Authors

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

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.

Keywords

Pseudo-Hamiltonian neural networks; Physics-informed machine learning; Hybrid machine learning

Citation

  • Journal: Physica D: Nonlinear Phenomena
  • Year: 2023
  • Volume: 446
  • Issue:
  • Pages: 133673
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.physd.2023.133673

BibTeX

@article{Eidnes_2023,
  title={{Pseudo-Hamiltonian neural networks with state-dependent external forces}},
  volume={446},
  ISSN={0167-2789},
  DOI={10.1016/j.physd.2023.133673},
  journal={Physica D: Nonlinear Phenomena},
  publisher={Elsevier BV},
  author={Eidnes, Sølve and Stasik, Alexander J. and Sterud, Camilla and Bøhn, Eivind and Riemer-Sørensen, Signe},
  year={2023},
  pages={133673}
}

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References