Literature

Literature#

This page lists scholarly publications that develop, extend, or apply Operator Inference.

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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#

Structure Preservation#

Theory#

Software / Implementation#

Applications#

Dissertations and Theses#

BibTex File#

Sorted alphabetically by author

@article{almeida2022chaotic,
    title = {Non-Intrusive reduced models based on operator inference for chaotic systems},
    author = {Jo\~{a}o Lucas de Sousa Almeida and Arthur Cancellieri Pires and Klaus Feine Vaz Cid and Alberto Costa Nogueira Jr},
    journal = {arXiv},
    volume = {2206.01604},
    year = {2022},
}

@inproceedings{aretz2024enforcing,
    title = {Enforcing structure in data-driven reduced modeling through nested {O}perator {I}nference},
    author = {Nicole Aretz and Karen Willcox},
    booktitle = {63rd IEEE Conference on Decision and Control (CDC)},
    year = {2024},
    organization = {IEEE},
    doi = {10.1109/CDC56724.2024.10885857},
}

@article{benner2020deim,
    title = {Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms},
    author = {Peter Benner and Pawan Goyal and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {372},
    pages = {113433},
    year = {2020},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2020.113433},
}

@article{benner2022incompressible,
    title = {Operator inference and physics-informed learning of low-dimensional Models for incompressible flows},
    author = {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
    journal = {Electronic Transactions on Numerical Analysis},
    volume = {56},
    year = {2022},
    doi = {10.1553/etna_vol56s28},
}

@article{benner2023quaddecoder,
    title = {A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems},
    author = {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
    journal = {Proceedings in Applied Mathematics and Mechanics},
    volume = {23},
    number = {1},
    pages = {e202200049},
    year = {2023},
    doi = {10.1002/pamm.202200049},
}

@inbook{blonigan2025thermal,
    title = {Operator inference-based model order reduction of thermal protection system finite element simulations},
    author = {Patrick J. Blonigan and John Tencer and Sean Babiniec and Jonathan Murray},
    booktitle = {AIAA SciTech 2025 Forum},
    pages = {2133},
    year = {2025},
    doi = {10.2514/6.2025-2133},
}

@article{boef2024stablesparse,
    title = {Stable sparse operator inference for nonlinear structural dynamics},
    author = {Pascal {den Boef} and Diana Manvelyan and Joseph Maubach and Wil Schilders and Nathan {van de Wouw}},
    journal = {arXiv},
    volume = {2407.21672},
    year = {2024},
    doi = {10.48550/arXiv.2407.21672},
}

@article{bychkov2024quadratization,
    title = {Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems},
    author = {Andrey Bychkov and Opal Issan and Gleb Pogudin and Boris Kramer},
    journal = {SIAM Journal of Applied Dynamical Systems},
    volume = {23},
    number = {1},
    pages = {982-1016},
    year = {2024},
    doi = {10.1137/23M1561129},
}

@article{farcas2024distributed,
    title = {Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    journal = {arXiv},
    volume = {2407.09994},
    year = {2024},
    doi = {10.48550/arXiv.2407.09994},
}

@article{farcas2024domaindecomposition,
    title = {Domain decomposition for data-driven reduced modeling of large-scale systems},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    journal = {AIAA Journal},
    volume = {62},
    number = {11},
    pages = {4071-4086},
    year = {2024},
    doi = {10.2514/1.J063715},
}

@inbook{farcas2025parallel,
    title = {A parallel implementation of reduced-order modeling of large-scale systems},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    booktitle = {AIAA SciTech 2025 Forum},
    pages = {1170},
    year = {2025},
    doi = {10.2514/6.2025-1170},
}

@article{filanova2023mechanical,
    title = {An operator inference oriented approach for linear mechanical systems},
    author = {Yevgeniya Filanova and Igor Pontes Duff and Pawan Goyal and Peter Benner},
    journal = {Mechanical Systems and Signal Processing},
    volume = {200},
    pages = {110620},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.ymssp.2023.110620},
}

@misc{freitag2024stochastic,
    title = {Learning stochastic reduced models from data: a nonintrusive approach},
    author = {Melina A. Freitag and Jan Martin Nicolaus and Martin Redmann},
    journal = {arXiv},
    volume = {2407.05724},
    year = {2024},
    doi = {10.48550/arXiv.2407.05724},
}

