Data-driven identification of latent port-Hamiltonian systems

Authors

Johannes Rettberg, Jonas Kneifl, Julius Herb, Patrick Buchfink, Jörg Fehr, Bernard Haasdonk

Abstract

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional latent space. In this space, a linear pH system that satisfies the pH properties per construction is parameterized by the weights of a neural network. The mathematical requirements are met by defining the pH matrices through Cholesky factorizations. The neural networks that define the coordinate transformation and the pH system are identified in a joint optimization process to match the dynamics observed in the data while defining a linear pH system in the latent space. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size. The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example, as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.

Keywords

autoencoder, port-hamiltonian systems, structure-preserving reduced-order modeling, system identification

Citation

• Journal: Computational Science and Engineering
• Year: 2025
• Volume: 2
• Issue: 1
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s44207-025-00007-2

BibTeX

@article{Rettberg_2025,
  title={{Data-driven identification of latent port-Hamiltonian systems}},
  volume={2},
  ISSN={2948-1597},
  DOI={10.1007/s44207-025-00007-2},
  number={1},
  journal={Computational Science and Engineering},
  publisher={Springer Science and Business Media LLC},
  author={Rettberg, Johannes and Kneifl, Jonas and Herb, Julius and Buchfink, Patrick and Fehr, Jörg and Haasdonk, Bernard},
  year={2025}
}

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