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arXiv · 2206.02660

Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces

Sølve Eidnes·Alexander J. Stasik·Camilla Sterud·Eivind Bøhn·Signe Riemer-Sørensen
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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.

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Sølve Eidnes, Alexander J. Stasik, Camilla Sterud, Eivind Bøhn, Signe Riemer-Sørensen. 2022-06-06. Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces. https://doi.org/10.1016/j.physd.2023.133673

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