@article{geelen2022localized,
    title = {Localized non-intrusive reduced-order modelling in the operator inference framework},
    author = {Rudy Geelen and Karen Willcox},
    journal = {Philosophical Transactions of the Royal Society A},
    volume = {380},
    number = {2229},
    pages = {20210206},
    year = {2022},
    doi = {10.1098/rsta.2021.0206},
}

@inproceedings{geelen2023latent,
    author = {Rudy Geelen and Laura Balzano and Karen Willcox},
    booktitle = {2023 62nd IEEE Conference on Decision and Control (CDC)},
    title = {Learning latent representations in high-dimensional state spaces using polynomial manifold constructions},
    year = {2023},
    volume = {},
    number = {},
    pages = {4960-4965},
    doi = {10.1109/CDC49753.2023.10384209},
}

@article{geelen2023quadmanifold,
    title = {Operator inference for non-intrusive model reduction with quadratic manifolds},
    author = {Rudy Geelen and Stephen Wright and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {403},
    pages = {115717},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115717},
}

@article{geelen2024nonlinmanifold,
    title = {Learning physics-based reduced-order models from data using nonlinear manifolds},
    author = {Rudy Geelen and Laura Balzano and Stephen Wright and Karen Willcox},
    journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
    volume = {34},
    number = {3},
    pages = {033122},
    year = {2024},
    doi = {10.1063/5.0170105},
}

@article{geng2024gradient,
    title = {Gradient preserving {O}perator {I}nference: {D}ata-driven reduced-order models for equations with gradient structure},
    author = {Yuwei Geng and Jasdeep Singh and Lili Ju and Boris Kramer and Zhu Wang},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {427},
    pages = {117033},
    year = {2024},
    doi = {10.1016/j.cma.2024.117033},
}

@article{geng2025porthamiltonian,
    title = {Data-driven reduced-order models for port-{H}amiltonian systems with {O}perator {I}nference},
    author = {Yuwei Geng and Lili Ju and Boris Kramer and Zhu Wang},
    journal = {arXiv},
    volume = {2501.02183},
    year = {2025},
    doi = {10.48550/arXiv.2501.02183},
}

@article{ghattas2021acta,
    title = {Learning physics-based models from data: {P}erspectives from inverse problems and model reduction},
    author = {Omar Ghattas and Karen Willcox},
    journal = {Acta Numerica},
    volume = {30},
    pages = {445--554},
    year = {2021},
    publisher = {Cambridge University Press},
    doi = {10.1017/S0962492921000064},
}

@article{gkimisis2025spatiallylocal,
    title = {Non-intrusive reduced-order modeling for dynamical systems with spatially localized features},
    author = {Leonidas Gkimisis and Nicole Aretz and Marco Tezzele and Thomas Richter and Peter Benner and Karen E. Willcox},
    journal = {arXiv},
    volume = {2501.04400},
    year = {2025},
    doi = {10.48550/arXiv.2501.04400},
}

@article{goyal2023stablequad,
    title = {Guaranteed stable quadratic models and their applications in {SINDy} and operator inference},
    author = {Pawan Goyal and Igor Pontes Duff and Peter Benner},
    journal = {arXiv},
    volume = {2308.13819},
    year = {2023},
}

@article{gruber2023hamiltonian,
    title = {Canonical and noncanonical {H}amiltonian operator inference},
    author = {Anthony Gruber and Irina Tezaur},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {416},
    year = {2023},
    doi = {10.1016/j.cma.2023.116334},
}

@article{gruber2025variational,
    author = {Anthony Gruber and Irina Tezaur},
    title = {Variationally consistent {H}amiltonian model reduction},
    journal = {SIAM Journal on Applied Dynamical Systems},
    volume = {24},
    number = {1},
    pages = {376-414},
    year = {2025},
    doi = {10.1137/24M1652490},
}

@article{guo2022bayesopinf,
    title = {Bayesian operator inference for data-driven reduced-order modeling},
    author = {Mengwu Guo and Shane A McQuarrie and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {402},
    pages = {115336},
    year = {2022},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115336},
}

@article{issan2023shifted,
    title = {Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference},
    author = {Opal Issan and Boris Kramer},
    journal = {Journal of Computational Physics},
    volume = {473},
    pages = {111689},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.jcp.2022.111689},
}

@inproceedings{jain2021performance,
    title = {Performance comparison of data-driven reduced models for a single-injector combustion process},
    author = {Parikshit Jain and Shane McQuarrie and Boris Kramer},
    booktitle = {AIAA Propulsion and Energy 2021 Forum},
    pages = {3633},
    year = {2021},
    doi = {10.2514/6.2021-3633},
}

