paper

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3. Physics-informed CNNs for super-resolution of sparse observations on dynamical systems. NIPS, 2022. paper

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4. Deep-pretrained-FWI: Combining supervised learning with physics-informed neural network. NIPS, 2022. paper

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5. Learning time-dependent PDEs with a linear and nonlinear separate convolutional neural network. JCP, 2022. paper

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6. PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs. JCP, 2022. paper

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7. Spline-PINN: Approaching PDEs without data using fast, physics-informed Hermite-Spline CNNs. AAAI, 2019. paper

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8. Deep convolutional Ritz method: Parametric PDE surrogates without labeled data. arXiv, 2022. paper

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9. Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems. arXiv, 2022. paper

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10. Phase2Vec: Dynamical systems embedding with a physics-informed convolutional network. arXiv, 2022. paper

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11. Numerical approximation based on deep convolutional neural network for high-dimensional fully nonlinear merged PDEs and 2BSDEs. arXiv, 2022. paper

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12. SplineCNN: Fast geometric deep learning with continuous B-spline kernels. CVPR, 2018. paper

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13. Physics-informed deep super-resolution for spatiotemporal data. arXiv, 2022. paper

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14. MeshFreeFLowNet: A physics-constrained deep continuous space-time super-resolution framework. SC20, 2020. paper

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15. Convolutional neural operators. arXiv, 2023. paper

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16. An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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17. Clifford neural layers for PDE modeling. ICLR, 2023. paper

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18. Neural partial differential equations with functional convolution. arXiv, 2023. paper

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19. Multilevel CNNs for parametric PDEs. arXiv, 2023. paper

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20. Encoding physics to learn reaction–diffusion processes. NMI, 2023. paper

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21. PhySR: Physics-informed deep super-resolution for spatiotemporal data. JCP, 2023. paper

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22. Local convolution enhanced global Fourier neural operator for multiscale dynamic spaces prediction. arXiv, 2023. paper

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23. A practical existence theorem for reduced order models based on convolutional autoencoders. arXiv, 2024. paper

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24. Closure discovery for coarse-grained partial differential equations using multi-agent reinforcement learning. arXiv, 2024. paper

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25. PARCv2: Physics-aware recurrent convolutional neural networks for spatiotemporal dynamics modeling. arXiv, 2024. paper

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26. Neural operators with localized integral and differential kernels. arXiv, 2024. paper

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27. PDE-CNNs: Axiomatic derivations and applications. arXiv, 2024. paper

    Gijs Bellaard, Sei Sakata, Bart M. N. Smets, and Remco Duits.

28. PDE-CNNs: Axiomatic derivations and applications. arXiv, 2024. paper

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29. Symmetric basis convolutions for learning Lagrangian fluid mechanics. ICLR, 2024. paper

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1. Integral autoencoder network for discretization-invariant learning. JMLR, 2022. paper

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2. Variational autoencoding neural operators. arXiv, 2023. paper

   Jacob H. Seidman, Georgios Kissas, George J. Pappas, and Paris Perdikaris.

3. PI-VEGAN: Physics informed variational embedding generative adversarial networks for stochastic differential equations. arXiv, 2023. paper

   Ruisong Gao, Yufeng Wang, Min Yang, and Chuanjun Chen.

4. On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields. arXiv, 2023. paper

   Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, and Paolo Zunino.

5. Modeling unknown stochastic dynamical system via Autoencoder. arXiv, 2023. paper

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1. Multiwavelet-based operator learning for differential equations. NIPS, 2021. paper

   Gaurav Gupta, Xiongye Xiao, and Paul Bogdan.

2. On the representation of solutions to elliptic PDEs in Barron space. NIPS, 2021. paper

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3. Low-rank registration based manifolds for convection-dominated PDEs. AAAI, 2021. paper

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4. Isogeometric neural networks: A new deep learning approach for solving parameterized partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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5. A nonlocal physics-informed deep learning framework using the peridynamic differential operator. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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6. Kernel flows: From learning kernels from data into the abyss. JCP, 2019. paper

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7. On neurosymbolic solutions for PDEs. arXiv, 2022. paper

   Ritam Majumdar, Vishal Jadhav, Anirudh Deodhar, Shirish Karande, and Lovekesh Vig.

8. An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis. arXiv, 2022. paper

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9. Nonparametric learning of kernels in nonlocal operators. arXiv, 2022. paper

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10. Spectral neural operators. arXiv, 2022. paper

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11. NOMAD: Nonlinear manifold decoders for operator learning. arXiv, 2022. paper

    Jacob H. Seidman, Georgios Kissas, Paris Perdikaris, and George J. Pappas.

12. U-NO: U-shaped neural operators. arXiv, 2022. paper

    Md Ashiqur Rahman, Zachary E. Ross, and Kamyar Azizzadenesheli.

13. Wavelet neural operator: A neural operator for parametric partial differential equations. arXiv, 2022. paper

    Tapas Tripura and Souvik Chakraborty.

14. Pseudo-differential integral operator for learning solution operators of partial differential equations. arXiv, 2022. paper

    Jin Young Shin, Jae Yong Lee, and Hyung Ju Hwang.

15. Nonlinear reconstruction for operator learning of PDEs with discontinuities. arXiv, 2022. paper

    Samuel Lanthaler, Roberto Molinaro, Patrik Hadorn, and Siddhartha Mishra.

16. GeONet: A neural operator for learning the Wasserstein geodesic. arXiv, 2022. paper

    Andrew Gracyk and Xiaohui Chen.

17. Render unto numerics: Orthogonal polynomial neural operator for PDEs with non-periodic boundary conditions. arXiv, 2022. paper

    Ziyuan Liu, Haifeng Wang, Kaijuna Bao, Xu Qian, Hong Zhang, and Songhe Song.

18. DOSNet as a non-black-box PDE solver: When deep learning meets operator splitting. arXiv, 2022. paper

    Yuan Lan, Zhen Li, Jie Sun, and Yang Xiang.

19. Guiding continuous operator learning through physics-based boundary constraints. arXiv, 2022. paper

    Nadim Saad, Gaurav Gupta, Shima Alizadeh, and Danielle C. Maddix.

20. BelNet: Basis enhanced learning, a mesh-free neural operator. arXiv, 2022. paper

    Zecheng Zhang, Wing Tat Leung, and Hayden Schaeffer.

21. INO: Invariant neural operators for learning complex physical systems with momentum conservation. arXiv, 2022. paper

    Ning Liu, Yue Yu, Huaiqian You, and Neeraj Tatikola.

22. BINN: A deep learning approach for computational mechanics problems based on boundary integral equations. arXiv, 2023. paper

    Jia Sun, Yinghua Liu, Yizheng Wang, Zhenhan Yao, and Xiaoping Zheng.

23. Koopman neural operator as a mesh-free solver of non-linear partial differential equations. arXiv, 2023. paper

    Wei Xiong, Xiaomeng Huang, Ziyang Zhang, Ruixuan Deng, Pei Sun, and Yang Tian.

24. Physics-informed Koopman network. arXiv, 2022. paper

    Yuying Liu, Aleksei Sholokhov, Hassan Mansour, and Saleh Nabi.

25. Deep operator learning lessens the curse of dimensionality for PDEs. arXiv, 2023. paper

    Ke Chen, Chunmei Wang, and Haizhao Yang.

26. Algorithmically designed artificial neural networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. arXiv, 2023. paper

    Arnulf Jentzen, Adrian Riekert, and Philippe von Wurstemberger.

27. Entropy-dissipation informed neural network for McKean-Vlasov type. arXiv, 2023. paper

    Zebang Shen and Zhenfu Wang.

28. A neural PDE solver with temporal stencil modeling. ICML, 2023. paper

    Zhiqing Sun, Yiming Yang, and Shinjae Yoo.

29. Neural operator learning for long-time integration in dynamical systems with recurrent neural networks. arXiv, 2023. paper

    Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, and Signe Riemer-Sørensen.

30. Coupled multiwavelet operator learning for coupled differential equations. ICLR, 2023. paper

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31. LNO: Laplace neural operator for solving differential equations. arXiv, 2023. paper

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32. Vandermonde neural operator. arXiv, 2023. paper

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33. Energy-dissipative evolutionary deep operator neural networks. arXiv, 2023. paper

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34. Physics informed WNO. arXiv, 2023. paper

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14. Learning prediction function of prior measures for statistical inverse problems of partial differential equations. arXiv, 2023. paper

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1. Neural rough differential equations for long time series. ICML, 2021. paper

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2. LEADS: Learning dynamical systems that generalize across environments. NIPS, 2021. paper

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12. A stable and scalable method for solving initial value PDEs with neural networks. ICLR, 2023. paper

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17. Data-adaptive probabilistic likelihood approximation for ordinary differential equations. arXiv, 2023. paper

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18. Neural signature kernels as infinite-width-depth-limits of controlled ResNets. ICML, 2023. paper

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19. AbODE: Ab initio antibody design using conjoined ODEs. ICML, 2023. paper

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20. On the forward invariance of neural ODEs. ICML, 2023. paper

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21. Predicting ordinary differential equations with Transformers. ICML, 2023. paper

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22. Elucidating the solution space of extended reverse-time SDE for diffusion models. arXiv, 2023. paper

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23. ODE-based recurrent model-free reinforcement learning for POMDPs. arXiv, 2023. paper

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24. A spectral approach for learning spatiotemporal neural differential equations. arXiv, 2023. paper

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25. Invariant physics-informed neural networks for ordinary differential equations. arXiv, 2023. paper

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26. Stability-informed initialization of neural ordinary differential equations. arXiv, 2023. paper

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29. stable neural stochastic differential equations in analyzing irregular time series data. ICLR, 2024. paper

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1. Prompting in-context operator learning with sensor data, equations, and natural language. arXiv, 2023. paper

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2. CrunchGPT: A chatGPT assisted framework for scientific machine learning. Journal of Machine Learning for Modeling and Computing, 2023. paper

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3. Data-efficient operator learning via unsupervised pretraining and in-context learning. arXiv, 2024. paper

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4. UPS: Towards foundation models for PDE solving via cross-modal adaptation. arXiv, 2024. paper

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5. Towards a foundation model for partial differential equation: Multi-operator learning and extrapolation. arXiv, 2024. paper

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1. PDEBench: An extensive benchmark for scientific machine learning. NIPS, 2022. paper

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2. DeepXDE: A deep learning library for solving differential equations. SIAM Review, 2021. paper

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3. A research framework for writing differentiable PDE discretizations in JAX. NIPS, 2021. paper

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4. An extensible benchmarking graph-mesh dataset for studying steady-state incompressible Navier-Stokes equations. ICLR, 2022. paper

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5. PhiFlow: A differentiable PDE solving framework for deep learning via physical simulations. NIPS, 2020. paper

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6. NVIDIA SimNet™: An AI-accelerated multi-physics simulation framework. ICCS, 2021. paper

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7. PyDEns: A python framework for solving differential equations with neural networks. arXiv, 2019. paper

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9. Physics-driven machine learning models coupling PyTorch and Firedrake. arXiv, 2023. paper

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10. PINNacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs. arXiv, 2023. paper

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11. BubbleML: A multi-physics dataset and benchmarks for machine learning. arXiv, 2023. paper

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12. LagrangeBench: A Lagrangian fluid nechanics benchmarking suite. NIPS, 2023. paper

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13. Zero coordinate shift: Whetted automatic differentiation for physics-informed operator learning. arXiv, 2023. paper

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14. CFDBench: A comprehensive benchmark for machine learning methods in fluid dynamics. arXiv, 2023. paper

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16. ClimSim: A large multi-scale dataset for hybrid physics-ML climate emulation. NIPS, 2023. paper

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17. Benchmarking the robustness of neural network-based partial differential equation solvers. ICCAD, 2023. paper

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18. Physics-informed neural networks for advanced modeling. Journal of Open Source Software, 2024. paper/Github

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19. A novel A.I enhanced reservoir characterization with a combined mixture of experts -- NVIDIA modulus based physics informed neural operator forward model. arXiv, 2024. paper

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1. Characterizing possible failure modes in physics-informed neural networks. NIPS, 2021. paper

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2. Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 2021. paper

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3. When and why PINNs fail to train: A neural tangent kernel perspective. JCP, 2022. paper

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4. When do extended physics-informed neural networks (XPINNs) improve generalization? SIAM Journal on Scientific Computing, 2022. paper

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5. MARS: A method for the adaptive removal of stiffness in PDEs. JCP, 2022. paper

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6. Learning similarity metrics for numerical simulations. ICML, 2020. paper

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7. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2021. paper

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8. Parametric complexity bounds for approximating PDEs with neural networks. NIPS, 2021. paper

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9. Respecting causality for training physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2024. paper

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10. CP-PINNS: Changepoints detection in PDEs using physics informed neural networks with total-variation penalty. arXiv, 2022. paper

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11. Stochastic projection based approach for gradient free physics informed learning. arXiv, 2022. paper

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12. Understanding the difficulty of training physics-informed neural networks on dynamical systems. arXiv, 2022. paper

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13. Mitigating learning complexity in physics and equality constrained artificial neural networks. arXiv, 2022. paper

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14. Improved training of physics-informed neural networks with model ensembles. arXiv, 2022. paper

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15. The cost-accuracy trade-off in operator learning with neural networks. arXiv, 2022. paper

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16. Separable PINN: Mitigating the curse of dimensionality in physics-informed neural networks. NIPS, 2022. paper

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17. A curriculum-training-based strategy for distributing collocation points during physics-informed neural network training. NIPS, 2022. paper

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18. Robustness of physics-informed neural networks to noise in sensor data. arXiv, 2022. paper

    Jian Cheng Wong, Pao-Hsiung Chiu, Chin Chun Ooi, and My Ha Da.

