Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
This addresses the challenge of modeling imperfectly symmetric dynamics in physics and engineering applications, offering an incremental improvement over existing symmetry-based methods.
The paper tackles the problem that real-world dynamical data rarely conforms to strict mathematical symmetry due to noise or symmetry-breaking features, by exploring approximately equivariant networks that relax strict symmetry constraints. The result shows these models outperform both no-symmetry and strict-symmetry baselines in simulated turbulence and real-world multi-stream jet flow.
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.