@article{khodabakhshi2022diffalg,
    title = {Non-intrusive data-driven model reduction for differential algebraic equations derived from lifting transformations},
    author = {Parisa Khodabakhshi and Karen E. Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {389},
    pages = {114296},
    year = {2022},
    doi = {10.1016/j.cma.2021.114296},
}

@article{kim2025stateconstraints,
    title = {Physically consistent predictive reduced-order modeling by enhancing {O}perator {I}nference with state constraints},
    author = {Hyeonghun Kim and Boris Kramer},
    journal = {arXiv},
    volume = {2502.03672},
    year = {2025},
    doi = {10.48550/arXiv.2502.03672},
}

@inproceedings{koike2024energy,
    title = {Energy-preserving reduced operator inference for efficient design and control},
    author = {Tomoki Koike and Elizabeth Qian},
    booktitle = {AIAA SciTech 2024 Forum},
    pages = {1012},
    year = {2024},
    doi = {10.2514/6.2024-1012},
}

@article{kramer2021quadstability,
    title = {Stability domains for quadratic-bilinear reduced-order models},
    author = {Boris Kramer},
    journal = {SIAM Journal on Applied Dynamical Systems},
    volume = {20},
    issue = {2},
    pages = {981--996},
    year = {2021},
    publisher = {SIAM},
    doi = {10.1137/20M1364849},
}

@article{kramer2024survey,
    title = {Learning nonlinear reduced models from data with operator inference},
    author = {Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Annual Review of Fluid Mechanics},
    volume = {56},
    pages = {521--548},
    year = {2024},
    publisher = {Annual Reviews},
    doi = {10.1146/annurev-fluid-121021-025220},
}

@article{mcquarrie2021combustion,
    title = {Data-driven reduced-order models via regularised operator inference for a single-injector combustion process},
    author = {Shane A McQuarrie and Cheng Huang and Karen Willcox},
    journal = {Journal of the Royal Society of New Zealand},
    volume = {51},
    issue = {2},
    pages = {194-211},
    year = {2021},
    publisher = {Taylor \& Francis},
    doi = {10.1080/03036758.2020.1863237},
}

@article{mcquarrie2023parametric,
    title = {Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference},
    author = {Shane A McQuarrie and Parisa Khodabakhshi and Karen Willcox},
    journal = {SIAM Journal on Scientific Computing},
    volume = {45},
    issue = {4},
    pages = {A1917-A1946},
    year = {2023},
    publisher = {SIAM},
    doi = {10.1137/21M1452810},
}

@phdthesis{mcquarrie2023thesis,
    title = {Data-driven parametric reduced-order models: {O}perator inference for reactive flow applications},
    author = {Shane Alexander McQuarrie},
    school = {The University of Texas at Austin},
    year = {2023},
    doi = {10.26153/tsw/50172},
}

@article{mcquarrie2025gpbayesopinf,
    title = {Bayesian learning with {G}aussian processes for low-dimensional representations of time-dependent nonlinear systems},
    author = {Shane A. McQuarrie and Anirban Chaudhuri and Karen E. Willcox and Mengwu Guo},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {475},
    pages = {134572},
    year = {2025},
    doi = {10.1016/j.physd.2025.134572},
}

@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},
}

@article{peherstorfer2020reprojection,
    title = {Sampling low-dimensional {M}arkovian dynamics for preasymptotically recovering reduced models from data with operator inference},
    author = {Benjamin Peherstorfer},
    journal = {SIAM Journal on Scientific Computing},
    volume = {42},
    issue = {5},
    pages = {A3489-a3515},
    year = {2020},
    publisher = {SIAM},
    doi = {10.1137/19M1292448},
}

@inproceedings{qian2019transform,
    author = {Elizabeth Qian and Boris Kramer and Alexandre N. Marques and Karen E. Willcox},
    title = {Transform \& {L}earn: {A} data-driven approach to nonlinear model reduction},
    booktitle = {AIAA Aviation 2019 Forum},
    pages = {3707},
    year = {2019},
    doi = {10.2514/6.2019-3707},
}

@article{qian2020liftandlearn,
    title = {Lift \& {L}earn: {P}hysics-informed machine learning for large-scale nonlinear dynamical systems},
    author = {Elizabeth Qian and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {406},
    pages = {132401},
    year = {2020},
    publisher = {Elsevier},
    doi = {10.1016/j.physd.2020.132401},
}

