Data-driven identification of latent port-Hamiltonian systems
<|reference_start|>Data-driven identification of latent port-Hamiltonian systems: 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.<|reference_end|>
@article{rettberg2024data-driven,
    title={Data-driven identification of latent port-Hamiltonian systems},
    author={Johannes Rettberg, Jonas Kneifl, Julius Herb, Patrick Buchfink, J"org
  Fehr, Bernard Haasdonk},
    journal={arXiv preprint arXiv:2408.08185},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.08185},
    primaryClass={math.DS cs.LG}
}