Incorporating Symmetry into Deep Dynamics Models for Improved Generalization

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 the distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into deep 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 the symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh-Benard Convection and real-world ocean currents and temperatures. This is the first time that equivariant neural networks have been used to forecast physical dynamics.