19. Investigations on convergence behaviour of physics informed neural networks across spectral ranges and derivative orders. arXiv, 2023. paper

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20. Stochastic projection based approach for gradient free physics informed learning. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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21. Temporal consistency loss for physics-informed neural networks. arXiv, 2023. paper

    Sukirt Thakur, Maziar Raissi, Harsa Mitra, and Arezoo Ardekani.

22. Can physics-informed neural networks beat the finite element method? arXiv, 2023. paper

    Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz, and Carola-Bibiane Schönlieb.

23. LSA-PINN: Linear boundary connectivity loss for solving PDEs on complex geometry. arXiv, 2023. paper

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24. On the Hyperparameters influencing a PINN’s generalization beyond the training domain. arXiv, 2023. paper

    Andrea Bonfanti, Roberto Santana, Marco Ellero, and Babak Gholami.

25. DPM: A novel training method for physics-informed neural networks in extrapolation. AAAI, 2021. paper

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26. Guiding continuous operator learning through physics-based boundary constraints. ICLR, 2023. paper

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27. Probing optimisation in physics-informed neural networks. ICLR, 2023. paper

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28. Nearly optimal VC-dimension and Pseudo-dimension bounds for deep neural network derivatives. arXiv, 2023. paper

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29. PDE+: Enhancing generalization via PDE with adaptive distributional diffusion. arXiv, 2023. paper

    Yige Yuan, Bingbing Xu, Bo Lin, Liang Hou, Fei Sun, Huawei Shen, and Xueqi Cheng.

30. Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior. arXiv, 2023. paper

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31. Understanding and mitigating extrapolation failures in physics-informed neural networks. arXiv, 2023. paper

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32. Physics-informed neural network based on a new adaptive gradient descent algorithm for solving partial differential equations of flow problems. Physics of Fluids, 2023. paper

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33. The curse of dimensionality in operator learning. arXiv, 2023. paper

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34. Inverse evolution layers: Physics-informed regularizers for deep neural networks. arXiv, 2023. paper

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35. Positional embeddings for solving PDEs with evolutional deep neural networks. arXiv, 2023. paper

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36. Learning specialized activation functions for physics-informed neural networks. arXiv, 2023. paper

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37. Size lowerbounds for deep operator networks. arXiv, 2023. paper

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38. How important are specialized transforms in neural operators? arXiv, 2023. paper

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39. Neural oscillators for generalization of physics-informed machine learning. arXiv, 2023. paper

    Taniya Kapoor, Abhishek Chandra, Daniel M. Tartakovsky, Hongrui Wang, Alfredo Nunez, and Rolf Dollevoet.

40. Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the L^p-sense. arXiv, 2023. paper

    Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, and Joshua Lee Padgett.

41. An operator preconditioning perspective on training in physics-informed machine learning. arXiv, 2023. paper

    Tim De Ryck, Florent Bonnet, Siddhartha Mishra, and Emmanuel de Bézenac.

42. A trial solution for imposing boundary conditions of partial differential equations in physics-informed neural networks. EAAI, 2023. paper

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43. Multiple physics pretraining for physical surrogate models. arXiv, 2023. paper

    Michael McCabe, Bruno Régaldo-Saint Blancard, Liam Holden Parker, Ruben Ohana, Miles Cranmer, Alberto Bietti, Michael Eickenberg, Siavash Golkar, Geraud Krawezik, Francois Lanusse, Mariel Pettee, Tiberiu Tesileanu, Kyunghyun Cho, and Shirley Ho.

44. Lie point symmetry and physics informed networks. NIPS, 2023. paper

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45. Stacked networks improve physics-informed training: Applications to neural networks and deep operator networks. arXiv, 2023. paper

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46. Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent? Physica D: Nonlinear Phenomena, 2023. paper

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47. Can physics informed neural operators self improve? NIPS, 2023. paper

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48. Bias-variance trade-off in physics-informed neural networks with randomized smoothing for high-dimensional PDEs. arXiv, 2023. paper

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49. From plateaus to progress: Unveiling training dynamics of PINNs. NIPS, 2023. paper

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50. An integrated framework for accelerating reactive flow simulation using GPU and machine learning models. arXiv, 2023. paper

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51. Greedy training algorithms for neural networks and applications to PDEs. JCP, 2023. paper

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52. How much can one learn a partial differential equation from its solution? Foundations of Computational Mathematics, 2023. paper

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54. Generalizable neural physics solvers by baldwinian evolution. arXiv, 2023. paper

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55. Mind the gap: Constraining physics-informed neural operators to improve the quality of auto-regressive predictions. AIAA, 2024. paper

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56. Refined generalization analysis of the deep Ritz method and physics-informed neural networks. arXiv, 2024. paper

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57. PirateNets: Physics-informed deep learning with residual adaptive networks. arXiv, 2024. paper

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58. An operator learning perspective on parameter-to-observable maps. arXiv, 2024. paper

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59. Architectural strategies for the optimization of physics-informed neural networks. arXiv, 2024. paper

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60. Closure discovery for coarse-grained partial differential equations using multi-agent reinforcement learning. arXiv, 2024. paper

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61. Kolmogorov n-widths for multitask physics-informed machine learning (PIML) methods: Towards robust metrics. arXiv, 2024. paper

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62. Parametric encoding with attention and convolution mitigate spectral bias of neural partial differential equation solvers. arXiv, 2024. paper

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63. End-to-end mesh optimization of a hybrid deep learning black-box PDE solver. arXiv, 2024. paper

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1. Meta-auto-decoder for solving parametric partial differential equations. NIPS, 2022. paper

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2. Transfer learning with physics-informed neural networks for efficient simulation of branched flows. NIPS, 2022. paper

   Raphaël Pellegrin, Blake Bullwinkel, Marios Mattheakis, and Pavlos Protopapas.

3. Identifying physical law of hamiltonian systems via meta-learning. ICLR, 2021. paper

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4. One-shot learning for solution operators of partial differential equations. ICLR, 2021. paper

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5. A metalearning approach for physics-informed neural networks (PINNs): Application to parameterized PDEs. JCP, 2023. paper

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6. Meta-MgNet: Meta multigrid networks for solving parameterized partial differential equations. JCP, 2022. paper

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7. Mosaic flows: A transferable deep learning framework for solving PDEs on unseen domains. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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8. Meta-learning PINN loss functions. JCP, 2022. paper

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9. HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks. NIPS, 2021. paper

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10. Adversarial multi-task learning enhanced physics-informed neural networks for solving partial differential equations. IJCNN, 2022. paper

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11. Transfer physics informed neural network: A new framework for distributed physics informed neural networks via parameter sharing. Engineering with Computers, 2022. paper

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12. Meta-PDE: Learning to solve PDEs quickly without a mesh. arXiv, 2022. paper

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13. SVD-PINNs: Transfer learning of physics-informed neural networks via singular value decomposition. arXiv, 2022. paper

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14. Physics-informed neural networks (PINNs) for parameterized PDEs: A meta-learning approach. arXiv, 2021. paper

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15. Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs. arXiv, 2022. paper

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16. Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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17. TransNet: Transferable neural networks for partial differential equations. arXiv, 2023. paper

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18. Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems. arXiv, 2023. paper

    Sarah Perez, Suryanarayana Maddu, Ivo F. Sbalzarini, and Philippe Poncet.

19. GPT-PINN: Generative pre-trained physics-informed neural networks toward non-intrusive meta-learning of parametric PDEs. arXiv, 2023. paper

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20. Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations. arXiv, 2023. paper

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21. Towards foundation models for scientific machine learning: Characterizing scaling and transfer behavior. arXiv, 2023. paper

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22. Adaptive transfer learning for PINN. JCP, 2023. paper

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23. Meta learning of interface conditions for multi-domain physics-informed neural networks. ICML, 2023. paper

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24. A sequential meta-transfer (SMT) learning to combat complexities of physics-informed neural networks: Application to composites autoclave processing. arXiv, 2023. paper

    Milad Ramezankhani and Abbas S. Milani.

25. HyperLoRA for PDEs. arXiv, 2023. paper

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26. In-context operator learning with data prompts for differential equation problems. PNAS, 2023. paper

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27. SONets: Sub-operator learning enhanced neural networks for solving parametric partial differential equations. JCP, 2023. paper

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28. Hypernetwork-based meta-learning for low-rank physics-informed neural networks. NIPS, 2023. paper

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29. Meta-learning of physics-informed neural networks for efficiently solving newly given PDEs. arXiv, 2023. paper

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30. Generalized one-shot transfer learning of linear ordinary and partial differential equations. NIPS, 2023. paper

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31. One-shot transfer learning for nonlinear ODEs. NIPS, 2023. paper

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32. PDE generalization of in-context operator networks: A study on 1D scalar nonlinear conservation laws. arXiv, 2024. paper

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33. DIMON: Learning solution operators of partial differential equations on a diffeomorphic family of domains. arXiv, 2024. paper

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34. Transferable neural networks for partial differential equations. Journal of Scientific Computing, 2024. paper

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35. Using uncertainty quantification to characterize and improve out-of-domain learning for PDEs. arXiv, 2024. paper

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36. Neural parameter regression for explicit representations of PDE solution operators. ICLR, 2024. paper

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1. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. JCP, 2021. paper

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2. Adaptive deep neural networks methods for high-dimensional partial differential equations. JCP, 2022. paper

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3. Self-adaptive loss balanced Physics-informed neural networks. Neurocomputing, 2022. paper

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4. Multi-objective loss balancing for physics-informed deep learning. arXiv, 2021. paper

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5. Self-scalable Tanh (Stan): Faster convergence and better generalization in physics-informed neural networks. arXiv, 2022. paper

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6. Is L2 physics-informed loss always suitable for training physics-informed neural network? arXiv, 2022. paper

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7. Loss landscape engineering via data regulation on PINNs. arXiv, 2022. paper

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8. Implicit stochastic gradient descent for training physics-informed neural networks. AAAI, 2023. paper

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9. About optimal loss function for training physics-informed neural networks under respecting causality. arXiv, 2023. paper

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10. Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. arXiv, 2023. paper

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11. Learning from integral losses in physics informed neural networks. arXiv, 2023. paper

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12. A symmetry group based supervised learning method for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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1. ADLGM: An efficient adaptive sampling deep learning Galerkin method. JCP, 2023. paper

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2. DMIS: Dynamic mesh-based importance sampling for training physics-informed neural networks. AAAI, 2023. paper

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3. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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4. Mitigating propagation failures in PINNs using evolutionary sampling. arXiv, 2022. paper

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5. Residual-quantile adjustment for adaptive training of physics-informed neural network. arXiv, 2022. paper

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6. Adversarial sampling for solving differential equations with neural networks. NIPS, 2021. paper

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7. A novel adaptive causal sampling method for physics-informed neural networks. arXiv, 2022. paper

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8. Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving PDEs with sharp solutions. arXiv, 2023. paper

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9. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

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10. Adversarial adaptive sampling: Unify PINN and optimal yransport for the approximation of PDEs. ICLR, 2024. paper

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11. Coupling parameter and particle dynamics for adaptive sampling in neural Galerkin schemes. arXiv, 2023. paper

    Yuxiao Wen, Eric Vanden-Eijnden, and Benjamin Peherstorfer.

12. Mitigating propagation failures in physics-informed neural networks using retain-resample-release (R3) sampling. ICML, 2023. paper

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13. Good lattice training: Physics-informed neural networks accelerated by number theory. arXiv, 2023. paper

    Takashi Matsubara and Takaharu Yaguchi.

14. Adaptive importance sampling for Deep Ritz. arXiv, 2023. paper

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15. DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations. JCP, 2023. paper

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16. Deep adaptive sampling for surrogate modeling without labeled data. arXiv, 2024. paper

    Xili Wang, Kejun Tang, Jiayu Zhai, Xiaoliang Wan, and Chao Yang.

17. Physics-informed neural networks for sampling. ICLR, 2024. paper

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18. PINNACLE: PINN adaptive collocation and experimental points selection. ICLR, 2024. paper

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1. MeshingNet: A new mesh generation method based on deep learning. ICCS, 2022. paper

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2. M2N: Mesh movement networks for PDE solvers. arXiv, 2022. paper

   Wenbin Song, Mingrui Zhang, Joseph G. Wallwork, Junpeng Gao, Zheng Tian, Fanglei Sun, Matthew D. Piggott, Junqing Chen, Zuoqiang Shi, Xiang Chen, and Jun Wang.

3. RANG: A residual-based adaptive node generation method for physics-informed neural networks. arXiv, 2022. paper

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4. Learning a mesh motion technique with application to fluid-structure interaction and shape optimization. arXiv, 2022. paper

   Johannes Haubne and Miroslav Kuchta.

5. Accelerated training of physics-informed neural networks (PINNs) using meshless discretizations. arXiv, 2022. paper

   Ramansh Sharma and Varun Shankar.

6. An improved structured mesh generation method based on physics-informed neural networks. arXiv, 2022. paper

   Xinhai Chen, Jie Liu, Junjun Yan, Zhichao Wang, and Chunye Gong.

7. Mesh-free Eulerian physics-informed neural networks. arXiv, 2022. paper

   Fabricio Arend Torres, Marcello Massimo Negri, Monika Nagy-Huber, Maxim Samarin, and Volker Roth.

