Mastering high-dimensional dynamics with Hamiltonian neural networks

TL;DR

This paper demonstrates that integrating physics into neural network architectures, specifically Hamiltonian neural networks, enhances the learning and prediction of complex high-dimensional dynamical systems, outperforming traditional neural networks.

Contribution

It introduces Hamiltonian neural networks for high-dimensional dynamics, showing their advantages over conventional neural networks through a map building perspective.

Findings

Hamiltonian neural networks outperform traditional neural networks in high-dimensional systems.

The approach clarifies the relationship between data, system dimension, and learning performance.

Physics-informed neural networks improve forecasting accuracy for nonlinear dynamical systems.

Abstract

We detail how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. A map building perspective elucidates the superiority of Hamiltonian neural networks over conventional neural networks. The results clarify the critical relation between data, dimension, and neural network learning performance.