Extracting Nonlinear Symmetries from Trained Neural Networks on Dynamics Data

Abstract

To support scientists who are developing the reduced model of complex physics systems, we propose a method for extracting interpretable physics information from a deep neural network (DNN) trained on time series data of a physics system. Specifically, we propose a framework for estimating the hidden nonlinear symmetries of a system from a DNN trained on time series data that can be regarded as a finite-degree-of-freedom classical Hamiltonian dynamical system. Our proposed framework can estimate the nonlinear symmetries corresponding to the Laplace-Lunge-Renz vector, a conservation value that keeps the long-axis direction of the elliptical motion of a planet constant, and visualize its Lie manifold.