Forecasting Hamiltonian dynamics without canonical coordinates

TL;DR

This paper introduces a method to train Hamiltonian neural networks using generalised coordinates, broadening their applicability to systems where canonical coordinates are difficult to obtain, thus improving efficiency in forecasting Hamiltonian dynamics.

Contribution

It presents a simple approach to train Hamiltonian neural networks with any set of generalized coordinates, extending their use beyond canonical coordinates.

Findings

Enables training of Hamiltonian neural networks with observable coordinates

Improves efficiency in modeling Hamiltonian systems without canonical coordinates

Broadens applicability to real-world dynamical systems

Abstract

Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here we significantly expand the scope of such networks by demonstrating a simple way to train them with any set of generalised coordinates, including easily observable ones.