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Updated: Sep 7, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Localized non-intrusive reduced-order modelling in the operator inference framework.

Rudy Geelen1, Karen Willcox1

  • 1Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 20, 2022
PubMed
Summary

This study introduces data-driven localized reduced models, adapting to local dynamics for efficient computation. This non-intrusive operator inference method accelerates simulations of complex systems like partial differential equations.

Keywords:
data clusteringlocalizationmodel reductionnonlinear partial differential equationsoperator inferenceproper orthogonal decomposition

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Area of Science:

  • Computational Science
  • Applied Mathematics
  • Data-Driven Modeling

Background:

  • Reduced models are crucial for simulating complex dynamical systems, but global approaches struggle with nonlinearities and parameter sensitivity.
  • Existing methods often require intrusive modifications to high-fidelity codes, limiting their applicability.
  • Nonlinear partial differential equations (PDEs) present significant computational challenges due to localized phenomena and parameter variations.

Purpose of the Study:

  • To develop a data-driven, non-intrusive method for learning localized reduced models.
  • To enable adaptive reduced-order modeling that efficiently captures local dynamics.
  • To improve the computational speed and accuracy of simulating complex physical systems.

Main Methods:

  • Employs multiple local approximation subspaces instead of a single global basis.
  • Utilizes operator inference to learn localized reduced operators from snapshot data in an offline phase.
  • Implements an online phase with adaptive selection of local bases based on the system's current state.

Main Results:

  • Demonstrates significant computational speedups for the Burgers' equation and Cahn-Hilliard equation.
  • Maintains good accuracy in reduced models by adapting to local dynamics.
  • The non-intrusive approach is shown to be portable and applicable to legacy or proprietary codes.

Conclusions:

  • Localized operator inference provides an efficient and accurate data-driven approach for reduced-order modeling.
  • The method's non-intrusive nature broadens its applicability across diverse scientific and engineering problems.
  • This technique offers a powerful tool for accelerating the simulation of nonlinear PDEs and complex dynamical systems.