Literature#

This page lists scholarly publications that develop, extend, or apply Operator Inference, categorized into topics and sorted by publication year, then by the last name of the first author. Although some could be placed in multiple categories, each publication is only listed once.

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Original Paper#

  • Data-driven operator inference for nonintrusive projection-based model reduction
    B. Peherstorfer and K. Willcox
    Computer Methods in Applied Mechanics and Engineering, 2016

    BibTeX
    @article{peherstorfer2016opinf,
      title = {Data-driven operator inference for nonintrusive projection-based model reduction},
      author = {Benjamin Peherstorfer and Karen Willcox},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      volume = {306},
      pages = {196–215},
      year = {2016},
      publisher = {Elsevier},
      doi = {10.1016/j.cma.2016.03.025},
    }

Surveys#

Methodology#

Lifting and Nonlinearity#

Operator Inference learns reduced-order models with polynomial structure. The methods developed in the following papers focus on dealing with non-polynomial nonlinearities through variable transformations (lifting) and/or coupling Operator Inference methods with other approximation strategies.

Re-projection#

In some cases, if the training data are chosen judiciously, Operator Inference can recover traditional reduced-order models defined by intrusive projection. The following papers develop and apply this idea.

Structure Preservation#

The methods developed in these works augment Operator Inference so that the resulting reduced-order models automatically inherit certain properties from the full-order system, such as block structure, symmetries, energy conservation, gradient structure, and more.

Parametric Problems#

Many systems depend on independent parameters that describe material properties or other physical characteristics of the phenomenon being modeled. The following papers develop Operator Inference approaches that are specifically designed for parametric problems.

Statistical Methods#

These papers focus on problems with noisy or missing data, stochastic systems, and methods for constructing probabilistic reduced-order models with Operator Inference.

Domain Decomposition#

The methods in the following papers focus on scalability and accuracy improvements by decomposition spatial or latent space domains and learning a coupled system of reduced-order models.

Nonlinear Manifolds#

Traditional model reduction methods approximate the high-dimensional system state with a low-dimensional linear (or affine) representation. The methods in these papers explore using nonlinear low-dimensional representations in the context of Operator Inference.

Scalability#

These works focus on the computational challenge of applying Operator Inference to large-scale problems.

Applications#

Dissertations and Theses#

BibTex File#