8. Fixed-budget online adaptive mesh learning for physics-informed neural networks. Towards parameterized problem inference. arXiv, 2022. paper

   Thi Nguyen Khoa Nguyen, Thibault Dairay, Raphaël Meunier, Christophe Millet, and Mathilde Mougeot.

9. Learning controllable adaptive simulation for multi-resolution physics. ICLR, 2023. paper

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10. A closest point method for surface PDEs with interior boundary conditions for geometry processing. arXiv, 2023. paper

    Nathan King, Haozhe Su, Mridul Aanjaneya, Steven Ruuth, and Christopher Batty.

11. Efficient training of physics-informed neural networks with direct grid refinement algorithm. arXiv, 2023. paper

    Shikhar Nilabh and Fidel Grandia.

12. Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations. arXiv, 2023. paper

    Rajat Kumar Sarkar, Ritam Majumdar, Vishal Jadhav, Sagar Srinivas Sakhinana, and Venkataramana Runkana.

13. MMPDE-Net and moving sampling physics-informed neural networks based on moving mesh method. arXiv, 2023. paper

    Yu Yang, Qihong Yang, Yangtao Deng, and Qiaolin He.

14. Reinforcement learning for adaptive mesh refinement. AISTATS, 2023. paper

    Jiachen Yang, Tarik Dzanic, Brenden Petersen, Jun Kudo, Ketan Mittal, Vladimir Tomov, Jean-Sylvain Camier, Tuo Zhao, Hongyuan Zha, Tzanio Kolev, Robert Anderson, and Daniel Faissol.

15. Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulations. arXiv, 2024. paper

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16. Learning mesh motion techniques with application to fluid–structure interaction. Computer Methods in Applied Mechanics and Engineering, 2024. paper

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17. Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids. arXiv, 2024. paper

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1. Composing partial differential equations with physics-aware neural networks. ICLR, 2022. paper

   Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, and Martin V. Butz.

2. Learning composable energy surrogates for PDE order reduction. NIPS, 2020. paper

   Alex Beatson, Jordan T. Ash, Geoffrey Roeder, Tianju Xue, and Ryan P. Adams.

3. Neural basis functions for accelerating solutions to high mach euler equations. ICML, 2022. paper

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4. PFNN-2: A domain decomposed penalty-free neural network method for solving partial differential equations. arXiv, 2022. paper

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5. Finite basis physics-informed neural networks (FBPINNs): A scalable domain decomposition approach for solving differential equations. arXiv, 2021. paper

   Ben Moseley, Andrew Markham, and Tarje Nissen-Meyer.

6. Finite basis physics-informed neural networks as a Schwarz domain decomposition method. arXiv, 2022. paper

   Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

7. NeuralStagger: Accelerating physics constrained neural PDE solver with spatial-temporal decomposition. ICML, 2023. paper

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8. Augmenting physical models with deep networksfor complex dynamics forecasting. Journal of Statistical Mechanics: Theory and Experiment, 2021. paper

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9. LordNet: Learning to solve parametric partial differential equations without simulated data. arXiv, 2022. paper

   Wenlei Shi, Xinquan Huang, Xiaotian Gao, Xinran Wei, Jia Zhang, Jiang Bian, Mao Yang, and Tieyan Liu.

10. An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations. arXiv, 2022. paper

    Ivan Prusak, Monica Nonino, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza.

11. NUNO: A general gramework for learning parametric PDEs with non-uniform data. ICML, 2023. paper

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12. Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. arXiv, 2023. paper

    Alena Kopaničáková, Hardik Kothari, George Em Karniadakis, and Rolf Krause.

13. Multilevel domain decomposition-based architectures for physics-informed neural networks. arXiv, 2023. paper

    Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, and Ben Moseley.

14. Friedrichs' systems discretized with the Discontinuous Galerkin method: Domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions. arXiv, 2023. paper

    Francesco Romor, Davide Torlo, and Gianluigi Rozza.

15. A deep domain decomposition method based on Fourier features. Journal of Computational and Applied Mathematics, 2023. paper

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16. A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions. arXiv, 2023. paper

    Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, and Robert M. Kirby.

17. A generalized Schwarz-type non-overlapping domain decomposition method using physics-constrained neural networks. arXiv, 2023. paper

    Shamsulhaq Basir and Inanc Senocak.

18. Breaking boundaries: Distributed domain decomposition with scalable physics-informed neural PDE solvers. arXiv, 2023. paper

    Arthur Feeney, Zitong Li, Ramin Bostanabad, and Aparna Chandramowlishwaran.

19. Efficient learning of PDEs via Taylor expansion and sparse decomposition into value and Fourier domains. arXiv, 2023. paper

    Md Nasim and Yexiang Xue.

20. Adaptive task decomposition physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2023. paper

    Jianchuan Yang, Xuanqi Liu, Yu Diao, Xi Chen, and Haikuo Hu.

21. PF-DMD: Physics-fusion dynamic mode decomposition for accurate and robust forecasting of dynamical systems with imperfect data and physics. arXiv, 2023. paper

    Yuhui Yin, Chenhui Kou, Shengkun Jia, Lu Lu, Xigang Yuan, and Yiqing Luo.

22. Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs. JCP, 2023. paper

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23. Adaptive deep Fourier residual method via overlapping domain decomposition. arXiv, 2024. paper

    Jamie M. Taylor, Manuela Bastidas, Victor M. Calo, and David Pardo.

1. PDE-driven spatiotemporal disentanglement. ICLR, 2021. paper

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2. Disentangling physical dynamics from unknown factors for unsupervised video prediction. CVPR, 2020. paper

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1. Solver-in-the-loop: Learning from differentiable physics to interact with iterative PDE-solvers. NIPS, 2020. paper

   Kiwon Um, Robert Brand, Yun (Raymond) Fei, Philipp Holl, and Nils Thuerey.

2. Lie point symmetry data augmentation for neural PDE solvers. ICML, 2022. paper

   Johannes Brandstetter, Max Welling, and Daniel E. Worrall.

3. Incorporating symmetry into deep dynamics models for improved generalization. ICLR, 2021. paper

   Rui Wang, Robin Walters, and Rose Yu.

4. HyperSolvers: Toward fast continuous-depth models. NIPS, 2020. paper

   Michael Poli, Stefano Massaroli, Atsushi Yamashita, Hajime Asama, and Jinkyoo Park.

5. PIXEL: Physics-informed cell representations for fast and accurate PDE solvers. NIPS, 2022. paper

   Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong, Seok-Bae Yun, and Eunbyung Park.

6. NeuralSim: Augmenting differentiable simulators with neural networks. ICRA, 2021. paper

   Eric Heiden, David Millard, Erwin Coumans, Yizhou Sheng, and Gaurav S. Sukhatme.

7. DPM: A deep learning PDE augmentation method with application to large-eddy simulation. JCP, 2020. paper

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8. General covariance data augmentation for neural PDE solvers. ICML, 2023. paper

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9. Learning preconditioners for conjugate gradient PDE solvers. ICML, 2023. paper

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10. Autoregressive Renaissance in neural PDE solvers. ICLR, 2023. paper

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11. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

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12. Training deep surrogate models with large scale online learning. ICML, 2023. paper

    Lucas Meyer, Marc Schouler, Robert A. Caulk, Alejandro Ribes, and Bruno Raffin.

13. Self-supervised learning with Lie symmetries for partial differential equations. arXiv, 2023. paper

    Grégoire Mialon, Quentin Garrido, Hannah Lawrence, Danyal Rehman, Yann LeCun, and Bobak T. Kiani.

14. Interpretable neural PDE solvers using symbolic frameworks. arXiv, 2023. paper

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15. Modeling accurate long rollouts with temporal neural PDE solvers. ICML, 2023. paper

    Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E. Turner, and Johannes Brandstetter.

16. Neural-integrated meshfree (NIM) method: A differentiable programming-based hybrid solver for computational mechanics. arXiv, 2023. paper

    Honghui Du and Qizhi He.

17. A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic partial differential equations. Computers & Mathematics with Applications, 2023. paper

    Endah R.M. Putri, Muhammad L. Shahab, Mohammad Iqbal, Imam Mukhlash, Amirul Hakam, Lutfi Mardianto, and Hadi Susanto.

18. Physics-enhanced deep surrogates for partial differential equations. NMI, 2023. paper

    Raphaël Pestourie, Youssef Mroueh, Chris Rackauckas, Payel Das, and Steven G. Johnson .

19. Better neural PDE solvers through data-free mesh movers. arXiv, 2023. paper

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20. Generating synthetic data for neural operators. arXiv, 2024. paper

    Erisa Hasani and Rachel A. Ward.

21. A deep branching solver for fully nonlinear partial differential equations. JCP, 2024. paper

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22. Accelerating data generation for neural operators via Krylov subspace recycling. ICLR, 2024. paper

    Hong Wang, Zhongkai Hao, Jie Wang, Zijie Geng, Zhen Wang, Bin Li, and Feng Wu.

23. Space and time continuous physics simulation from partial observations. ICLR, 2024. paper

    Janny Steeven, Nadri Madiha, Digne Julie, and Wolf Christian.

24. Speeding up and reducing memory usage for scientific machine learning via mixed precision. arXiv, 2024. paper

    Joel Hayford, Jacob Goldman-Wetzler, Eric Wang, and Lu Lu.

25. Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving. arXiv, 2024. paper

    Alexander Rudikov, Vladimir Fanaskov, Ekaterina Muravleva, Yuri M. Laevsky, and Ivan Oseledets.

26. Learning operators with stochastic gradient descent in general Hilbert spaces. arXiv, 2024. paper

    Lei Shi and Jiaqi Yang.

27. Accelerating PDE data generation via differential operator action in solution space. arXiv, 2024. paper

    Huanshuo Dong, Hong Wang, Haoyang Liu, Jian Luo, and Jie Wang.

28. Correctness verification of neural networks approximating differential equations. arXiv, 2024. paper

    Petros Ellinas, Rahul Nellikath, Ignasi Ventura, Jochen Stiasny, and Spyros Chatzivasileiadis.

29. DOF: Accelerating high-order differential operators with forward propagation. arXiv, 2024. paper

    Ruichen Li, Chuwei Wang, Haotian Ye, Di He, and Liwei Wang.

30. Sobolev training for operator learning. arXiv, 2024. paper

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31. Scaling physics-informed hard constraints with mixture-of-experts. ICLR, 2024. paper

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32. Learning semilinear neural operators: A unified recursive framework for prediction and data assimilation. ICLR, 2024. paper

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33. Efficient and stable SAV-based methods for gradient flows arising from deep learning. JCP, 2024. paper

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34. Generative downscaling of PDE solvers with physics-guided diffusion models. arXiv, 2024. paper

    Yulong Lu and Wuzhe Xu.

1. Auto-PINN: Understanding and optimizing physics-informed neural architecture. arXiv, 2022. paper

   Yicheng Wang, Xiaotian Han, Chiayuan Chang, Daochen Zha, Ulisses Braga-Neto, and Xia Hu.

2. Building high accuracy emulators for scientific simulations with deep neural architecture search. Machine Learning: Science and Technology, 2022. paper

   M F Kasim, D Watson-Parris, L Deaconu, S Oliver, P Hatfield, D H Froula, G Gregori, M Jarvis, S Khatiwala, J Korenaga, J Topp-Mugglestone, E Viezzer, and S M Vinko.

3. Learning operations for neural PDE solvers. ICLR, 2019. paper

   Nicholas Roberts, Mikhail Khodak, Tri Dao, Liam Li, Christopher Re, and Ameet Talwalkar.

4. AutoPINN: When AutoML meets physics-informed neural networks. arXiv, 2022. paper

   Xinle Wu, Dalin Zhang, Miao Zhang, Chenjuan Guo, Shuai Zhao, Yi Zhang, Huai Wang, and Bin Yang.

5. NAS-PINN: Neural architecture search-guided physics-informed neural network for solving PDEs. arXiv, 2023. paper

   Yifan Wang and Linlin Zhong.

1. Neural implicit flow: A mesh-agnostic dimensionality reduction paradigm of spatio-temporal data. arXiv, 2022. paper

   Shaowu Pan, Steven L. Brunton, and J. Nathan Kutz.

2. CROM: Continuous reduced-order modeling of PDEs using implicit neural representations. ICLR, 2023. paper

   Peter Yichen Chen, Jinxu Xiang, Dong Heon Cho, Yue Chang, G A Pershing, Henrique Teles Maia, Maurizio Chiaramonte, Kevin Carlberg, and Eitan Grinspun.

3. MAgNet: Mesh agnostic neural PDE solver. NIPS, 2022. paper

   Oussama Boussif, Dan Assouline, Loubna Benabbou, and Yoshua Bengio.

4. NTopo: Mesh-free topology optimization using implicit neural representations. NIPS, 2021. paper

   Jonas Zehnder, Yue Li, Stelian Coros, and Bernhard Thomaszewski.

5. ContactNets: Learning discontinuous contact dynamics with smooth, implicit representations. ICLR, 2020. paper

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6. Continuous PDE dynamics forecasting with implicit neural representations. ICLR, 2023. paper

   Yuan Yin, Matthieu Kirchmeyer, Jean-Yves Franceschi, Alain Rakotomamonjy, and Patrick Gallinari.

7. Stability of implicit neural networks for long-term forecasting in dynamical systems. ICLR, 2023. paper

   Leon Migus, Julien Salomon, and Patrick Gallinari.

