Incorporating Symmetry into Deep Dynamics Models for Improved Generalization

TL;DR

This paper enhances deep dynamics models by integrating symmetry principles into neural networks, leading to better accuracy and generalization in predicting complex physical systems like ocean currents.

Contribution

It introduces symmetry-enforcing methods into convolutional neural networks for physical dynamics, improving robustness and sample efficiency under distributional shifts.

Findings

Models are robust to symmetry transformations.

Improved prediction accuracy over baseline models.

Effective on real-world physical systems like ocean currents.

Abstract

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into convolutional neural networks. Specifically, we employ a variety of methods each tailored to enforce a different symmetry. Our models are both theoretically and experimentally robust to distributional shift by symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh B\'enard convection and real-world ocean currents and temperatures. Compared with image or text applications, our work is a significant step towards applying equivariant neural networks to high-dimensional systems with complex dynamics. We open-source our simulation, data, and code at \url{https://github.com/Rose-STL-Lab/Equivariant-Net}.