Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1218-1229, 2021.

Abstract

The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we present a comparative analysis of the energy-conserving neural networks - for example, deep Lagrangian network, Hamiltonian neural network, etc. - wherein the underlying physics is encoded in their computation graph. We focus on ten neural network models and explain the similarities and differences between the models. We compare their performance in 4 different physical systems. Our result highlights that using a high-dimensional coordinate system and then imposing restrictions via explicit constraints can lead to higher accuracy in the learned dynamics. We also point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-zhong21a, title = {Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data}, author = {Zhong, Yaofeng Desmond and Dey, Biswadip and Chakraborty, Amit}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1218--1229}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/zhong21a/zhong21a.pdf}, url = {https://proceedings.mlr.press/v144/zhong21a.html}, abstract = {The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we present a comparative analysis of the energy-conserving neural networks - for example, deep Lagrangian network, Hamiltonian neural network, etc. - wherein the underlying physics is encoded in their computation graph. We focus on ten neural network models and explain the similarities and differences between the models. We compare their performance in 4 different physical systems. Our result highlights that using a high-dimensional coordinate system and then imposing restrictions via explicit constraints can lead to higher accuracy in the learned dynamics. We also point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers. } }
Endnote
%0 Conference Paper %T Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data %A Yaofeng Desmond Zhong %A Biswadip Dey %A Amit Chakraborty %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-zhong21a %I PMLR %P 1218--1229 %U https://proceedings.mlr.press/v144/zhong21a.html %V 144 %X The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we present a comparative analysis of the energy-conserving neural networks - for example, deep Lagrangian network, Hamiltonian neural network, etc. - wherein the underlying physics is encoded in their computation graph. We focus on ten neural network models and explain the similarities and differences between the models. We compare their performance in 4 different physical systems. Our result highlights that using a high-dimensional coordinate system and then imposing restrictions via explicit constraints can lead to higher accuracy in the learned dynamics. We also point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.
APA
Zhong, Y.D., Dey, B. & Chakraborty, A.. (2021). Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1218-1229 Available from https://proceedings.mlr.press/v144/zhong21a.html.

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