8. Operator learning with neural fields: Tackling PDEs on general geometries. arXiv, 2023. paper

   Louis Serrano, Lise Le Boudec, Armand Kassaï Koupaï, Thomas X Wang, Yuan Yin, Jean-Noël Vittaut, and Patrick Gallinari.

9. Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature. arXiv, 2023. paper

   Marzieh Alireza Mirhoseini and Matthew J. Zahr.

10. Implicit neural spatial representations for time-dependent PDEs. ICML, 2023. paper

    Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, and Peter Yichen Chen.

11. Reduced-order modeling for parameterized PDEs via implicit neural representations. NIPS, 2023. paper

    Tianshu Wen, Kookjin Lee, and Youngsoo Choi.

12. Geom-DeepONet: A point-cloud-based deep operator network for field predictions on 3D parameterized geometries. arXiv, 2024. paper

    Junyan He, Seid Koric, Diab Abueidda, Ali Najafi, and Iwona Jasiuk.

1. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. arXiv, 2021. paper

   Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis.

2. Adversarial uncertainty quantification in physics-informed neural networks. JCP, 2021. paper

   Yibo Yang and Paris Perdikaris.

3. Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models. JCP, 2020. paper

   Ramakrishna Tipireddy, David A.Barajas-Solano, and Alexandre M.Tartakovsky.

4. Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. JCP, 2019. paper

   Yinhao Zhu, Nicholas Zabarasa, Phaedon-Stelios Koutsourelakisb, and Paris Perdikaris.

5. Error-aware B-PINNs: Improving uncertainty quantification in Bayesian physics-informed neural networks. arXiv, 2022. paper

   Olga Graf, Pablo Flores, Pavlos Protopapas, and Karim Pichara.

6. Physics-informed information field theory for modeling physical systems with uncertainty quantification. arXiv, 2023. paper

   Alex Alberts and Ilias Bilionis.

7. Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles. arXiv, 2023. paper

   Romit Maulik, Romain Egele, Krishnan Raghavan, and Prasanna Balaprakash.

8. Physics-informed variational inference for uncertainty quantification of stochastic differential equations. JCP, 2023. paper

   Hyomin Shin and Minseok Choi.

9. Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. JCP, 2023. paper

   Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, and George Em Karniadakis.

10. Auto-weighted Bayesian physics-informed neural networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution. arXiv, 2023. paper

    Sarah Perez and Philippe Poncet.

11. Neural SPDE solver for uncertainty quantification in high-dimensional space-time dynamics. arXiv, 2023. paper

    Maxime Beauchamp, Hugo Georgenthum, and Ronan Fablet.

12. Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows. NIPS, 2023. paper

    Victor J. Leon, Noah Ford, Honest Mrema, Jeffrey Gilbert, and Alexander New.

13. Evaluating Uncertainty Quantification approaches for Neural PDEs in scientific applications. NIPS, 2023. paper

    Vardhan Dongre and Gurpreet Singh Hora.

14. Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators. arXiv, 2023. paper

    Zongren Zou, Xuhui Meng, and George Em Karniadakis.

15. Data-driven autoencoder numerical solver with uncertainty quantification for fast physical simulations. arXiv, 2023. paper

    Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, and Jonathan L. Belof.

16. Randomized physics-informed machine learning for uncertainty quantification in high-dimensional inverse problems. arXiv, 2023. paper

    Yifei Zong, David Barajas-Solano, and Alexandre M. Tartakovsky.

17. Bayesian deep learning framework for uncertainty quantification in stochastic partial differential equations. SIAM Journal on Scientific Computing, 2024. paper

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18. Uncertainty quantification for forward and inverse problems of PDEs via latent global evolution. AAAI, 2024. paper

    Tailin Wu, Willie Neiswanger, Hongtao Zheng, Stefano Ermon, and Jure Leskovec.

19. Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification. arXiv, 2024. paper

    Himanshu Sharma, Lukáš Novák, and Michael D. Shields.

20. Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification. arXiv, 2024. paper

    Himanshu Sharma, Lukáš Novák, and Michael D. Shields.

21. Conformalized-DeepOnet: A distribution-free framework for uncertainty quantification in deep operator networks. arXiv, 2024. paper

    Christian Moya, Amirhossein Mollaali, Zecheng Zhang, Lu Lu, and Guang Lin.

22. Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning. arXiv, 2024. paper

    Zongren Zou, Tingwei Meng, Paula Chen, Jérôme Darbon, and George Em Karniadakis.

1. A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks. NCS, 2021. paper

   Teeratorn Kadeethum, Daniel O’Malley, Jan Niklas Fuhg, Youngsoo Choi, Jonghyun Lee, Hari S. Viswanathan, and Nikolaos Bouklas.

2. Neural SDEs as infinite-dimensional GANs. ICML, 2021. paper

   Patrick Kidger, James Foster, Xuechen Li, and Terry J Lyons.

3. PID-GAN: A GAN framework based on a physics-informed discriminator for uncertainty quantification with physics. KDD, 2021. paper

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7. Competitive physics informed networks. ICLR, 2023. paper

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8. Learning generative neural networks with physics knowledge. Research in the Mathematical Sciences, 2022. paper

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9. Diffusion generative models in infinite dimensions. arXiv, 2022. paper

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10. Revisiting PINNs: Generative adversarial physics-informed neural networks and point-weighting method. arXiv, 2022. paper

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11. PIAT: Physics informed adversarial training for solving partial differential equations. arXiv, 2022. paper

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12. Physics-constrained generative adversarial networks for 3D turbulence. arXiv, 2022. paper

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13. Score-based diffusion models in function space. arXiv, 2023. paper

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14. Infinite-dimensional diffusion models for function spaces. arXiv, 2023. paper

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15. A physics-informed diffusion model for high-fidelity flow field reconstruction. JCP, 2023. paper

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16. Generative modelling with inverse heat dissipation. ICLR, 2023. paper

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17. Differentiable Gaussianization layers for inverse problems regularized by deep generative models. ICLR, 2023. paper

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18. Transformer meets boundary value inverse problems. ICLR, 2023. paper

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19. ViTO: Vision Transformer-operator. arXiv, 2023. paper

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20. Latent PINNs: Generative physics-informed neural networks via a latent representation learning. arXiv, 2023. paper

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21. Generative diffusion learning for parametric partial differential equations. arXiv, 2023. paper

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22. Scalable Transformer for PDE surrogate modeling. arXiv, 2023. paper

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23. Latent traversals in generative models as potential flows. ICML, 2023. paper

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24. Learning space-time continuous neural PDEs from partially observed states. arXiv, 2023. paper

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25. DiTTO: Diffusion-inspired temporal Transformer operator. arXiv, 2023. paper

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26. PINNsFormer: A Transformer-based framework For physics-informed neural networks. arXiv, 2023. paper

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27. CoCoGen: Physically-consistent and conditioned score-based generative models for forward and inverse problems. arXiv, 2023. paper

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1. Learning operators with coupled attention. JMLR, 2022. paper

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2. Choose a Transformer: Fourier or Galerkin. NIPS, 2021. paper

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3. Predicting physics in mesh-reduced space with temporal attention. ICLR, 2022. paper

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4. SiT: Simulation transformer for particle-based physics simulation. ICLR, 2022. paper

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5. Physics-informed long-sequence forecasting from multi-resolution spatiotemporal data. IJCAI, 2022. paper

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6. TransFlowNet: A physics-constrained Transformer framework for spatio-temporal super-resolution of flow simulations. Journal of Computational Science, 2022. paper

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7. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

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8. Transformer for partial differential equations' operator learning. arXiv, 2022. paper

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9. Physics-informed attention-based neural network for hyperbolic partial differential equations: Application to the Buckley–Leverett problem. Scientific Reports, 2022. paper

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10. Self-adaptive physics-informed neural networks using a soft attention mechanism. AAAI-MLPS, 2021. paper

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11. Nonlinear reconstruction for operator learning of PDEs with discontinuities. ICLR, 2023. paper

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12. GNOT: A general neural operator transformer for operator learning. ICML, 2023. paper

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13. In-context operator learning for differential equation problems. arXiv, 2023. paper

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14. Learning neural PDE solvers with parameter-guided channel attention. ICML, 2023. paper

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15. Physics informed token Transformer. arXiv, 2023. paper

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16. Improved operator learning by orthogonal attention. arXiv, 2023. paper

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17. Multi-scale time-stepping of partial differential equations with Transformers. arXiv, 2023. paper

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18. Deciphering and integrating invariants for neural operator learning with various physical mechanisms. arXiv, 2023. paper

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19. Attention-enhanced neural differential equations for physics-informed deep learning of ion transport. NIPS, 2023. paper

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20. Inducing point operator Transformer: A flexible and scalable architecture for solving PDEs. arXiv, 2023. paper

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21. Loss-attentional physics-informed neural networks. JCP, 2024. paper

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22. PirateNets: Physics-informed deep learning with residual adaptive networks. arXiv, 2024. paper

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23. DPOT: Auto-regressive denoising operator transformer for large-scale PDE pre-training. arXiv, 2024. paper

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1. Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations. arXiv, 2022. paper

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2. Solving PDEs by variational physics-informed neural networks: A posteriori error analysis. arXiv, 2022. paper

   Stefano Berrone, Claudio Canuto, and Moreno Pintore.

3. A unified framework for the error analysis of physics-informed neural networks. arXiv, 2023. paper

   Marius Zeinhofer, Rami Masri, and Kent-André Mardal.

4. Neural tangent kernel analysis of PINN for advection-diffusion equation. arXiv, 2022. paper

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5. Error estimates for DeepONets: A deep learning framework in infinite dimensions. Transactions of Mathematics and Its Applications, 2022. paper

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6. Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks. arXiv, 2023. paper

   Zheyuan Hu, Zekun Shi, George Em Karniadakis, and Kenji Kawaguchi.

7. An analysis of universal differential equations for data-driven discovery of ordinary differential equations. arXiv, 2023. paper

   Mattia Silvestri, Federico Baldo, Eleonora Misino, and Michele Lombardi.

8. Exponential convergence of deep operator networks for elliptic partial differential equations. SIAM Journal on Numerical Analysis, 2023. paper

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9. A discretization-invariant extension and analysis of some deep operator networks. arXiv, 2023. paper

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10. Machine learning for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality. ICLR, 2022. paper

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11. Elliptic PDE learning is provably data-efficient. arXiv, 2023. paper

    Nicolas Boullé, Diana Halikias, and Alex Townsend.

12. Error estimates of residual minimization using neural networks for linear PDEs. Journal of Machine Learning for Modeling and Computing, 2023. paper

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13. Analysis of the generalization error of deep learning based on randomized quasi-Monte Carlo for solving linear Kolmogorov PDEs. arXiv, 2023. paper

    Jichang Xiao, Fengjiang Fu, and Xiaoqun Wang.

14. Rigorous a posteriori error bounds for PDE-defined PINNs. TNNLS, 2023. paper

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15. Error estimation for physics-informed neural networks with implicit Runge-Kutta methods. arXiv, 2023. paper

    Jochen Stiasny and Spyros Chatzivasileiadis.

16. Approximation of solution operators for high-dimensional PDEs. arXiv, 2024. paper

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17. Accuracy analysis of physics-informed neural networks for approximating the critical SQG equation. arXiv, 2024. paper

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18. Deep Ritz method for elliptical multiple eigenvalue problems. Journal of Scientific Computing, 2024. paper

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19. Inf-Sup neural networks for high-dimensional elliptic PDE problems. arXiv, 2024. paper

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20. The challenges of the nonlinear regime for physics-informed neural networks. arXiv, 2024. paper

    Andrea Bonfanti, Giuseppe Bruno, and Cristina Cipriani.

21. A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples. arXiv, 2024. paper

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22. A priori error estimation of physics-informed neural networks solving Allen--Cahn and Cahn--Hilliard equations. arXiv, 2024. paper

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1. PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations. arXiv, 2022. paper

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2. Solving and learning nonlinear PDEs with Gaussian processes. JCP, 2021. paper

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3. Neural-net-induced Gaussian process regression for function approximation and PDE solution. JCP, 2019. paper

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4. Learning neural optimal interpolation models and solvers. arXiv, 2022. paper

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5. Inference of nonlinear partial differential equations via constrained Gaussian processes. arXiv, 2022. paper

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6. Gaussian process priors for systems of linear partial differential equations with constant coefficients. arXiv, 2022. paper

   Marc Härkönen, Markus Lange-Hegermann, and Bogdan Raiţă.

7. Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes. arXiv, 2023. paper

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8. A mini-batch method for solving nonlinear PDEs with Gaussian processes. arXiv, 2023. paper

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9. Random grid neural processes for parametric partial differential equations. ICML, 2023. paper

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10. Gaussian process priors for systems of linear partial differential equations with constant coefficients. ICML, 2023. paper

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11. GPLaSDI: Gaussian process-based interpretable latent space dynamics identification through deep autoencoder. arXiv, 2023. paper

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12. Solving high frequency and multi-scale PDEs with Gaussian processes. ICLR, 2024. paper

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13. Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations. arXiv, 2024. paper

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1. PI-VAE: Physics-informed variational auto-encoder for stochastic differential equations. Computer Methods in Applied Mechanics and Engineering, 2022. paper

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2. Robust SDE-based variational formulations for solving linear PDEs via deep learning. ICML, 2022. paper

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3. HP-VPINNs: Variational physics-informed neural networks with domain decomposition. Computer Methods in Applied Mechanics and Engineering, 2021. paper

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4. Variational onsager neural networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs. Journal of the Mechanics and Physics of Solids, 2022. paper

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5. Variational Monte Carlo approach to partial differential equations with neural networks. arXiv, 2022. paper

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6. Energetic variational neural network discretizations to gradient flows. arXiv, 2022. paper

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7. Variational Bayes deep operator network: A data-driven Bayesian solver for parametric differential equations. arXiv, 2022. paper

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8. Variational inference in neural functional prior using normalizing flows: Application to differential equation and operator learning problems. arXiv, 2023. paper

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9. Neural network approximations of PDEs beyond linearity: A representational perspective. ICML, 2023. paper

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1. Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data. JCP: X, 2022. paper

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2. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. JCP, 2021. paper

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3. Approximate Bayesian neural operators: Uncertainty quantification for parametric PDEs. arXiv, 2022. paper

   Emilia Magnani, Nicholas Krämer, Runa Eschenhagen, Lorenzo Rosasco, and Philipp Hennig.

4. Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants. arXiv, 2022. paper

   L. Mars Gao and J. Nathan Kutz.

5. Bayesian physics informed neural networks for data assimilation and spatio-temporal modelling of wildfires. arXiv, 2022. paper

   Joel Janek Dabrowski, Daniel Edward Pagendam, James Hilton, Conrad Sanderson, Daniel MacKinlay, Carolyn Huston, Andrew Bolt, and Petra Kuhnert.

6. Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE. arXiv, 2023. paper

   Zecheng Zhang, Christian Moya, Wing Tat Leung, Guang Lin, and Hayden Schaeffer.

7. Bayesian deep learning framework for uncertainty quantification in stochastic partial differential equations. SIAM Journal on Scientific Computing, 2024. paper

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1. Multiscale simulations of complex systems by learning their effective dynamics. NMI, 2022. paper

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2. A latent space solver for PDE generalization. ICLR, 2021. paper

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3. Approximate latent force model inference. AAAI, 2021. paper

   Jacob D. Moss, Felix L. Opolka, Bianca Dumitrascu, and Pietro Lió.

4. Learning to accelerate partial differential equations via latent global evolution. NIPS, 2022. paper

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5. Exploring physical latent spaces for deep learning. arXiv, 2022. paper

   Chloe Paliard, Nils Thuerey, and Kiwon Um.

6. Certified data-driven physics-informed greedy auto-encoder simulator. arXiv, 2022. paper

   Xiaolong He, Youngsoo Choi, William D. Fries, Jonathan L. Belof, and Jiun-Shyan Chen.

7. Deep latent regularity network for modeling stochastic partial differential equations. AAAI, 2023. paper

   Shiqi Gong, Peiyan Hu, Qi Meng, Yue Wang, Rongchan Zhu, Bingguang Chen, Zhiming Ma, Hao Ni, and Tieyan Liu.

8. Learning in latent spaces improves the predictive accuracy of deep neural operators. arXiv, 2023. paper

   Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, and Michael D. Shields.

9. Solving high-dimensional PDEs with latent spectral models. ICML, 2023. paper

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10. Physics-informed generator-encoder adversarial networks with latent space matching for stochastic differential equations. arXiv, 2023. paper

    Ruisong Gao, Min Yang, and Jin Zhang.

11. Smooth and sparse latent dynamics in operator learning with Jerk regularization arXiv, 2024. paper

    Xiaoyu Xie, Saviz Mowlavi, and Mouhacine Benosman.

12. Latent neural PDE solver: A reduced-order modelling framework for partial differential equations arXiv, 2024. paper

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1. Lagrangian PINNs: A causality–conforming solution to failure modes of physics-informed neural networks. arXiv, 2022. paper

   Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh.

2. AL-PINNs: Augmented Lagrangian relaxation method for physics-informed neural networks. arXiv, 2022. paper

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3. Lagrangian flow networks for conservation laws. arXiv, 2023. paper

   Fabricio Arend Torres, Marcello Massimo Negri, Marco Inversi, and Jonathan Aellen.

4. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

   Shamsulhaq Basir and Inanc Senocak.

5. Constrained optimization via exact augmented Lagrangian and randomized iterative sketching. ICML, 2023. paper

   Ilgee Hong, Sen Na, Michael W. Mahoney, and Mladen Kolar.

6. An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks. arXiv, 2023. paper

   Shamsulhaq Basir and Inanc Senocak.

7. Partitioned neural network approximation for partial differential equations enhanced with Lagrange multipliers and localized loss functions. arXiv, 2023. paper

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1. Hierarchical deep learning of multiscale differential equation time-steppers. Philosophical Transactions of the Royal Society A, 2022. paper

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2. NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems. JCP, 2022. paper

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3. Deep multiscale model learning. JCP, 2020. paper

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4. Multi-scale deep neural networks for solving high dimensional PDEs. arXiv, 2019. paper

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5. Towards multi-spatiotemporal-scale generalized PDE modeling. arXiv, 2022. paper

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6. MultiAdam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural networks. ICML, 2023. paper

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7. Learning homogenization for elliptic operators. arXiv, 2023. paper

   Kaushik Bhattacharya, Nikola Kovachki, Aakila Rajan, Andrew M. Stuart, and Margaret Trautner.

8. Multi-grade deep learning for partial differential equations with applications to the Burgers equation. arXiv, 2023. paper

   Yuesheng Xu and Taishan Zeng.

9. Multiscale neural operators for solving time-independent PDEs. NIPS, 2023. paper

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10. Multilevel scalable solvers for stochastic linear and nonlinear problems. arXiv, 2023. paper

    Sudhi Sharma, Pierre Jolivet, Victorita Dolean, and Abhijit Sarkar.

11. Local convolution enhanced global Fourier neural operator for multiscale dynamic spaces prediction. arXiv, 2023. paper

    Xuanle Zhao, Yue Sun, Tielin Zhang, and Bo Xu.

12. Mitigating spectral bias for the multiscale operator learning. JCP, 2024. paper

    Xinliang Liu, Bo Xu, Shuhao Cao, and Lei Zhang.

13. SineNet: Learning temporal dynamics in time-dependent partial differential equations. ICLR, 2024. paper

    Xuan Zhang, Jacob Helwig, Yuchao Lin, Yaochen Xie, Cong Fu, Stephan Wojtowytsch, and Shuiwang Ji.

14. Multiscale attention wavelet neural operator for capturing steep trajectories in biochemical systems. AAAI, 2024. paper

    Jiayang Su, Junbo Ma, Songyang Tong, Enze Xu, and Minghan Chen.

1. Multifidelity deep operator networks. arXiv, 2022. paper

   Amanda A. Howard, Mauro Perego, George Em Karniadakis, and Panos Stinis.

2. Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion. JCP, 2022. paper

   Lulu Zhang, Tao Luo, Yaoyu Zhang, Weinan E, Zhiqin John Xu, and Zheng Ma.

3. A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. JCP, 2020. paper

   Xuhui Meng and George Em Karniadakis.

4. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Physical Review Research, 2022. paper

   Lu Lu, Raphaël Pestourie, Steven G. Johnson, and Giuseppe Romano.

5. Multi-fidelity reduced-order surrogate modeling. arXiv, 2023. paper

   Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, and J. Nathan Kutz.

6. Multifidelity deep operator networks for data-driven and physics-informed problems. JCP, 2023. paper

   Amanda A. Howard, Mauro Perego, George Em Karniadakis, and Panos Stinis.

7. A multi-fidelity machine learning based semi-Lagrangian finite volume scheme for linear transport equations and the nonlinear Vlasov-Poisson system. arXiv, 2023. paper

   Yongsheng Chen, Wei Guo, and Xinghui Zhong.

8. Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations. arXiv, 2023. paper

   Xuhui Zhou, Jiequn Han, Muhammad I. Zafar, Christopher J. Roy, Heng Xiao.

9. Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics. AAAI, 2024. paper

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1. Learning to optimize multigrid PDE solvers. ICML, 2019. paper

   Daniel Greenfeld, Meirav Galun, Ronen Basri, Irad Yavneh, and Ron Kimmel.

2. Reducing operator complexity in algebraic multigrid with machine learning approaches. arXiv, 2023. paper

   Ru Huang, Kai Chang, Huan He, Ruipeng Li, and Yuanzhe Xi.

3. Multi-grid tensorized Fourier neural operator for high-resolution PDEs. arXiv, 2023. paper

   Jean Kossaifi, Nikola Kovachki, Kamyar Azizzadenesheli, and Anima Anandkumar.

4. MgNO: Efficient parameterization of linear operators via multigrid. arXiv, 2023. paper

   Juncai He, Xinliang Liu, and Jinchao Xu.

5. MGCNN: A learnable multigrid solver for linear PDEs on structured grids. arXiv, 2023. paper

   Yan Xie, Minrui Lv, and Chensong Zhang.

6. Neural physical simulation with multi-resolution hash grid encoding. AAAI, 2024. paper

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1. Neural Galerkin scheme with active learning for high-dimensional evolution equations. arXiv, 2022. paper

   Joan Bruna, Benjamin Peherstorfer, and Eric Vanden-Eijnden.

2. Discovering and forecasting extreme events via active learning in neural operators. arXiv, 2022. paper

   Ethan Pickering, Stephen Guth, George Em Karniadakis, and Themistoklis P. Sapsis.

3. Active learning based sampling for high-dimensional nonlinear partial differential equations. JCP, 2023. paper

   Wenhan Gao and Chunmei Wang.

4. An extreme learning machine-based method for computational PDEs in higher dimensions. arXiv, 2023. paper

   Yiran Wang and Suchuan Dong.

5. Multi-resolution active learning of Fourier neural operators. arXiv, 2023. paper

   Shibo Li, Xin Yu, Wei Xing, Mike Kirby, Akil Narayan, and Shandian Zhe.

6. A foundational neural operator that continuously learns without forgetting. arXiv, 2023. paper

   Tapas Tripura and Souvik Chakraborty.

7. Neural Galerkin schemes with active learning for high-dimensional evolution equations. JCP, 2023. paper

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1. Fast PDE-constrained optimization via self-supervised operator learning. arXiv, 2021. paper

   Sifan Wang, Mohamed Aziz Bhouri, and Paris Perdikaris.

2. An extended physics informed neural network for preliminary analysis of parametric optimal control problems. arXiv, 2021. paper

   Nicola Demo, Maria Strazzullo, and Gianluigi Rozza.

3. Optimal control of PDEs using physics-informed neural networks. JCP, 2023. paper

   Saviz Mowlavi and Saleh Nabi.

4. Solving PDE-constrained control problems using operator learning. AAAI, 2022. paper

   Rakhoon Hwang, Jae Yong Lee, Jin Young Shin, and Hyung Ju Hwang.

5. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

   Zhiyu Zhang, Ashok Cutkosky, and Ioannis Paschalidis.

6. Control of partial differential equations via physics-informed neural networks. Journal of Optimization Theory and Applications, 2022. paper

   Carlos J. García-Cervera, Mathieu Kessler, and Francisco Periago.

7. A machine learning framework for solving high-dimensional mean field game and mean field control problems. PNAS, 2020. paper

   Lars Ruthottoa, Stanley J. Osherc, Wuchen Lic, Levon Nurbekyanc, and Samy Wu Fung.

8. Bi-level physics-informed neural networks for PDE constrained optimization using Broyden's hypergradients. ICLR, 2023. paper

   Zhongkai Hao, Chengyang Ying, Hang Su, Jun Zhu, Jian Song, and Ze Cheng.

9. A combination technique for optimal control problems constrained by random PDEs. arXiv, 2022. paper

   Fabio Nobile and Tommaso Vanzan.

10. A multilevel reinforcement learning framework for PDE-based control. arXiv, 2022. paper

    Atish Dixit and Ahmed H. Elsheikh.

11. Optimal learning of high-dimensional classification problems using deep neural networks. arXiv, 2022. paper

    Philipp Petersen and Felix Voigtlaender.

12. The ADMM-PINNs algorithmic framework for nonsmooth PDE-constrained optimization: A deep learning approach. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

13. Learning differentiable solvers for systems with hard constraints. ICLR, 2023. paper

    Geoffrey Négiar, Geoffrey_Négiar, Michael W. Mahoney, and Aditi Krishnapriyan.

14. Volumetric optimal transportation by fast Fourier transform. ICLR, 2023. paper

    Na Lei, DONGSHENG An, Min Zhang, Xiaoyin Xu, and David Gu.

15. PDE-based optimal strategy for unconstrained online learning. ICML, 2022. paper

    Zhiyu Zhang, Ashok Cutkosky, and Ioannis Paschalidis.

16. PDE-constrained models with neural network terms: Optimization and global convergence. JCP, 2023. paper

    Justin Sirignano, Jonathan MacArt, and Konstantinos Spiliopoulos.

17. Topology optimization using neural networks with conditioning field initialization for improved efficiency. arXiv, 2023. paper

    Hongrui Chen, Aditya Joglekar, and Levent Burak Kara.

18. Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology. JCP, 2023. paper

    Yusuf Nasir and Louis J. Durlofsky.

19. Constrained optimization via exact augmented lagrangian and randomized iterative sketching. ICML, 2023. paper

    Ilgee Hong, Sen Na, Michael W. Mahoney, and Mladen Kolar.

20. Efficient PDE-constrained optimization under high-dimensional uncertainty using derivative-informed neural operators. arXiv, 2023. paper

    Dingcheng Luo, Thomas O'Leary-Roseberry, Peng Chen, and Omar Ghattas.

21. Dimension-independent certified neural network watermarks via mollifier smoothing. ICML, 2023. paper

    Jiaxiang Ren, Yang Zhou, Jiayin Jin, Lingjuan Lyu, and Da Yan.

22. Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

23. Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems. arXiv, 2023. paper

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue.

24. Operator learning for continuous spatial-temporal model with a hybrid optimization scheme. arXiv, 2023. paper

    Chuanqi Chen and Jinlong Wu.

25. Deep neural operators as accurate surrogates for shape optimization. EAAI, 2023. paper

    Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Nicholas Plewacki, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, and George Em Karniadakis.

26. Accelerating Bayesian optimal experimental design with derivative-informed neural operators. arXiv, 2023. paper

    Jinwoo Go and Peng Chen.

27. A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling. arXiv, 2024. paper

    Jianbo Cui, Shu Liu, and Haomin Zhou.

28. Optimization in SciML -- A function space perspective. arXiv, 2024. paper

    Johannes Müller and Marius Zeinhofer.

29. Inverse design method for horn antennas based on knowledge-embedded physics-informed neural networks. IEEE Antennas and Wireless Propagation Letters, 2024. paper

    Jinpin Liu, Bingzhong Wang, Chuansheng Chen, and Ren Wang.

30. G-RepsNet: A fast and general construction of equivariant networks for arbitrary matrix groups. arXiv, 2024. paper

    Sourya Basu, Suhas Lohit, and Matthew Brandr.

1. Physics-informed neural networks (PINNs) for fluid mechanics: A review. Acta Mechanica Sinica, 2021. paper

   Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, and George Em Karniadakis.

2. Neural operator prediction of linear instability waves in high-speed boundary layers. JCP, 2022. paper

   Patricio Clark Di Leoni, Lu Lu, Charles Meneveau, George Karniadakis, and Tamer A. Zaki.

3. A physics-informed convolutional neural network for the simulation and prediction of two-phase darcy flows in heterogeneous porous media. JCP, 2023. paper

   Zhao Zhang, Xia Yan, Piyang Liu, Kai Zhang, Renmin Han, and Sheng Wang.

4. DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization. Computer Methods in Applied Mechanics and Engineering, 2021. paper

   Rishikesh Ranade, Chris Hillb, and Jay Pathak.

5. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Computer Methods in Applied Mechanics and Engineering, 2020. paper

   Luning Sun, Han Gao, Shaowu Pan, and Jianxun Wang.

6. Towards physics-informed deep learning for turbulent flow prediction. KDD, 2020. paper

   Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, and Rose Yu.

7. Learning to estimate and refine fluid motion with physical dynamics. ICML, 2022. paper

   Mingrui Zhang, Jianhong Wang, James Tlhomole, and Matthew D. Piggott.

8. Physics informed neural fields for smoke reconstruction with sparse data. ACM Transactions on Graphics, 2022. paper

   Mengyu Chu, Lingjie Liu, Quan Zheng, Erik Franz, Hans-Peter Seidel, Christian Theobalt, and Rhaleb Zayer.

9. Physics-informed deep learning for traffic state estimation: A hybrid paradigm informed by second-order traffic models. AAAI, 2021. paper

   Rongye Shi, Zhaobin Mo, and Xuan Di.

10. Residual-based adaptivity for two-phase flow simulation in porous media using physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 2022. paper

    John M.Hanna, José V.Aguado, Sebastien Comas-Cardona, Ramz Askri, and Domenico Borzacchiello.

11. Learned turbulence modelling with differentiable fluid solvers: Physics-based loss-functions and optimisation horizons. JFM, 2022. paper

    Björn List, Liwei Chen, and Nils Thuerey.

12. Learning hydrodynamic equations for active matter from particle simulations and experiments. PNAS, 2023. paper

    Rohit Supekar, Boya Song, Alasdair Hastewell, Gary P. T. Choi, Alexander Mietke, and Jörn Dunkel.

13. Physics informed neural networks: A case study for gas transport problems. JCP, 2023. paper

    Erik Laurin Strelow, Alf Gerisch, Jens Lang, and Marc E. Pfetsch.

14. Turbulence model augmented physics informed neural networks for mean flow reconstruction. arXiv, 2023. paper

    Yusuf Patel, Vincent Mons, Olivier Marquet, and Georgios Rigas.

15. RANS-PINN based simulation surrogates for predicting turbulent flows. arXiv, 2023. paper

    Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis, and Biswadip Dey.

16. Meta-learning for airflow simulations with graph neural networks. arXiv, 2023. paper

    Wenzhuo Liu, Mouadh Yagoubi, and Marc Schoenauer.

17. Learning operators for identifying weak solutions to the Navier-Stokes equations. arXiv, 2023. paper

    Dixi Wang and Cheng Yu.

18. Physics-informed neural networks modeling for systems with moving immersed boundaries: Application to an unsteady flow past a plunging foil. arXiv, 2023. paper

    Rahul Sundar, Dipanjan Majumdar, Didier Lucor, and Sunetra Sarkar.

19. A machine learning pressure emulator for hydrogen embrittlement. ICML, 2023. paper

    Minh Triet Chau, João Lucas de Sousa Almeida, Elie Alhajjar, and Alberto Costa Nogueira Junior.

20. A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty. arXiv, 2023. paper

    Atul Agrawal and Phaedon-Stelios Koutsourelakis.

21. Physics-informed machine learning for calibrating macroscopic traffic flow models. arXiv, 2023. paper

    Yu Tang, Li Jin, and Kaan Ozbay.

22. Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows. Physics of Fluids, 2023. paper

    Yang Xiao, Liming Yang, Yinjie Du, Yuxin Song, and Chang Shu.

23. Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator. Physics of Fluids, 2023. paper

    Zhijie Li, Wenhui Peng, Zelong Yuan, and Jianchun Wang.

24. Physics-informed neural networks for parametric compressible Euler equations. arXiv, 2023. paper

    Simon Wassing, Stefan Langer, and Philipp Bekemeyer.

25. Simulation of rarefied gas flows using physics-informed neural network combined with discrete velocity method. Physics of Fluids, 2023. paper

    Linying Zhang, Wenjun Ma, Qin Lou, and Jun Zhang.

26. Influence of adversarial training on super-resolution turbulence models. arXiv, 2023. paper

    Ludovico Nista, Christoph David Karl Schumann, Mathis Bode, Temistocle Grenga, Jonathan F. MacArt, Antonio Attili, and Heinz Pitsch.

27. Turbulent flow simulation using autoregressive conditional diffusion models. arXiv, 2023. paper

    Georg Kohl, Liwei Chen, and Nils Thuerey.

28. Physics-informed neural networks for studying heat transfer in porous media. International Journal of Heat and Mass Transfer, 2023. paper

    Jiaxuan Xu, Han Wei, and Hua Bao.

29. Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks. arXiv, 2023. paper

    Zhicheng Wang, Xuhui Meng, Xiaomo Jiang, Hui Xiang, and George Em Karniadakis.

30. Towards real-time training of physics-informed neural networks: Applications in ultrafast ultrasound blood flow imaging. arXiv, 2023. paper

    Haotian Guan, Jinping Dong, and Weining Lee.

31. Multi-physical predictions in electro-osmotic micromixer by auto-encoder physics-informed neural networks. Physics of Fluids, 2023. paper

    Naiwen Chang, Ying Huai, Tingting Liu, Xi Chen, and Yuqi Jin.

32. Studying turbulent flows with physics-informed neural networks and sparse data. International Journal of Heat and Fluid Flow, 2023. paper

    S. Hanrahan, M. Kozul, and R.D. Sandberg.

33. Enhancing physics informed neural networks for solving Navier–Stokes equations. International Journal for Numerical Methods in Fluids, 2023. paper

    Ayoub Farkane, Mounir Ghogho, Mustapha Oudani, and Mohamed Boutayeb.

34. Physics-informed tensor basis neural network for turbulence closure modeling. arXiv, 2023. paper

    Leon Riccius, Atul Agrawal, and Phaedon-Stelios Koutsourelakis.

35. Investigation of low and high-speed fluid dynamics problems using physics-informed neural network. International Journal of Computational Fluid Dynamics, 2023. paper

    Anubhav Joshi,Alexandros Papados, and Rakesh Kumar.

36. Singular layer physics informed neural network method for plane parallel flows. arXiv, 2023. paper

    Tengyuan Chang, Gungmin Gie, Youngjoon Hong, and Chang-Yeol Jung.

37. Data-efficient operator learning for solving high Mach number fluid flow problems. arXiv, 2023. paper

    Noah Ford, Victor J. Leon, Honest Merman, Jeffrey Gilbert, and Alexander New.

38. Three-dimensional laminar flow using physics informed deep neural networks featured. Physics of Fluids, 2023. paper

    Saykat Kumar Biswas and N. K. Anand.

39. Real-time prediction of gas flow dynamics in diesel engines using a deep neural operator framework. Applied Intelligence, 2023. paper

    Varun Kumar, Somdatta Goswami, Daniel Smith, and George Em Karniadakis.

40. Semi-analytic physics informed neural network for convection-dominated boundary layer problems in 2D. arXiv, 2023. paper

    Gungmin Gie, Youngjoon Hong, Chang-Yeol Jung, and Dongseok Lee.

41. The improved backward compatible physics-informed neural networks for reducing error accumulation and applications in data-driven higher-order rogue waves. arXiv, 2023. paper

    Shuning Lin and Yong Chen.

42. Learning characteristic parameters and dynamics of centrifugal pumps under multi-phase flow using physics-informed neural networks. arXiv, 2023. paper

    Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, and George Em Karniadakis.

43. On the locality of local neural operator in learning fluid dynamics. arXiv, 2023. paper

    Ximeng Ye, Hongyu Li, Jingjie Huang, and Guoliang Qin.

44. Multi-viscosity physics-informed neural networks for generating ultra high resolution flow field data. International Journal of Computational Fluid Dynamics, 2023. paper

    Sen Zhang, Xiaowei Guo, Chao Li, Ran Zhao, Canqun Yang, Wei Wang, and Yanxu Zhong.

45. Towards high-accuracy deep learning inference of compressible flows over aerofoils. Computers & Fluids, 2023. paper

    Liwei Chen and Nils Thuerey.

46. Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source. International Journal of Heat and Mass Transfer, 2023. paper

    Seid Koric and Diab W. Abueidda.

47. Energy-preserving reduced operator inference for efficient design and control. arXiv, 2024. paper

    Tomoki Koike and Elizabeth Qian.

48. Variable linear transformation improved physics-informed neural networks to solve thin-layer flow problems. JCP, 2024. paper

    Jiahao Wu, Yuxin Wu, Guihua Zhang, and Yang Zhang.

49. Riemannonets: Interpretable neural operators for Riemann problems. arXiv, 2024. paper

    Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap, and George Em Karniadakis.

50. Physics-informed neural networks for incompressible flows with moving boundaries. Physics of Fluids, 2024. paper

    Yongzheng Zhu, Weizhen Kong, Jian Deng, and Xin Bian.

51. Solving the one dimensional vertical suspended sediment mixing equation with arbitrary eddy diffusivity profiles using temporal normalized physics-informed neural networks. Physics of Fluids, 2024. paper

    Shaotong Zhang, Jiaxin Deng, Xi'an Li, Zixi Zhao, Jinran Wu, Weide Li,Yougan Wang, and Dongsheng Jeng.

52. Neural SPH: Improved neural modeling of Lagrangian fluid dynamics. arXiv, 2024. paper

    Artur P. Toshev, Jonas A. Erbesdobler, Nikolaus A. Adams, and Johannes Brandstetter.

53. Continuous and discontinuous compressible flows in a converging–diverging channel solved by physics-informed neural networks without exogenous data. Scientific Reports, 2024. paper

    Hong Liang, Zilong Song, Chong Zhao, and Xin Bian.

54. Gauss-Newton natural gradient descent for physics-informed computational fluid dynamics. arXiv, 2024. paper

    Anas Jnini, Flavio Vella, and Marius Zeinhofer.

55. Residual-enhanced physics-guided machine learning with hard constraints for subsurface flow in reservoir engineering. TGRS, 2024. paper

    Haibo Cheng, Yunpeng He, Peng Zeng, and Valeriy Vyatkin.

56. Discovering artificial viscosity models for discontinuous Galerkin approximation of conservation laws using physics-informed machine learning. arXiv, 2024. paper

    Matteo Caldana, Paola F. Antonietti, and Luca Dede'.

57. EuLagNet: Eulerian fluid prediction with Lagrangian dynamics. arXiv, 2024. paper

    Qilong Ma, Haixu Wu, Lanxiang Xing, Jianmin Wang, and Mingsheng Long.

58. Physics-informed neural networks with domain decomposition for the incompressible Navier–Stokes equations. Physics of Fluids, 2024. paper

    Linyan Gu, Shanlin Qin, Lei Xu, and Rongliang Chen.

59. Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. JCP, 2024. paper

    Jin Song, Ming Zhong, George Em Karniadakis, and Zhenya Yan.

60. Continuous and discontinuous compressible flows in a converging–diverging channel solved by physics-informed neural networks without exogenous data. Scientific Reports, 2024. paper

    Hong Liang, Zilong Song, Chong Zhao, and Xin Bian.

61. A fast general thermal simulation model based on multi-branch physics-informed deep operator neural network. Physics of Fluids, 2024. paper

    Zibo Lu, Yuanye Zhou, Yanbo Zhang, Xiaoguang Hu, Qiao Zhao, and Xuyang Hu.

