Learning Stochastic Reduced Models from Data: A Nonintrusive Approach
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912421116903424 |
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| author | Freitag, M. A. Nicolaus, J. M. Redmann, M. |
| author_facet | Freitag, M. A. Nicolaus, J. M. Redmann, M. |
| contents | A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_05724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Stochastic Reduced Models from Data: A Nonintrusive Approach Freitag, M. A. Nicolaus, J. M. Redmann, M. Numerical Analysis 60H10, 60H35, 65C30, 60G51 A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD. |
| title | Learning Stochastic Reduced Models from Data: A Nonintrusive Approach |
| topic | Numerical Analysis 60H10, 60H35, 65C30, 60G51 |
| url | https://arxiv.org/abs/2407.05724 |