Data-driven identification of low-dimensional port-Hamiltonian Systems
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Conventional modeling techniques involve high effort, 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 which is suitable for multi-physics systems incorporating the useful system theoretical properties of passivity and stability [1]. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional and possibly nonlinear state data serves as the input for the autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional manifold following the approach of [2]. In the resulting latent space, a pH system that fulfils the corresponding constraints is identified by using the weights of a neural network as entries of triangular matrices that strongly satisfy the pH matrix properties through Cholesky factorizations. In a joint optimization process over the loss term, the pH matrices are adjusted to match the dynamics in the data, and the low-dimensional data automatically become pH variables. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size [3]. The method is exemplified by an academic nonlinear example and the high-dimensional model of a disc brake with linear thermoelastic behavior. REFERENCES [1] Mehrmann, V.; Unger, B.: Control of port-Hamiltonian differential-algebraic systems and applications, Acta Numerica, 32, 395-515. doi:10.1017/S0962492922000083, 2023. [2] Champion, K.; Lusch, B.; Kutz, J. N.; Brunton, S. L.: Data-driven discovery of coordinates and governing equations, Proceedings of the National Academy of Sciences, 116(45), 22445–22451. doi:10.1073/pnas.1906995116, 2019. [3] Rettberg, J.; Kneifl, J.; Herb, J.; Buchfink, P.; Fehr, J.; Haasdonk, B.: Data-driven identification of low-dimensional port-Hamiltonian Systems, in preparation, 2023.