Team DAE member Julius Herb worked together with researchers from ITM (Johannes Rettberg, Jonas Kneifl, Jörg Fehr) and IANS (Patrick Buchfink, Bernard Haasdonk) on an article about the identification of port-Hamiltonian systems via physics-augmented machine learning methods. The work is now available as a preprint on Arxiv.
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.
Article information
Rettberg, J., Kneifl, J., Herb, J., Buchfink, P., Fehr, J. & Haasdonk, B. (2024). Data-driven identification of latent port-Hamiltonian systems. Available at Arxiv: https://arxiv.org/abs/2408.08185