Data-driven identification of latent port-Hamiltonian systems
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914913615609856 |
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| author | Rettberg, Johannes Kneifl, Jonas Herb, Julius Buchfink, Patrick Fehr, Jörg Haasdonk, Bernard |
| author_facet | Rettberg, Johannes Kneifl, Jonas Herb, Julius Buchfink, Patrick Fehr, Jörg Haasdonk, Bernard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven identification of latent port-Hamiltonian systems Rettberg, Johannes Kneifl, Jonas Herb, Julius Buchfink, Patrick Fehr, Jörg Haasdonk, Bernard Dynamical Systems Machine Learning 93B30, 37E99 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. |
| title | Data-driven identification of latent port-Hamiltonian systems |
| topic | Dynamical Systems Machine Learning 93B30, 37E99 |
| url | https://arxiv.org/abs/2408.08185 |