Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Nihar Sawant, Boris Kramer, Benjamin Peherstorfer

Research output: Contribution to journalArticlepeer-review


Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

Original languageEnglish (US)
Article number115836
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Feb 1 2023


  • Model reduction
  • Non-intrusive methods
  • Operator inference
  • Polynomial models
  • Scientific machine learning
  • Structure preservation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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