Learning Hamiltonian Systems considering System Symmetries in Neural Networks

Machine learning techniques, especially neural networks, rapidly gain importance in a variety of applications, headed by image analysis and text or speech recognition. Comparably fewer works address the learning of nonlinear dynamical systems - probably because of the challenging task of learning physical laws. To bridge this gap, Hamiltonian Neural Networks have been introduced, which are especially tailored to learning dynamical systems which preserve the Hamiltonian structure. In this contribution, we build on this approach by introducing symmetry-preserving extensions of the Hamiltonian neural networks' architecture. We discuss discrete symmetry, i.e. periodicity, as well as continuous symmetries in terms of translational or rotational invariances. The proposed learning algorithm provides neural network representations of example systems with improved conservation properties. Copyright (C) 2021 The Authors.