Sampling low-dimensional markovian dynamics for preasymptotically recovering reduced models from data with operator inference

Benjamin Peherstorfer

Research output: Contribution to journalArticlepeer-review

Abstract

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed preasymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. The numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

Original languageEnglish (US)
Pages (from-to)A3489-A3515
JournalSIAM Journal on Scientific Computing
Volume42
Issue number5
DOIs
StatePublished - 2020

Keywords

  • Data-driven modeling
  • Nonintrusive model reduction
  • Operator inference
  • Proper orthogonal decomposition
  • Reduced basis method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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