Approximately Equivariant Networks for Imperfectly Symmetric Dynamics

Rui Wang, Robin Walters, Rose Yu
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:23078-23091, 2022.

Abstract

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-wang22aa, title = {Approximately Equivariant Networks for Imperfectly Symmetric Dynamics}, author = {Wang, Rui and Walters, Robin and Yu, Rose}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {23078--23091}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/wang22aa/wang22aa.pdf}, url = {https://proceedings.mlr.press/v162/wang22aa.html}, abstract = {Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.} }
Endnote
%0 Conference Paper %T Approximately Equivariant Networks for Imperfectly Symmetric Dynamics %A Rui Wang %A Robin Walters %A Rose Yu %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-wang22aa %I PMLR %P 23078--23091 %U https://proceedings.mlr.press/v162/wang22aa.html %V 162 %X Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.
APA
Wang, R., Walters, R. & Yu, R.. (2022). Approximately Equivariant Networks for Imperfectly Symmetric Dynamics. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:23078-23091 Available from https://proceedings.mlr.press/v162/wang22aa.html.

Related Material