@phdthesis{qian2021thesis,
    title = {A scientific machine learning approach to learning reduced models for nonlinear partial differential equations},
    author = {Elizabeth Yi Qian},
    school = {Massachusetts Institute of Technology},
    year = {2021},
}

@article{qian2022pdes,
    title = {Reduced operator inference for nonlinear partial differential equations},
    author = {Elizabeth Qian and Ionut-Gabriel Farcas and Karen Willcox},
    journal = {SIAM Journal on Scientific Computing},
    volume = {44},
    issue = {4},
    pages = {A1934-a1959},
    year = {2022},
    publisher = {SIAM},
    doi = {10.1137/21M1393972},
}

@inproceedings{rocha2022c02,
    title = {Data-driven reduced-order model for atmospheric {CO}2 dispersion},
    author = {Pedro Roberto Barbosa Rocha and Marcos Sebasti\~{a}o de Paula Gomes and Jo\~{a}o Lucas de Sousa Almeida and Allan M Carvalho and Alberto Costa Nogueira Jr},
    booktitle = {AAAI Fall Symposium},
    year = {2022},
}

@article{rocha2023convection,
    title = {Reduced-order modeling of the two-dimensional {R}ayleigh--{B}\'{e}nard convection flow through a non-intrusive operator inference},
    author = {Pedro Roberto Barbosa Rocha and Jo\~{a}o Lucas de Sousa Almeida and Marcos Sebasti\~{a}o de Paula Gomes and Alberto Costa Nogueira Jr},
    journal = {Engineering Applications of Artificial Intelligence},
    volume = {126},
    pages = {106923},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.engappai.2023.106923},
}

@mastersthesis{salinger2021thesis,
    title = {Toward predictive digital twins for self-aware unmanned aerial vehicles: {N}on-intrusive reduced order models and experimental data analysis},
    author = {Stephanie Joyce Salinger},
    school = {The University of Texas at Austin},
    year = {2021},
}

@article{sawant2023pireg,
    title = {Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference},
    author = {Nihar Sawant and Boris Kramer and Benjamin Peherstorfer},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {404},
    pages = {115836},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115836},
}

@phdthesis{sawant2023thesis,
    title = {Learning structured and stable reduced models from data with operator inference},
    author = {Nihar Sawant},
    year = {2023},
    school = {New York University},
}

@article{sharma2022hamiltonian,
    title = {Hamiltonian operator inference: {P}hysics-preserving learning of reduced-order models for canonical {H}amiltonian systems},
    author = {Harsh Sharma and Zhu Wang and Boris Kramer},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {431},
    pages = {133122},
    year = {2022},
    publisher = {Elsevier},
    doi = {10.1016/j.physd.2021.133122},
}

@article{sharma2024lagrangian,
    title = {Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems},
    author = {Harsh Sharma and David A Najera-Flores and Michael D Todd and Boris Kramer},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {423},
    pages = {116865},
    year = {2024},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2024.116865},
}

@article{sharma2024preserving,
    title = {Preserving {L}agrangian structure in data-driven reduced-order modeling of large-scale mechanical systems},
    author = {Harsh Sharma and Boris Kramer},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {462},
    pages = {134128},
    year = {2024},
    doi = {10.1016/j.physd.2024.134128},
}

@mastersthesis{swischuk2019thesis,
    title = {Physics-based machine learning and data-driven reduced-order modeling},
    author = {Renee Copland Swischuk},
    school = {Massachusetts Institute of Technology},
    year = {2019},
}

@article{swischuk2020combustion,
    title = {Learning physics-based reduced-order models for a single-injector combustion process},
    author = {Renee Swischuk and Boris Kramer and Cheng Huang and Karen Willcox},
    journal = {AIAA Journal},
    volume = {58},
    issue = {6},
    pages = {2658--2672},
    year = {2020},
    publisher = {American Institute of Aeronautics and Astronautics},
    doi = {10.2514/1.J058943},
}

@article{uy2021error,
    title = {Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations},
    author = {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
    journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
    volume = {55},
    issue = {3},
    pages = {735--761},
    year = {2021},
    publisher = {EDP Sciences},
    doi = {10.1051/m2an/2021010},
}

