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HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions

Experiment code for "HomPINNs".

@article{hompinns,
  title={HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions},
  author={Zheng, Haoyang and Huang, Yao and Huang, Ziyang and Hao, Wenrui and Lin, Guang},
  journal={Journal of Computational Physics},
  pages={112751},
  year={2024},
  publisher={Elsevier}
}

Prerequisites

Please refer to "requirement.txt"

The first example

$$\left\{\begin{aligned} &\frac{\partial ^2 u(x)}{\partial x^2}=-\lambda\left(1+ u^4\right),\ \ x\in (0,1)\\\ &{\left.\frac{\partial u(x)}{\partial x}\right |_{x=0}=\left.u(x)\right |_{x=1}=0}. \end{aligned}\right.$$

with $\lambda=1.20$

Please run:

python3 main_HomPINN.py

Results:

pred1

The second example

$$\left\{ \begin{aligned} &\frac{\partial ^2 u(x)}{\partial x^2} =u^4-\lambda u^2,\ \ x\in (0\ ,1),\\\ &\left.\frac{\partial u(x)}{\partial x}\right |_{x=0}=\left.u(x)\right |_{x=1}=0. \end{aligned}\right.$$

with $\lambda=18.00$

Please run:

python3 main_HomPINN.py --data_dir ./data/obs_ex2.mat --n_epoch 20000 --max_epoch 40000 --num_sol 3 --num_obs 100 --lr_low 1e-4 --lr_gap 0.98

Results:

pred2

Contact

Haoyang Zheng, School of Mechanical Engineering, Purdue University

Email: zheng+528 at purdue dot edu

More Aboue Me: link

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