Report
Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference
| العنوان: | Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference |
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| المؤلفون: | McQuarrie, Shane A, Khodabakhshi, Parisa, Willcox, Karen E |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Computational Engineering, Finance, and Science, Mathematics - Numerical Analysis, 35B30, 35R30, 65F22 |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2110.07653 |
| رقم الانضمام: | edsarx.2110.07653 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |