Learning reversible symplectic dynamics

TL;DR

This paper introduces a neural network architecture designed to learn time-reversible dynamical systems, especially symplectic systems, emphasizing the importance of incorporating time-reversal symmetry in machine learning models for physics-informed applications.

Contribution

The paper proposes a novel neural network architecture that enforces time-reversibility, specifically tailored for symplectic systems, advancing the integration of symmetry in data-driven dynamical modeling.

Findings

Successfully models time-reversible dynamics

Preserves symplectic structure in learned systems

Enhances physics-informed learning approaches

Abstract

Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility. In this paper we propose a new neural network architecture for learning time-reversible dynamical systems from data. We focus in particular on an adaptation to symplectic systems, because of their importance in physics-informed learning.