1
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference

      Preprint
      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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.

          Related collections

          Author and article information

          Journal
          14 October 2021
          Article
          2110.07653
          b4e6c0d4-b820-4229-8286-836ee8c95a36

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          35B30, 35R30, 65F22
          cs.CE cs.NA math.NA

          Numerical & Computational mathematics,Applied computer science
          Numerical & Computational mathematics, Applied computer science

          Comments

          Comment on this article