@article{uy2021partial,
    title = {Operator inference of non-{M}arkovian terms for learning reduced models from partially observed state trajectories},
    author = {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
    journal = {Journal of Scientific Computing},
    volume = {88},
    issue = {3},
    pages = {1--31},
    year = {2021},
    publisher = {Springer},
    doi = {10.1007/s10915-021-01580-2},
}

@article{uy2023active,
    title = {Active operator inference for learning low-dimensional dynamical-system models from noisy data},
    author = {Wayne Isaac Tan Uy and Yuepeng Wang and Yuxiao Wen and Benjamin Peherstorfer},
    journal = {SIAM Journal on Scientific Computing},
    volume = {45},
    issue = {4},
    pages = {A1462-a1490},
    year = {2023},
    publisher = {SIAM},
    doi = {10.1137/21M1439729},
}

@article{uy2023rollouts,
    title = {Operator inference with roll outs for learning reduced models from scarce and low-quality data},
    author = {Wayne Isaac Tan Uy and Dirk Hartmann and Benjamin Peherstorfer},
    journal = {Computers \& Mathematics with Applications},
    volume = {145},
    pages = {224--239},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.camwa.2023.06.012},
}

@article{vijaywargiya2025tensoropinf,
    title = {Tensor parametric {H}amiltonian operator inference},
    author = {Arjun Vijaywargiya and Shane A. McQuarrie and Anthony Gruber},
    journal = {arXiv},
    volume = {2502.10888},
    year = {2025},
    doi = {10.48550/arXiv.2502.10888},
}

@article{yildiz2021shallow,
    title = {Learning reduced-order dynamics for parametrized shallow water equations from data},
    author = {S\"{u}leyman Y\i{}ld\i{}z and Pawan Goyal and Peter Benner and B\"{u}lent Karas\"{o}zen},
    journal = {International Journal for Numerical Methods in Fluids},
    volume = {93},
    issue = {8},
    pages = {2803--2821},
    year = {2021},
    publisher = {Wiley Online Library},
    doi = {10.1002/fld.4998},
}

@inproceedings{zastrow2023flutter,
    title = {Data-driven model reduction via operator inference for coupled aeroelastic flutter},
    author = {Benjamin G Zastrow and Anirban Chaudhuri and Karen Willcox and Anthony S Ashley and Michael C Henson},
    booktitle = {AIAA SciTech 2023 Forum},
    pages = {0330},
    year = {2023},
    doi = {10.2514/6.2023-0330},
}

Sorted by year then alphabetically by author

@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},
}

@inproceedings{qian2019transform,
    author = {Elizabeth Qian and Boris Kramer and Alexandre N. Marques and Karen E. Willcox},
    title = {Transform \& {L}earn: {A} data-driven approach to nonlinear model reduction},
    booktitle = {AIAA Aviation 2019 Forum},
    pages = {3707},
    year = {2019},
    doi = {10.2514/6.2019-3707},
}

@mastersthesis{swischuk2019thesis,
    title = {Physics-based machine learning and data-driven reduced-order modeling},
    author = {Renee Copland Swischuk},
    school = {Massachusetts Institute of Technology},
    year = {2019},
}

@article{benner2020deim,
    title = {Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms},
    author = {Peter Benner and Pawan Goyal and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {372},
    pages = {113433},
    year = {2020},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2020.113433},
}

@article{peherstorfer2020reprojection,
    title = {Sampling low-dimensional {M}arkovian dynamics for preasymptotically recovering reduced models from data with operator inference},
    author = {Benjamin Peherstorfer},
    journal = {SIAM Journal on Scientific Computing},
    volume = {42},
    issue = {5},
    pages = {A3489-a3515},
    year = {2020},
    publisher = {SIAM},
    doi = {10.1137/19M1292448},
}

@article{qian2020liftandlearn,
    title = {Lift \& {L}earn: {P}hysics-informed machine learning for large-scale nonlinear dynamical systems},
    author = {Elizabeth Qian and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {406},
    pages = {132401},
    year = {2020},
    publisher = {Elsevier},
    doi = {10.1016/j.physd.2020.132401},
}

@article{swischuk2020combustion,
    title = {Learning physics-based reduced-order models for a single-injector combustion process},
    author = {Renee Swischuk and Boris Kramer and Cheng Huang and Karen Willcox},
    journal = {AIAA Journal},
    volume = {58},
    issue = {6},
    pages = {2658--2672},
    year = {2020},
    publisher = {American Institute of Aeronautics and Astronautics},
    doi = {10.2514/1.J058943},
}

