Learning reduced-order dynamics for parametrized shallow water equations from data

Yildiz S., Goyal P., Benner P., Karasözen B.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, vol.93, no.8, pp.2803-2821, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 93 Issue: 8
  • Publication Date: 2021
  • Doi Number: 10.1002/fld.4998
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2803-2821
  • Keywords: data&#8208, driven modeling, model order reduction, operator inference, scientific machine learning, shallow water equation, FINITE-ELEMENT APPROXIMATIONS, MODEL-REDUCTION, OCEAN, IDENTIFICATION, DECOMPOSITION, STABILITY, GALERKIN
  • Middle East Technical University Affiliated: Yes


This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider the shallow water equation in non-traditional form (NTSWE). We focus on learning low-dimensional models in a non-intrusive way. That means, we assume not to have access to a discretized form of the NTSWE in any form. Instead, we have snapshots that can be obtained using a black-box solver. Consequently, we aim at learning reduced-order models only from the snapshots. Precisely, a reduced-order model is learnt by solving an appropriate least-squares optimization problem in a low-dimensional subspace. Furthermore, we discuss computational challenges that particularly arise from the optimization problem being ill-conditioned. Moreover, we extend the non-intrusive model order reduction framework to a parametric case, where we make use of the parameter dependency at the level of the partial differential equation. We illustrate the efficiency of the proposed non-intrusive method to construct reduced-order models for NTSWE and compare it with an intrusive method (proper orthogonal decomposition). We furthermore discuss the predictive capabilities of both models outside the range of the training data.