Learning Symmetries of Classical Integrable Systems

TL;DR

This paper introduces neural network architectures designed to learn symmetries in Hamiltonian systems, specifically symplectic transformations, to better understand integrable models in physics.

Contribution

It presents novel neural architectures that preserve Hamiltonian structure, enabling the learning of symmetries in integrable systems, a significant advancement over traditional methods.

Findings

Successfully learned symmetries of integrable models

Maintained Hamiltonian structure with novel neural architectures

Demonstrated applicability to classical physics problems

Abstract

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel network architectures that parametrize symplectic transformations. We demonstrate the utility of these architectures by learning the structure of integrable models. Our work exemplifies the adaptation of neural transformations to a family constrained by more than the condition of invertibility, which we expect to be a common feature of applications of these methods.