Learning Trajectories of Hamiltonian Systems with Neural Networks

TL;DR

This paper introduces an enhanced Hamiltonian neural network framework that estimates continuous trajectories of conservative systems, improving performance with low sampling rates and noisy data.

Contribution

It proposes integrating a deep hidden physics model with HNNs to better estimate continuous trajectories, especially under challenging data conditions.

Findings

Improved trajectory estimation with low sampling rates.

Enhanced robustness to noisy and irregular observations.

Effective integration scheme for Hamiltonian neural networks.

Abstract

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.