Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
Rui Wang, Robin Walters, Rose Yu
TL;DR
This work tackles the challenge of generalizing deep dynamics models to predicting high-dimensional physical systems by enforcing symmetries directly in neural networks. It introduces four symmetry-focused architectures (translation, rotation, uniform motion, and scale) built on equivariant convolutions to guarantee G-equivariance, aiming to improve both predictive accuracy and physical consistency. Through experiments on Rayleigh–Bénard convection and real ocean data, the authors demonstrate reduced energy-spectrum errors and better generalization under distribution shifts, often outperforming data-augmented baselines. The findings suggest symmetry-aware neural networks as a robust path toward reliable, physics-consistent forecasting in complex fluid dynamics, with potential for extension to 3D settings and broader symmetry groups.
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 Bénard 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}.