What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field

TL;DR

This paper explores methods for predicting Hamiltonian system dynamics from discrete vector field observations, comparing informed and uninformed approaches to assess their efficiency and effectiveness across various systems.

Contribution

It introduces and empirically evaluates multiple methods for Hamiltonian dynamics prediction, highlighting the benefits of incorporating Hamiltonian information.

Findings

Hamiltonian-informed methods are more effective

Different methods offer trade-offs between efficiency and accuracy

System-specific performance varies significantly

Abstract

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.