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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.16033 |
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| _version_ | 1866915628197085184 |
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| author | Wen, Xuelian Li, Qiuqi Zhang, Juan |
| author_facet | Wen, Xuelian Li, Qiuqi Zhang, Juan |
| contents | This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf methodology, we reformulate the matrix equations into a structured representation that explicitly shows the parameter dependence in polynomial form. This reformulation is crucial for efficient model reduction. This approach constructs reduced-order models via regression on solution snapshots, bypassing the need for expensive full-order operators and thus overcoming the primary bottlenecks of intrusive methods in high-dimensional contexts. Numerical experiments confirm their accuracy and computational efficiency, demonstrating that our work is a scalable and practical solution for parameter-dependent matrix equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven Model Reduction for Parameter-Dependent Matrix Equations via Operator Inference Wen, Xuelian Li, Qiuqi Zhang, Juan Numerical Analysis This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf methodology, we reformulate the matrix equations into a structured representation that explicitly shows the parameter dependence in polynomial form. This reformulation is crucial for efficient model reduction. This approach constructs reduced-order models via regression on solution snapshots, bypassing the need for expensive full-order operators and thus overcoming the primary bottlenecks of intrusive methods in high-dimensional contexts. Numerical experiments confirm their accuracy and computational efficiency, demonstrating that our work is a scalable and practical solution for parameter-dependent matrix equations. |
| title | Data-driven Model Reduction for Parameter-Dependent Matrix Equations via Operator Inference |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.16033 |