Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces

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-Ha...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Eidnes, Sølve, Stasik, Alexander J, Sterud, Camilla, Bøhn, Eivind, Riemer-Sørensen, Signe
Format: Article
Language:English
Subjects:
Deviation
Machine learning
Mass-spring systems
Mechanical systems
Neural networks
Training
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2206.02660