Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911998107713536 |
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| author | Chavelli, Félix Khoo, Zi-Yu Wu, Dawen Low, Jonathan Sze Choong Bressan, Stéphane |
| author_facet | Chavelli, Félix Khoo, Zi-Yu Wu, Dawen Low, Jonathan Sze Choong Bressan, Stéphane |
| contents | The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables.
This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems Chavelli, Félix Khoo, Zi-Yu Wu, Dawen Low, Jonathan Sze Choong Bressan, Stéphane Artificial Intelligence The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables. This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables. |
| title | Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2408.11691 |