Learning Nonlinear Reduced Models from Data with Operator Inference

Boris Kramer, Benjamin Peherstorfer, Karen E. Willcox

Research output: Contribution to journalReview articlepeer-review


This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Original languageEnglish (US)
Pages (from-to)521-548
Number of pages28
JournalAnnual Review of Fluid Mechanics
StatePublished - Jan 19 2024


  • Operator Inference
  • data-driven modeling
  • nonlinear model reduction
  • scientific machine learning
  • structure preservation

ASJC Scopus subject areas

  • Condensed Matter Physics


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