@article{ghattas2021acta,
    title = {Learning physics-based models from data: {P}erspectives from inverse problems and model reduction},
    author = {Omar Ghattas and Karen Willcox},
    journal = {Acta Numerica},
    volume = {30},
    pages = {445--554},
    year = {2021},
    publisher = {Cambridge University Press},
    doi = {10.1017/S0962492921000064},
}

@inproceedings{jain2021performance,
    title = {Performance comparison of data-driven reduced models for a single-injector combustion process},
    author = {Parikshit Jain and Shane McQuarrie and Boris Kramer},
    booktitle = {AIAA Propulsion and Energy 2021 Forum},
    pages = {3633},
    year = {2021},
    doi = {10.2514/6.2021-3633},
}

@article{kramer2021quadstability,
    title = {Stability domains for quadratic-bilinear reduced-order models},
    author = {Boris Kramer},
    journal = {SIAM Journal on Applied Dynamical Systems},
    volume = {20},
    issue = {2},
    pages = {981--996},
    year = {2021},
    publisher = {SIAM},
    doi = {10.1137/20M1364849},
}

@article{mcquarrie2021combustion,
    title = {Data-driven reduced-order models via regularised operator inference for a single-injector combustion process},
    author = {Shane A McQuarrie and Cheng Huang and Karen Willcox},
    journal = {Journal of the Royal Society of New Zealand},
    volume = {51},
    issue = {2},
    pages = {194-211},
    year = {2021},
    publisher = {Taylor \& Francis},
    doi = {10.1080/03036758.2020.1863237},
}

@phdthesis{qian2021thesis,
    title = {A scientific machine learning approach to learning reduced models for nonlinear partial differential equations},
    author = {Elizabeth Yi Qian},
    school = {Massachusetts Institute of Technology},
    year = {2021},
}

@mastersthesis{salinger2021thesis,
    title = {Toward predictive digital twins for self-aware unmanned aerial vehicles: {N}on-intrusive reduced order models and experimental data analysis},
    author = {Stephanie Joyce Salinger},
    school = {The University of Texas at Austin},
    year = {2021},
}

@article{uy2021partial,
    title = {Operator inference of non-{M}arkovian terms for learning reduced models from partially observed state trajectories},
    author = {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
    journal = {Journal of Scientific Computing},
    volume = {88},
    issue = {3},
    pages = {1--31},
    year = {2021},
    publisher = {Springer},
    doi = {10.1007/s10915-021-01580-2},
}

@article{uy2021error,
    title = {Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations},
    author = {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
    journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
    volume = {55},
    issue = {3},
    pages = {735--761},
    year = {2021},
    publisher = {EDP Sciences},
    doi = {10.1051/m2an/2021010},
}

@article{yildiz2021shallow,
    title = {Learning reduced-order dynamics for parametrized shallow water equations from data},
    author = {S\"{u}leyman Y\i{}ld\i{}z and Pawan Goyal and Peter Benner and B\"{u}lent Karas\"{o}zen},
    journal = {International Journal for Numerical Methods in Fluids},
    volume = {93},
    issue = {8},
    pages = {2803--2821},
    year = {2021},
    publisher = {Wiley Online Library},
    doi = {10.1002/fld.4998},
}

@article{almeida2022chaotic,
    title = {Non-Intrusive reduced models based on operator inference for chaotic systems},
    author = {Jo\~{a}o Lucas de Sousa Almeida and Arthur Cancellieri Pires and Klaus Feine Vaz Cid and Alberto Costa Nogueira Jr},
    journal = {arXiv},
    volume = {2206.01604},
    year = {2022},
}

@article{benner2022incompressible,
    title = {Operator inference and physics-informed learning of low-dimensional Models for incompressible flows},
    author = {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
    journal = {Electronic Transactions on Numerical Analysis},
    volume = {56},
    year = {2022},
    doi = {10.1553/etna_vol56s28},
}

@article{geelen2022localized,
    title = {Localized non-intrusive reduced-order modelling in the operator inference framework},
    author = {Rudy Geelen and Karen Willcox},
    journal = {Philosophical Transactions of the Royal Society A},
    volume = {380},
    number = {2229},
    pages = {20210206},
    year = {2022},
    doi = {10.1098/rsta.2021.0206},
}

