Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918521859997696 |
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| author | Codega, Gabriele Ivagnes, Anna Demo, Nicola Rozza, Gianluigi |
| author_facet | Codega, Gabriele Ivagnes, Anna Demo, Nicola Rozza, Gianluigi |
| contents | In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator on the POD coefficients. Differently from the state-of-the-art methodologies, where the operator is learned via least-squares optimisation, we propose to parametrise the operator by a Multi-Input Operators Network (MIONet). This way, we are able to build models with higher generalisation capabilities, where the operator itself is continuous in space -- thus agnostic of the domain discretisation -- and parameter-dependent. We test our model on two standard benchmarks in fluid dynamics and show that the correction term improves the accuracy of standard POD-based ROMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine Learning-based quadratic closures for non-intrusive Reduced Order Models Codega, Gabriele Ivagnes, Anna Demo, Nicola Rozza, Gianluigi Numerical Analysis 68T07, 35Q35, 65N99 In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator on the POD coefficients. Differently from the state-of-the-art methodologies, where the operator is learned via least-squares optimisation, we propose to parametrise the operator by a Multi-Input Operators Network (MIONet). This way, we are able to build models with higher generalisation capabilities, where the operator itself is continuous in space -- thus agnostic of the domain discretisation -- and parameter-dependent. We test our model on two standard benchmarks in fluid dynamics and show that the correction term improves the accuracy of standard POD-based ROMs. |
| title | Machine Learning-based quadratic closures for non-intrusive Reduced Order Models |
| topic | Numerical Analysis 68T07, 35Q35, 65N99 |
| url | https://arxiv.org/abs/2506.09830 |