Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908406077456384 |
|---|---|
| author | McQuarrie, Shane A Khodabakhshi, Parisa Willcox, Karen E |
| author_facet | McQuarrie, Shane A Khodabakhshi, Parisa Willcox, Karen E |
| contents | This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning and physics-based modeling. The parametric structure of the governing equations is embedded directly into the reduced-order model, and parameterized reduced-order operators are learned via a data-driven linear regression problem. The result is a reduced-order model that can be solved rapidly to map parameter values to approximate PDE solutions. Such parameterized reduced-order models may be used as physics-based surrogates for uncertainty quantification and inverse problems that require many forward solves of parametric PDEs. Numerical issues such as well-posedness and the need for appropriate regularization in the learning problem are considered, and an algorithm for hyperparameter selection is presented. The method is illustrated for a parametric heat equation and demonstrated for the FitzHugh-Nagumo neuron model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_07653 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference McQuarrie, Shane A Khodabakhshi, Parisa Willcox, Karen E Computational Engineering, Finance, and Science Numerical Analysis 35B30, 35R30, 65F22 This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning and physics-based modeling. The parametric structure of the governing equations is embedded directly into the reduced-order model, and parameterized reduced-order operators are learned via a data-driven linear regression problem. The result is a reduced-order model that can be solved rapidly to map parameter values to approximate PDE solutions. Such parameterized reduced-order models may be used as physics-based surrogates for uncertainty quantification and inverse problems that require many forward solves of parametric PDEs. Numerical issues such as well-posedness and the need for appropriate regularization in the learning problem are considered, and an algorithm for hyperparameter selection is presented. The method is illustrated for a parametric heat equation and demonstrated for the FitzHugh-Nagumo neuron model. |
| title | Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference |
| topic | Computational Engineering, Finance, and Science Numerical Analysis 35B30, 35R30, 65F22 |
| url | https://arxiv.org/abs/2110.07653 |