Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces

TL;DR

This paper introduces pseudo-Hamiltonian neural networks that effectively learn state-dependent external forces in mechanical systems, extending Hamiltonian models to handle non-conservative forces with improved numerical integration techniques.

Contribution

It presents a novel pseudo-Hamiltonian formulation that generalizes Hamiltonian models to include external forces, enabling better modeling of complex, non-conservative systems.

Findings

Successfully modeled external forces in mechanical systems

Demonstrated improved training with a symmetric fourth-order integrator

Validated on mass-spring and tank systems with noisy data

Abstract

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a generalization of the Hamiltonian formulation via the port-Hamiltonian formulation, and show that pseudo-Hamiltonian neural network models can be used to learn external forces acting on a system. We argue that this property is particularly useful when the external forces are state dependent, in which case it is the pseudo-Hamiltonian structure that facilitates the separation of internal and external forces. Numerical results are provided for a forced and damped mass-spring system and a tank system of higher complexity, and a symmetric fourth-order integration scheme is introduced for improved training on sparse and noisy data.