Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
This work addresses the challenge of applying deep learning to real-world physical systems with complex dynamics, representing an incremental advancement in using equivariant neural networks for high-dimensional systems.
The paper tackles the problem of limited physical accuracy and poor generalization of deep learning models for predicting physical dynamics by incorporating symmetries into convolutional neural networks, resulting in models that are robust to distributional shift and demonstrate improved performance on tasks like Rayleigh Bénard convection and ocean currents.
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}.