Improving Simulations with Symmetry Control Neural Networks

TL;DR

This paper introduces a method to incorporate symmetry constraints into neural networks for physical systems, improving accuracy by leveraging conserved quantities like momentum.

Contribution

It extends Hamiltonian Neural Networks by enforcing cyclic coordinates, enabling the learning and exploitation of symmetry constraints in physical dynamics.

Findings

Enhanced accuracy on classical dynamics tasks.

Networks recover conserved quantities such as angular momentum.

Method effectively utilizes symmetry constraints to improve physical modeling.

Abstract

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural Networks. By enforcing cyclic coordinates with appropriate loss functions, we find that we can achieve improved accuracy on simple classical dynamics tasks. By fitting analytic formulae to the latent variables in our network we recover that our networks are utilizing conserved quantities such as (angular) momentum.