Globalizing manifold-based reduced models for equations and data
Abstract One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local polynomial approximations and, hence, are limited by...
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| Format: | Article |
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Nature Portfolio
2025-07-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-025-61252-9 |
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| author | Bálint Kaszás George Haller |
| author_facet | Bálint Kaszás George Haller |
| author_sort | Bálint Kaszás |
| collection | DOAJ |
| description | Abstract One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local polynomial approximations and, hence, are limited by the unknown domains of convergence of their Taylor expansions. To address this limitation, we extend local expansions for invariant manifolds via Padé approximants, which re-express the Taylor expansions as rational functions for broader utility. This approach significantly expands the range of applicability of manifold-reduced models, enabling reduced modeling of global phenomena, such as large-scale oscillations and chaotic attractors of finite element models. We illustrate the power of globalized manifold-based model reduction on several equation-driven and data-driven examples from solid mechanics and fluid mechanics. |
| format | Article |
| id | doaj-art-82caea4fcda549bd98382b155e750381 |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-82caea4fcda549bd98382b155e7503812025-08-20T03:37:37ZengNature PortfolioNature Communications2041-17232025-07-0116111210.1038/s41467-025-61252-9Globalizing manifold-based reduced models for equations and dataBálint Kaszás0George Haller1Institute for Mechanical Systems, ETH ZürichInstitute for Mechanical Systems, ETH ZürichAbstract One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local polynomial approximations and, hence, are limited by the unknown domains of convergence of their Taylor expansions. To address this limitation, we extend local expansions for invariant manifolds via Padé approximants, which re-express the Taylor expansions as rational functions for broader utility. This approach significantly expands the range of applicability of manifold-reduced models, enabling reduced modeling of global phenomena, such as large-scale oscillations and chaotic attractors of finite element models. We illustrate the power of globalized manifold-based model reduction on several equation-driven and data-driven examples from solid mechanics and fluid mechanics.https://doi.org/10.1038/s41467-025-61252-9 |
| spellingShingle | Bálint Kaszás George Haller Globalizing manifold-based reduced models for equations and data Nature Communications |
| title | Globalizing manifold-based reduced models for equations and data |
| title_full | Globalizing manifold-based reduced models for equations and data |
| title_fullStr | Globalizing manifold-based reduced models for equations and data |
| title_full_unstemmed | Globalizing manifold-based reduced models for equations and data |
| title_short | Globalizing manifold-based reduced models for equations and data |
| title_sort | globalizing manifold based reduced models for equations and data |
| url | https://doi.org/10.1038/s41467-025-61252-9 |
| work_keys_str_mv | AT balintkaszas globalizingmanifoldbasedreducedmodelsforequationsanddata AT georgehaller globalizingmanifoldbasedreducedmodelsforequationsanddata |