Separable Hamiltonian Neural Networks

TL;DR

This paper introduces separable Hamiltonian neural networks that incorporate additive separability to improve the accuracy of Hamiltonian and vector field regression, leading to better energy conservation in dynamical system predictions.

Contribution

The paper proposes a novel class of separable HNNs that embed additive separability biases, enhancing regression accuracy and energy conservation over traditional HNNs.

Findings

Separable HNNs outperform standard HNNs in Hamiltonian regression.

Separable HNNs more accurately predict system dynamics.

Separable HNNs better conserve total energy in simulations.

Abstract

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.