Imposing conservation properties in deep dynamics modeling via contrastive learning

Wang Zhang, Subhro Das, Tsui-Wei Weng, Alexandre Megretski, Luca Daniel, Lam M. Nguyen

Keywords: dynamical system modeling, contrastive learning, learning conservation property

Abstract: Deep neural networks (DNN) has shown great capacity of modeling a dynamical system, but these DNN-based dynamical models usually do not obey conservation laws. To impose the learned DNN dynamical models with key physical properties such as conservation laws, this paper proposes a two-step approach to endow the invariant priors into the simulations. We first establish a contrastive learning framework to capture the system invariants along the trajectory observations. During the dynamics modeling, we design a projection layer of DNNs to preserve the system invariance. Through experiments, we show our method consistently outperforms the baseline in both coordinate error and conservation metrics and can be further extended to complex and large dynamics by leveraging autoencoder. Notably, a byproduct of our framework is the automated conservation law discovery for dynamical systems with single conservation property.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Machine Learning for Sciences (eg biology, physics, health sciences, social sciences, climate/sustainability )

TL;DR: We learn dynamical system conservation property through contrastive learning and impose it during simulation to improve prediction robustness.