Extracting Nonlinear Symmetries From Trained Neural Networks on Dynamics Data

Abstract

To support scientists developing reduced models of complex physics systems, we propose a method for extracting interpretable physical information from deep neural networks (DNNs) trained on time-series data of the physics system. Specifically, we propose a framework for estimating the hidden nonlinear symmetries of the system from DNNs trained on time-series data that can be regarded as a classical Hamiltonian dynamical system with finite degrees of freedom. The proposed framework is able to estimate the nonlinear symmetry corresponding to the Laplace--Lunge--Lenz vector, which is a conserved value that keeps the long axis direction of the elliptical motion of the planet constant, and visualize its Lie manifold.