Hybrid reduced-order integration with proper orthogonal decomposition and dynamic mode decomposition

Matthew O. Williams, Peter J. Schmid, J. Nathan Kutz

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A data-driven hybrid numerical integrator is introduced to exploit, numerically, the formation of nonlinear coherent structures that often appear in nonlinear PDEs. Full simulations of the PDE allow model reduction algorithms such as the proper orthogonal decomposition and dynamic mode decomposition to generate reduced order models in an "online" manner. Criteria based on the comparison of these two independent reduction techniques, similar to model predictive control, determine whether the reduced model is accurate without direct evaluation of the underlying PDE. The method is implemented and explored for two prototypical PDE example models and significantly reduces the computational cost of solving those equations even when bifurcations occur. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)522-544
Number of pages23
JournalMultiscale Modeling and Simulation
Volume11
Issue number2
DOIs
StatePublished - Jul 9 2013
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Modeling and Simulation
  • Chemistry(all)
  • Ecological Modeling
  • Computer Science Applications

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