Pieter-Jan Hoedt, Frederik Kratzert, Daniel Klotz, Christina Halmich, Markus Holzleitner, Grey Nearing, Sepp Hochreiter, Günter Klambauer

MC-LSTM is an adaptation of LSTM (Hochreiter & Schmidhuber, 1997) that allows to enforce conservation laws in regression problems. To test the benefits of this inductive bias in practice, we conducted experiments on a) arithmetic tasks (cf. Madsen et al., 2020), b) Traffic forecasting, c) energy prediction for pendulum (cf. Greydanus et al., 2019), and d) Rainfall-runoff modeling (Kratzert et al., 2019).

This repository contains code for the LSTM addition, traffic forecasting and pendulum experiments. The neural arithmetic experiments were conducted on a fork of the repository from Madsen et al. (2020). The experiments in hydrology were conducted using the neuralhydrology framework.

Openreview, Pre-print, ICML

The success of Convolutional Neural Networks (CNNs) in computer vision is mainly driven by their strong inductive bias, which is strong enough to allow CNNs to solve vision-related tasks with random weights, meaning without learning. Similarly, Long Short-Term Memory (LSTM) has a strong inductive bias towards storing information over time. However, many real-world systems are governed by conservation laws, which lead to the redistribution of particular quantities — e.g. in physical and economical systems. Our novel Mass-Conserving LSTM (MC-LSTM) adheres to these conservation laws by extending the inductive bias of LSTM to model the redistribution of those stored quantities. MC-LSTMs set a new state-of-the-art for neural arithmetic units at learning arithmetic operations, such as addition tasks, which have a strong conservation law, as the sum is constant overtime. Further, MC-LSTM is applied to traffic forecasting, modeling a pendulum, and a large benchmark dataset in hydrology, where it sets a new state-of-the-art for predicting peak flows. In the hydrology example, we show that MC-LSTM states correlate with real world processes and are therefore interpretable.

To cite this work, you can use the following bibtex entry:

@inproceedings{pmlr-v139-hoedt21a,
 title     = {MC-LSTM: Mass-Conserving LSTM},
 author    = {Hoedt, Pieter-Jan and Kratzert, Frederik and Klotz, Daniel and Halmich, Christina and Holzleitner, Markus and Nearing, Grey S and Hochreiter, Sepp and Klambauer, Guenter},
 booktitle = {Proceedings of the 38th International Conference on Machine Learning},
 pages     = {4275--4286},
 year      = {2021},
 editor    = {Meila, Marina and Zhang, Tong},
 volume    = {139},
 series    = {Proceedings of Machine Learning Research},
 month     = {18--24 Jul},
 publisher = {PMLR},
 pdf       = {http://proceedings.mlr.press/v139/hoedt21a/hoedt21a.pdf},
 url       = {http://proceedings.mlr.press/v139/hoedt21a.html},
}

The code in this repository (excluding the sub-repositories) should run as-is in an environment as specified by requirements.txt. When using conda, such an environment can be set up using

conda create -n mclstm --file requirements.txt -c pytorch

if you remove the autograd dependency! autograd must be installed with pip individually. Alternatively, you can use -c conda-forge, which does provide autograd.

• Greydanus, S., Dzamba, M., & Yosinski, J. (2019). Hamiltonian neural networks. Advances in Neural Information Processing Systems, 32, 15379-15389.
• Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8), 1735-1780. (pdf)
• Madsen, A., & Johansen, A. R. (2020). Neural Arithmetic Units. In International Conference on Learning Representations.
• Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., & Nearing, G. (2019). Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets. Hydrology and Earth System Sciences, 23(12), 5089-5110.