Learning physics-based reduced-order models from data using nonlinear manifolds
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910258892374016 |
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| author | Geelen, Rudy Balzano, Laura Wright, Stephen Willcox, Karen |
| author_facet | Geelen, Rudy Balzano, Laura Wright, Stephen Willcox, Karen |
| contents | We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02802 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning physics-based reduced-order models from data using nonlinear manifolds Geelen, Rudy Balzano, Laura Wright, Stephen Willcox, Karen Numerical Analysis We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation. |
| title | Learning physics-based reduced-order models from data using nonlinear manifolds |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2308.02802 |