@article{guo2022bayesopinf,
    title = {Bayesian operator inference for data-driven reduced-order modeling},
    author = {Mengwu Guo and Shane A McQuarrie and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {402},
    pages = {115336},
    year = {2022},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115336},
}

@article{khodabakhshi2022diffalg,
    title = {Non-intrusive data-driven model reduction for differential algebraic equations derived from lifting transformations},
    author = {Parisa Khodabakhshi and Karen E. Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {389},
    pages = {114296},
    year = {2022},
    doi = {10.1016/j.cma.2021.114296},
}

@article{qian2022pdes,
    title = {Reduced operator inference for nonlinear partial differential equations},
    author = {Elizabeth Qian and Ionut-Gabriel Farcas and Karen Willcox},
    journal = {SIAM Journal on Scientific Computing},
    volume = {44},
    issue = {4},
    pages = {A1934-a1959},
    year = {2022},
    publisher = {SIAM},
    doi = {10.1137/21M1393972},
}

@inproceedings{rocha2022c02,
    title = {Data-driven reduced-order model for atmospheric {CO}2 dispersion},
    author = {Pedro Roberto Barbosa Rocha and Marcos Sebasti\~{a}o de Paula Gomes and Jo\~{a}o Lucas de Sousa Almeida and Allan M Carvalho and Alberto Costa Nogueira Jr},
    booktitle = {AAAI Fall Symposium},
    year = {2022},
}

@article{sharma2022hamiltonian,
    title = {Hamiltonian operator inference: {P}hysics-preserving learning of reduced-order models for canonical {H}amiltonian systems},
    author = {Harsh Sharma and Zhu Wang and Boris Kramer},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {431},
    pages = {133122},
    year = {2022},
    publisher = {Elsevier},
    doi = {10.1016/j.physd.2021.133122},
}

@article{benner2023quaddecoder,
    title = {A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems},
    author = {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
    journal = {Proceedings in Applied Mathematics and Mechanics},
    volume = {23},
    number = {1},
    pages = {e202200049},
    year = {2023},
    doi = {10.1002/pamm.202200049},
}

@article{filanova2023mechanical,
    title = {An operator inference oriented approach for linear mechanical systems},
    author = {Yevgeniya Filanova and Igor Pontes Duff and Pawan Goyal and Peter Benner},
    journal = {Mechanical Systems and Signal Processing},
    volume = {200},
    pages = {110620},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.ymssp.2023.110620},
}

@article{geelen2023quadmanifold,
    title = {Operator inference for non-intrusive model reduction with quadratic manifolds},
    author = {Rudy Geelen and Stephen Wright and Karen Willcox},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {403},
    pages = {115717},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115717},
}

@inproceedings{geelen2023latent,
    author = {Rudy Geelen and Laura Balzano and Karen Willcox},
    booktitle = {2023 62nd IEEE Conference on Decision and Control (CDC)},
    title = {Learning latent representations in high-dimensional state spaces using polynomial manifold constructions},
    year = {2023},
    volume = {},
    number = {},
    pages = {4960-4965},
    doi = {10.1109/CDC49753.2023.10384209},
}

@article{goyal2023stablequad,
    title = {Guaranteed stable quadratic models and their applications in {SINDy} and operator inference},
    author = {Pawan Goyal and Igor Pontes Duff and Peter Benner},
    journal = {arXiv},
    volume = {2308.13819},
    year = {2023},
}

@article{gruber2023hamiltonian,
    title = {Canonical and noncanonical {H}amiltonian operator inference},
    author = {Anthony Gruber and Irina Tezaur},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {416},
    year = {2023},
    doi = {10.1016/j.cma.2023.116334},
}

@article{issan2023shifted,
    title = {Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference},
    author = {Opal Issan and Boris Kramer},
    journal = {Journal of Computational Physics},
    volume = {473},
    pages = {111689},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.jcp.2022.111689},
}

@article{mcquarrie2023parametric,
    title = {Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference},
    author = {Shane A McQuarrie and Parisa Khodabakhshi and Karen Willcox},
    journal = {SIAM Journal on Scientific Computing},
    volume = {45},
    issue = {4},
    pages = {A1917-A1946},
    year = {2023},
    publisher = {SIAM},
    doi = {10.1137/21M1452810},
}

@phdthesis{mcquarrie2023thesis,
    title = {Data-driven parametric reduced-order models: {O}perator inference for reactive flow applications},
    author = {Shane Alexander McQuarrie},
    school = {The University of Texas at Austin},
    year = {2023},
    doi = {10.26153/tsw/50172},
}

