Adaptable Hamiltonian neural networks

TL;DR

This paper introduces a parameter-cognizant Hamiltonian Neural Network capable of predicting the behavior of nonlinear Hamiltonian systems across different parameter values, even with limited training data, and successfully capturing transitions to chaos.

Contribution

The novel adaptable HNN architecture incorporates an input parameter channel, enabling cross-parameter predictions from limited training data, advancing physics-informed neural network capabilities.

Findings

HNN can predict system states across a parameter interval with training on only four parameter values.

The model accurately predicts routes to chaos using Lyapunov exponents and alignment indices.

Parameter-cognizant HNN outperforms previous models in generalizing to unseen parameter regimes.

Abstract

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which represent a major class of physics-enhanced neural networks. We introduce a class of HNNs capable of adaptable prediction of nonlinear physical systems: by training the neural network based on time series from a small number of bifurcation-parameter values of the target Hamiltonian system, the HNN can predict the dynamical states at other parameter values, where the network has not been exposed to any information about the system at these parameter values. The architecture of the HNN differs from the previous ones in that we incorporate an input parameter channel, rendering the HNN parameter--cognizant. We demonstrate, using paradigmatic Hamiltonian systems, that training the HNN using time series from as few as four parameter values bestows the neural machine with the ability to predict the state of the target system in an entire parameter interval. Utilizing the ensemble maximum Lyapunov exponent and the alignment index as indicators, we show that our parameter-cognizant HNN can successfully predict the route of transition to chaos. Physics-enhanced machine learning is a forefront area of research, and our adaptable HNNs provide an approach to understanding machine learning with broad applications.