Tensor parametric Hamiltonian operator inference
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913833351643136 |
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| author | Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony |
| author_facet | Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony |
| contents | This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints, a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave speed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor parametric Hamiltonian operator inference Vijaywargiya, Arjun McQuarrie, Shane A. Gruber, Anthony Numerical Analysis 15A69, 35B30, 65P10 This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with affine dependence as contractions of a generalized parameter vector against a constant tensor, this method leverages the operator inference framework to capture parametric dependence in the learned reduced-order model via the solution to a convex, least-squares optimization problem. This leads to a concise and straightforward implementation which compactifies previous parametric operator inference approaches and directly extends to learning parametric operators with symmetry constraints, a key feature required for constructing structure-preserving surrogates of Hamiltonian systems. The proposed approach is demonstrated on both a (non-Hamiltonian) heat equation with variable diffusion coefficient as well as a Hamiltonian wave equation with variable wave speed. |
| title | Tensor parametric Hamiltonian operator inference |
| topic | Numerical Analysis 15A69, 35B30, 65P10 |
| url | https://arxiv.org/abs/2502.10888 |