62. Potential of physics-informed neural networks for solving fluid flow problems with parametric boundary conditions. Physics of Fluids, 2024. paper

    F. Lorenzen, A. Zargaran, and U. Janoske.

63. Physics-informed neural networks for transonic flow around a cylinder with high Reynolds number. Physics of Fluids, 2024. paper

    Xiang Ren, Peng Hu, Hua Su, Feizhou Zhang, and Huahua Yu.

1. Machine learning accelerated PDE backstepping observers. arXiv, 2022. paper

   Yuanyuan Shi, Zongyi Li, Huan Yu, Drew Steeves, Anima Anandkumar, and Miroslav Krstic.

2. Neural solvers for fast and accurate numerical optimal control. NIPS, 2021. paper

   Federico Berto, Stefano Massaroli, Michael Poli, and Jinkyoo Park.

3. Bellman neural networks for the class of optimal control problems with integral quadratic cost. TAI, 2022. paper

   Enrico Schiassi, Andrea D'Ambrosio, and Roberto Furfaro.

4. Offline supervised learning vs online direct policy optimization: A comparative study and a unifie training paradigm for neural network-based optimal feedback control. arXiv, 2022. paper

   Yue Zhao and Jiequn Han.

5. Policy evaluation and temporal–difference learning in continuous time and space: A martingale approach. JMLR, 2022. paper

   Yanwei Jia and Xunyu Zhou.

6. Physics-informed kernel embeddings: Integrating prior system knowledge with data-driven control. arXiv, 2023. paper

   Adam J. Thorpe, Cyrus Neary, Franck Djeumou, Meeko M. K. Oishi, and Ufuk Topcu.

7. Distributed control of partial differential equations using convolutional reinforcement learning. arXiv, 2023. paper

   Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, and Kunihiko Taira.

8. Neural control of parametric solutions for high-dimensional evolution PDEs. arXiv, 2023. paper

   Nathan Gaby, Xiaojing Ye, and Haomin Zhou.

9. Bridging physics-informed neural networks with reinforcement learning: Hamilton-Jacobi-Bellman proximal policy optimization (HJBPPO). arXiv, 2023. paper

   Amartya Mukherjee and Jun Liu.

10. AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems. arXiv, 2023. paper

    Pengfei Yin, Guangqiang Xiao, Kejun Tang, and Chao Yang.

11. Neural operators for bypassing gain and control computations in PDE backstepping. arXiv, 2023. paper

    Luke Bhan, Yuanyuan Shi, and Miroslav Krstic.

12. Neural operators of backstepping controller and observer gain functions for reaction-diffusion PDEs. arXiv, 2023. paper

    Miroslav Krstic, Luke Bhan, and Yuanyuan Shi.

13. Leveraging multi-time Hamilton-Jacobi PDEs for certain scientific machine learning problems. arXiv, 2023. paper

    Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis.

14. Learning to control PDEs with differentiable physics. ICLR, 2020. paper

    Philipp Holl, Nils Thuerey, and Vladlen Koltun.

15. A generalizable physics-informed learning framework for risk probability estimation. L4DC, 2020. paper

    Zhuoyuan Wang and Yorie Nakahira.

16. Operator learning for nonlinear adaptive control. L4DC, 2023. paper

    Luke Bhan, Yuanyuan Shi and Miroslav Krstic.

17. Optimal temperature trajectory for tubular reactor using physics informed neural networks. JCP, 2023. paper

    Rahul Patel, Sharad Bhartiya, and Ravindra Gudi.

18. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. Journal of Process Control, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

19. **Physics-guided neural networks for inversion-based feedforward control applied to hybrid stepper motors.**arXiv, 2023. paper

    Daiwei Fan, Max Bolderman, Sjirk Koekebakker, Hans Butler, and Mircea Lazar.

20. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. JCP, 2023. paper

    Yingzhe Zheng, Cheng Hu, Xiaonan Wang, and Zhe Wu.

21. Optimal Dirichlet boundary control by Fourier neural operators applied to nonlinear optics. arXiv, 2023. paper

    Nils Margenberg, Franz X. Kärtner, and Markus Bause.

22. Neural operators for delay-compensating control of hyperbolic PIDEs. arXiv, 2023. paper

    Jie Qi, Jing Zhang, and Miroslav Krstic.

23. Physics-informed online learning of gray-box models by moving horizon estimation. European Journal of Control, 2023. paper

    Kristoffer Fink Løwenstein, Daniele Bernardini, Lorenzo Fagiano, and Alberto Bemporad.

24. Online identification and control of PDEs via reinforcement learning methods. arXiv, 2023. paper

    Alessandro Alla, Agnese Pacifico, Michele Palladino, and Andrea Pesare.

25. The hard-constraint PINNs for interface optimal control problems. arXiv, 2023. paper

    Ming-Chih Lai, Yongcun Song, Xiaoming Yuan, Hangrui Yue, and Tianyou Zeng.

26. Deep learning of delay-compensated backstepping for reaction-diffusion PDEs. arXiv, 2023. paper

    Shanshan Wang, Mamadou Diagne, and Miroslav Krstić.

27. Computationally efficient data-driven discovery and linear representation of nonlinear systems for control. arXiv, 2023. paper

    Madhur Tiwari, George Nehma, and Bethany Lusch.

28. Physics-informed state-space neural networks for transport phenomena. arXiv, 2023. paper

    Akshay J Dave and Richard B. Vilim.

29. A comparison of mesh-free differentiable programming and data-driven strategies for optimal control under PDE constraints. arXiv, 2023. paper

    Roussel Desmond Nzoyem, David A.W. Barton, and Tom Deakin.

30. A data-driven tracking control framework using physics-informed neural networks and deep reinforcement learning for dynamical systems. JCP, 2023. paper

    R.R. Faria, B.D.O. Capron, A.R. Secchi, and M.B. De Souza Jr.

31. Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. L4DC, 2023. paper

    Paula Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis.

32. Physics-informed neural network Lyapunov functions: PDE characterization, learning, and verification. arXiv, 2023. paper

    Jun Liu, Yiming Meng, Maxwell Fitzsimmons, and Ruikun Zhou.

33. Taming waves: A physically-interpretable machine learning framework for realizable control of wave dynamics. arXiv, 2023. paper

    Tristan Shah, Feruza Amirkulova, and Stas Tiomkin.

34. Neural operators for boundary stabilization of stop-and-go traffic. arXiv, 2023. paper

    Yihuai Zhang, Ruiguo Zhong, and Huan Yu.

35. Neural operator approximations of backstepping kernels for 2×2 hyperbolic PDEs. arXiv, 2023. paper

    Shanshan Wang, Mamadou Diagne, and Miroslav Krstić.

36. Lyapunov-based physics-informed long short-term memory (LSTM) neural network-based adaptive control. IEEE Control Systems Letters, 2023. paper

    Rebecca G. Hart, Emily J. Griffis, Omkar Sudhir Patil, and Warren E. Dixon.

37. Gain scheduling with a neural operator for a transport PDE with nonlinear recirculation. arXiv, 2024. paper

    Maxence Lamarque, Luke Bhan, Rafael Vazquez, and Miroslav Krstic.

38. Physics-informed deep learning approach to solve optimal control problem. AIAA, 2024. paper

    Kyung-Mi Na and Chang-Hun Lee.

39. Adaptive neural-operator backstepping control of a benchmark hyperbolic PDE. arXiv, 2024. paper

    Maxence Lamarque, Luke Bhan, Yuanyuan Shi, and Miroslav Krstic.

40. Physical-informed neural network for MPC-based trajectory tracking of vehicles with noise considered. TIV, 2024. paper

    Long Jin, Longqi Liu, Xingxia Wang, Mingsheng Shang, and Feiyue Wang.

41. Neural network approaches for parameterized optimal control. arXiv, 2024. paper

    Deepanshu Verma, Nick Winovich, Lars Ruthotto, and Bart van Bloemen Waanders.

42. Physics-informed neural network policy iteration: Algorithms, convergence, and verification. arXiv, 2024. paper

    Yiming Meng, Ruikun Zhou, Amartya Mukherjee, Maxwell Fitzsimmons, Christopher Song, and Jun Liu.

43. Nonlinear discrete-time observers with physics-informed neural networks. arXiv, 2024. paper

    Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis, Nikolaos Kazantzis, and Constantinos Siettos.

44. Pathwise relaxed optimal control of rough differential equations. arXiv, 2024. paper

    Prakash Chakraborty, Harsha Honnappa, and Samy Tindel.

45. Parametric PDE control with deep reinforcement learning and differentiable L^0-sparse polynomial policies. arXiv, 2024. paper

    Nicolò Botteghi and Urban Fasel.

1. FourCastNet: A global data-driven high-resolution weather model using adaptive Fourier neural operators. arXiv, 2022. paper

   Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, and Animashree Anandkumar.

2. Fourier neural operators for arbitrary resolution climate data downscaling. JMLR, 2023. paper

   Qidong Yang, Alex Hernandez-Garcia, Paula Harder, Venkatesh Ramesh, Prasanna Sattegeri, Daniela Szwarcman, Campbell D. Watson, and David Rolnick.

3. Modelling atmospheric dynamics with spherical Fourier neural operators. ICLR, 2023. paper

   Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, and Anima Anandkumar.

4. Spatiotemporal modeling of European paleoclimate using doubly sparse Gaussian processes. NIPS, 2022. paper

   Seth D. Axen, Alexandra Gessner, Christian Sommer, Nils Weitzel, and Álvaro Tejero-Cantero.

5. ClimSim: An open large-scale dataset for training high-resolution physics emulators in hybrid multi-scale climate simulators. arXiv, 2023. paper

   Sungduk Yu, Walter M. Hannah, Liran Peng, Mohamed Aziz Bhouri, Ritwik Gupta, Jerry Lin, Björn Lütjens, Justus C. Will, Tom Beucler, Bryce E. Harrop, Benjamin R. Hillman, Andrea M. Jenney, Savannah L. Ferretti, Nana Liu, Anima Anandkumar, Noah D. Brenowitz, Veronika Eyring, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Carl Vondrick, Rose Yu, Laure Zanna, Ryan P. Abernathey, Fiaz Ahmed, David C. Bader, Pierre Baldi, Elizabeth A. Barnes, Gunnar Behrens, Christopher S. Bretherton, Julius J. M. Busecke, Peter M. Caldwell, Wayne Chuang, Yilun Han, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas J. Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David A. Randall, Sara Shamekh, Akshay Subramaniam, Mark A. Taylor, Nathan M. Urban, Janni Yuval, Guang J. Zhang, Tian Zheng, and Michael S. Pritchard.

6. Seismic traveltime simulation for variable velocity models using physics-informed Fourier neural operator. arXiv, 2023. paper

   Chao Song, Tianshuo Zhao, Umair bin Waheed, and Cai Liu.

7. DeepPhysiNet: Bridging deep learning and atmospheric physics for accurate and continuous weather modeling. arXiv, 2024. paper

   Wenyuan Li, Zili Liu, Keyan Chen, Hao Chen, Shunlin Liang, Zhengxia Zou, and Zhenwei Shi.

8. Residual-enhanced physics-guided machine learning with hard constraints for subsurface flow in reservoir engineering. TGRS, 2024. paper

   Haibo Cheng, Yunpeng He, Peng Zeng, and Valeriy Vyatkin.

1. Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Tapas Tripura and Souvik Chakraborty.

2. Graph neural networks for airfoil design. arXiv, 2023. paper

   Florent Bonnet.

3. Exact Dirichlet boundary physics-informed neural network EPINN for solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Jiaji Wang, Y.L. Mo, Bassam Izzuddin, and Chul-Woo Kim.

4. Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Yu Diao, Jianchuan Yang, Ying Zhang, Dawei Zhang, and Yiming Du.

5. A novel key performance analysis method for permanent magnet coupler using physics-informed neural networks. Engineering with Computers, 2023. paper

   Huayan Pu, Bo Tan, Jin Yi, Shujin Yuan, Jinglei Zhao, Ruqing Bai, and Jun Luo.

6. Mechanical characterization and inverse design of stochastic architected metamaterials using neural operators. arXiv, 2023. paper

   Hanxun Jin, Enrui Zhang, Boyu Zhang, Sridhar Krishnaswamy, George Em Karniadakis, and Horacio D. Espinosa.

7. A deep learning energy-based method for classical elastoplasticity. International Journal of Plasticity, 2023. paper

   Junyan He, Diab Abueidda, Rashid Abu Al-Ru, Seid Koric, and Iwona Jasiuk.

8. Physics-informed neural networks for magnetostatic problems on axisymmetric transformer geometries. IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 2023. paper

   Philipp Brendel, Vlad Medvedev, and Andreas Rosskopf.

9. Neural born series operator for biomedical ultrasound computed tomography. arXiv, 2023. paper

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10. Learning thermoacoustic interactions in combustors using a physics-informed neural network. arXiv, 2024. paper

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11. Flight dynamic uncertainty quantification modeling using physics-informed neural networks. AIAA, 2024. paper

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12. Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses. arXiv, 2024. paper

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13. Stochastic dynamics of aircraft ground taxiing via improved physics-informed neural networks. Nonlinear Dynamics, 2024. paper

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14. Damage identification for plate structures using physics-informed neural networks. MSSP, 2024. paper

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15. Quantification of gradient energy coefficients using physics-informed neural networks. International Journal of Mechanical Sciences, 2024. paper

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16. MPIPN: A multi physics-informed PointNet for solving parametric acoustic-structure systems. arXiv, 2024. paper

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1. Hybrid learning of time-series inverse dynamics models for locally isotropic robot motion. RAL, 2022. paper

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2. NTFields: Neural time fields for physics-informed robot motion planning. ICLR, 2023. paper

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3. Online parameter estimation using physics-informed deep learning for vehicle stability algorithms. arXiv, 2023. paper

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4. A locality-based neural solver for optical motion capture. SIGGRAPH, 2023. paper

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5. Approximating high-dimensional minimal surfaces with physics-informed neural networks. arXiv, 2023. paper

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6. A spatial-temporally adaptive PINN framework for 3D bi-ventricular electrophysiological simulations and parameter inference. MICCAI, 2023. paper

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7. Using the Transformer model for physical simulation: An application on transient thermal analysis for 3D printing process simulation. NIPS, 2023. paper

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8. Physics-informed neural network for solution of forward and inverse kinematic wave problems. Journal of Hydrology, 2024. paper

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9. PhyGrasp: Generalizing robotic grasping with physics-informed large multimodal models. arXiv, 2024. paper

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10. Structure-preserving operator learning: Modeling the collision operator of kinetic equations. arXiv, 2024. paper

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1. Dynamic weights enabled physics-informed neural network for simulating the mobility of engineered nano-particles in a contaminated aquifer. NIPS, 2022. paper

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2. Learning two-phase microstructure evolution using neural operators and autoencoder architectures. NPJ Computational Materials, 2022. paper

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3. Predicting glass structure by physics-informed machine learning. NPJ Computational Materials, 2022. paper

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4. Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium. NPJ Computational Materials, 2022. paper

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5. Design of Turing systems with physics-informed neural networks. arXiv, 2022. paper

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6. Spatio-temporal super-resolution of dynamical systems using physics-informed deep-learning. AAAI, 2023. paper

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7. Rapid seismic waveform modeling and inversion with neural operators. TGRS, 2023. paper

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8. Accelerating heat exchanger design by combining Physics-Informed deep learning and transfer learning. Chemical Engineering Science, 2023. paper

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9. Energy stable neural network for gradient flow equations. arXiv, 2023. paper

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10. Physics-informed neural network with transfer learning (TL-PINN) based on domain similarity measure for prediction of nuclear reactor transients. Scientific Reports, 2023. paper

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11. Plasma surrogate modelling using Fourier neural operators. arXiv, 2023. paper

    Vignesh Gopakumar, Stanislas Pamela, Lorenzo Zanisi, Zongyi Li, Ander Gray, Daniel Brennand, Nitesh Bhatia, Gregory Stathopoulos, Matt Kusner, Marc Peter Deisenroth, Anima Anandkumar, JOREK Team, and MAST Team.

12. Training a deep operator network as a surrogate solver for two-dimensional parabolic-equation models. Journal of the Acoustical Society of America, 2023. paper

    Liang Xu, Haigang Zhang, and Minghui Zhang.

13. Grad-Shafranov equilibria via data-free physics informed neural networks. arXiv, 2023. paper

    Byoungchan Jang, Alan A. Kaptanoglu, Rahul Gaur, Shaw Pan, Matt Landreman, and William Dorland.

14. Physics-informed deep learning of rate-and-state fault friction. arXiv, 2023. paper

    Cody Rucker and Brittany A. Erickson.

15. Physics-informed neural networks with embedded analytical models: Inverse design of multilayer dielectric-loaded rectangular waveguide devices. IEEE Transactions on Microwave Theory and Techniques, 2023. paper

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16. En-DeepONet: An enrichment approach for enhancing the expressivity of neural operators with applications to seismology. Computer Methods in Applied Mechanics and Engineering, 2023. paper

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17. Solving seismic wave equations on variable velocity models with Fourier neural operator. TGRS, 2023. paper

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18. Calculating quasi-normal modes of Schwarzschild black holes with physics informed neural networks. arXiv, 2024. paper

    Nirmal Patel, Aycin Aykutalp, and Pablo Laguna.

19. Deep neural operator-driven real-time inference to enable digital twin solutions for nuclear energy systems. Scientific Reports, 2024. paper

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20. A physics-informed deep learning description of Knudsen layer reactivity reduction. arXiv, 2024. paper

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21. Inverse design method for horn antennas based on knowledge-embedded physics-informed neural networks. IEEE Antennas and Wireless Propagation Letters, 2024. paper

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22. Combined analysis of thermofluids and electromagnetism using physics-informed neural networks. EAAI, 2024. paper

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1. Learning to diffuse: A new perspective to design PDEs for visual analysis. TPAMI, 2016. paper

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2. Reformulating optical flow to solve image-based inverse problems and quantify uncertainty. TPAMI, 2022. paper

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3. WarpPINN: Cine-MR image registration with physics-informed neural networks. arXiv, 2022. paper

   Pablo Arratia Lopez, Hernan Mella, Sergio Uribe, Daniel E. Hurtado, and Francisco Sahli Costabal.

4. NODE-ImgNet: A PDE-informed effective and robust model for image denoising. arXiv, 2023. paper

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5. Microscopy image reconstruction with physics-informed denoising diffusion probabilistic model. arXiv, 2023. paper

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6. TGM-Nets: A deep learning framework for enhanced forecasting of tumor growth by integrating imaging and modeling. EAAI, 2023. paper

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7. The use of physics-informed neural network approach to image restoration via nonlinear PDE tools. Computers & Mathematics with Applications, 2023. paper

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8. Personalized predictions of glioblastoma infiltration: Mathematical models, physics-informed neural networks and multimodal scans. arXiv, 2023. paper

   Ray Zirui Zhang, Ivan Ezhov, Michal Balcerak, Andy Zhu, Benedikt Wiestler, Bjoern Menze, and John Lowengrub.

9. Real-time FJ/MAC PDE solvers via tensorized, back-propagation-free optical PINN training. arXiv, 2024. paper

   Yequan Zhao, Xian Xian, Xinling Yu, Ziyue Liu, Zhixiong Chen, Geza Kurczveil, Raymond G. Beausoleil, and Zheng Zhang.

10. Performance of Fourier-based activation function in physics-informed neural networks for patient-specific cardiovascular flows. Computer Methods and Programs in Biomedicine, 2024. paper

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1. Combustion chemistry acceleration with DeepONets. Fuel, 2024. paper

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1. Microstructure-sensitive deformation modeling and materials design with physics-informed neural networks. AIAA Journal, 2024. paper

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1. Symmetry-informed geometric representation for molecules, proteins, and crystalline materials. arXiv, 2023. paper

   Shengchao Liu, Weitao Du, Yanjing Li, Zhuoxinran Li, Zhiling Zheng, Chenru Duan, Zhiming Ma, Omar Yaghi, Anima Anandkumar, Christian Borgs, Jennifer Chayes, Hongyu Guo, and Jian Tang.

2. Solving nonconvex energy minimization problems in martensitic phase transitions with a mesh-free deep learning approach. Computer Methods in Applied Mechanics and Engineering, 2023. paper

   Xiaoli Chen, Phoebus Rosakis, Zhizhang Wu, and Zhiwen Zhang.

3. A physics-guided bi-fidelity Fourier-featured operator learning framework for predicting time evolution of drag and lift coefficients. arXiv, 2023. paper

   Amirhossein Mollaali, Izzet Sahin, Iqrar Raza, Christian Moya, Guillermo Paniagua, and Guang Lin.

4. Mixed form based physics-informed neural networks for performance evaluation of two-phase random materials. EAAI, 2023. paper

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5. Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow. Mathematics and Computers in Simulation, 2023. paper

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6. Physics-informed neural networks for solving dynamic two-phase interface problems. SIAM Journal on Scientific Computing, 2023. paper

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7. Rethinking materials simulations: Blending direct numerical simulations with neural operators. arXiv, 2023. paper

   Vivek Oommen, Khemraj Shukla, Saaketh Desai, Remi Dingreville, and George Em Karniadakis.

8. A conservative hybrid physics-informed neural network method for Maxwell-Ampère-Nernst-Planck equations. arXiv, 2023. paper

   Cheng Chang, Zhouping Xin, and Tieyong Zeng.

9. A data-driven physics-constrained deep learning computational framework for solving von Mises plasticity. EAAI, 2023. paper

   Arunabha M. Roy and Suman Guha.

10. Learning stiff chemical kinetics using extended deep neural operators. Computer Methods in Applied Mechanics and Engineering, 2024. paper

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11. Deep-learning based parameter identification enables rationalization of battery material evolution in complex electrochemical systems. Journal of Computational Science, 2023. paper

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12. AI-aided geometric design of anti-infection catheters. Science Advances, 2023. paper

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13. Physics-informed deep learning to solve three-dimensional Terzaghi’s consolidation equation: Forward and inverse problems. arXiv, 2024. paper

    Biao Yuan, Ana Heitor, He Wang, and Xiaohui Chen.

14. Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries. arXiv, 2024. paper

    Boyang Chen, Claire E. Heaney, Jefferson L. M. A. Gomes, Omar K. Matar, and Christopher C. Pain.

15. Combustion chemistry acceleration with DeepONets. Fuel, 2024. paper

    Anuj Kumar and Tarek Echekki.

16. Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks. arXiv, 2024. paper

    Wensi Wu, Mitchell Daneker, Kevin T. Turner, Matthew A. Jolley, and Lu Lu.

17. Adaptive data-driven deep-learning surrogate model for frontal polymerization in dicyclopentadiene. The Journal of Physical Chemistry B, 2024. paper

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1. Occupancy networks: Learning 3D reconstruction in function space. CVPR, 2019. paper

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2. Transfer learning for flow reconstruction based on multifidelity data. AIAA Journal, 2022. paper

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3. Learning-based state reconstruction for a scalar hyperbolic PDE under noisy lagrangian sensing. L4DC, 2022. paper

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1. Physics-informed neural networks for quantum eigenvalue problems. IJCNN, 2022. paper

   Henry Jin, Marios Mattheakis, and Pavlos Protopapas.

2. Quantum-inspired tensor neural networks for partial differential equations. arXiv, 2022. paper

   Raj Patel, Chia-Wei Hsing, Serkan Sahin, Saeed S. Jahromi, Samuel Palmer, Shivam Sharma, Christophe Michel, Vincent Porte, Mustafa Abid, Stephane Aubert, Pierre Castellani, Chi-Guhn Lee, Samuel Mugel, and Roman Orus.

3. Quantum Fourier networks for solving parametric PDEs. arXiv, 2023. paper

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4. Q-Flow: Generative modeling for differential equations of open quantum dynamics with normalizing flows. ICML, 2023. paper

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5. Physics-informed quantum machine learning: Solving nonlinear differential equations in latent spaces without costly grid evaluations. arXiv, 2023. paper

   Annie E. Paine, Vincent E. Elfving, and Oleksandr Kyriienko.

6. Physics-informed quantum machine learning for solving partial differential equations. arXiv, 2023. paper

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1. Approximating discontinuous Nash equilibria values of two-player general-sum differential games. arXiv, 2022. paper

   Lei Zhang, Mukesh Ghimire, Wenlong Zhang, Zhe Xu, and Yi Ren.

2. Solving two-player general-sum games between swarms. arXiv, 2023. paper

   Mukesh Ghimire, Lei Zhang, Wenlong Zhang, Yi Ren, and Zhe Xu.

3. Value approximation for two-player general-sum differential games with state constraints. arXiv, 2023. paper

   Lei Zhang, Mukesh Ghimire, Wenlong Zhang, Zhe Xu, and Yi Ren.

4. Pontryagin neural operator for solving parametric general-sum differential games. arXiv, 2024. paper

   Lei Zhang, Mukesh Ghimire, Zhe Xu, Wenlong Zhang, and Yi Ren.

5. Unsupervised solution operator learning for mean-field games via sampling-invariant parametrizations. arXiv, 2024. paper

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1. Physics-aware machine learning surrogates for real-time manufacturing digital twin. Manufacturing Letters, 2022. paper

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2. Multi-scale digital twin: Developing a fast and physics-informed surrogate model for groundwater contamination with uncertain climate models. arXiv, 2022. paper

   Lijing Wang, Takuya Kurihana, Aurelien Meray, Ilijana Mastilovic, Satyarth Praveen, Zexuan Xu, Milad Memarzadeh, Alexander Lavin, and Haruko Wainwright.

3. SciAI4Industry--Solving PDEs for industry-scale problems with deep learning. arXiv, 2022. paper

   Philipp A. Witte, Russell J. Hewett, Kumar Saurabh, AmirHossein Sojoodi, and Ranveer Chandra.

4. Operator learning framework for digital twin and complex engineering systems. arXiv, 2023. paper

   Kazuma Kobayashi, James Daniell, and Syed B. Alam.

5. Towards solving industry-grade surrogate modeling problems using physics informed machine learning. arXiv, 2023. paper

   Saakaar Bhatnagar, Andrew Comerford, and Araz Banaeizadeh.

6. Data-driven physics-informed neural networks: A digital twin perspective. arXiv, 2024. paper

   Sunwoong Yang, Hojin Kim, Yoonpyo Hong, Kwanjung Yee, Romit Maulik, and Namwoo Kang.

7. Physically informed synchronic-adaptive learning for industrial systems modeling in heterogeneous media with unavailable time-varying interface. arXiv, 2024. paper

   Aina Wang, Pan Qin, and Ximing Sun.

8. Improved generalization with deep neural operators for engineering systems: Path towards digital twin. EAAI, 2024. paper

   Kazuma Kobayashi, James Daniell, and Syed Bahauddin Alam.

9. A deep transfer operator learning method for temperature field reconstruction in a lithium-ion battery pack. TII, 2024. paper

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1. A deep learning based numerical PDE method for option pricing. Computational Economics, 2023. paper

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