@article{rocha2023convection,
    title = {Reduced-order modeling of the two-dimensional {R}ayleigh--{B}\'{e}nard convection flow through a non-intrusive operator inference},
    author = {Pedro Roberto Barbosa Rocha and Jo\~{a}o Lucas de Sousa Almeida and Marcos Sebasti\~{a}o de Paula Gomes and Alberto Costa Nogueira Jr},
    journal = {Engineering Applications of Artificial Intelligence},
    volume = {126},
    pages = {106923},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.engappai.2023.106923},
}

@article{sawant2023pireg,
    title = {Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference},
    author = {Nihar Sawant and Boris Kramer and Benjamin Peherstorfer},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {404},
    pages = {115836},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2022.115836},
}

@phdthesis{sawant2023thesis,
    title = {Learning structured and stable reduced models from data with operator inference},
    author = {Nihar Sawant},
    year = {2023},
    school = {New York University},
}

@article{uy2023active,
    title = {Active operator inference for learning low-dimensional dynamical-system models from noisy data},
    author = {Wayne Isaac Tan Uy and Yuepeng Wang and Yuxiao Wen and Benjamin Peherstorfer},
    journal = {SIAM Journal on Scientific Computing},
    volume = {45},
    issue = {4},
    pages = {A1462-a1490},
    year = {2023},
    publisher = {SIAM},
    doi = {10.1137/21M1439729},
}

@article{uy2023rollouts,
    title = {Operator inference with roll outs for learning reduced models from scarce and low-quality data},
    author = {Wayne Isaac Tan Uy and Dirk Hartmann and Benjamin Peherstorfer},
    journal = {Computers \& Mathematics with Applications},
    volume = {145},
    pages = {224--239},
    year = {2023},
    publisher = {Elsevier},
    doi = {10.1016/j.camwa.2023.06.012},
}

@inproceedings{zastrow2023flutter,
    title = {Data-driven model reduction via operator inference for coupled aeroelastic flutter},
    author = {Benjamin G Zastrow and Anirban Chaudhuri and Karen Willcox and Anthony S Ashley and Michael C Henson},
    booktitle = {AIAA SciTech 2023 Forum},
    pages = {0330},
    year = {2023},
    doi = {10.2514/6.2023-0330},
}

@article{bychkov2024quadratization,
    title = {Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems},
    author = {Andrey Bychkov and Opal Issan and Gleb Pogudin and Boris Kramer},
    journal = {SIAM Journal of Applied Dynamical Systems},
    volume = {23},
    number = {1},
    pages = {982-1016},
    year = {2024},
    doi = {10.1137/23M1561129},
}

@misc{freitag2024stochastic,
    title = {Learning stochastic reduced models from data: a nonintrusive approach},
    author = {Melina A. Freitag and Jan Martin Nicolaus and Martin Redmann},
    journal = {arXiv},
    volume = {2407.05724},
    year = {2024},
    doi = {10.48550/arXiv.2407.05724},
}

@article{geelen2024nonlinmanifold,
    title = {Learning physics-based reduced-order models from data using nonlinear manifolds},
    author = {Rudy Geelen and Laura Balzano and Stephen Wright and Karen Willcox},
    journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
    volume = {34},
    number = {3},
    pages = {033122},
    year = {2024},
    doi = {10.1063/5.0170105},
}

@inproceedings{koike2024energy,
    title = {Energy-preserving reduced operator inference for efficient design and control},
    author = {Tomoki Koike and Elizabeth Qian},
    booktitle = {AIAA SciTech 2024 Forum},
    pages = {1012},
    year = {2024},
    doi = {10.2514/6.2024-1012},
}

@article{kramer2024survey,
    title = {Learning nonlinear reduced models from data with operator inference},
    author = {Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
    journal = {Annual Review of Fluid Mechanics},
    volume = {56},
    pages = {521--548},
    year = {2024},
    publisher = {Annual Reviews},
    doi = {10.1146/annurev-fluid-121021-025220},
}

@article{sharma2024lagrangian,
    title = {Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems},
    author = {Harsh Sharma and David A Najera-Flores and Michael D Todd and Boris Kramer},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {423},
    pages = {116865},
    year = {2024},
    publisher = {Elsevier},
    doi = {10.1016/j.cma.2024.116865},
}

@article{sharma2024preserving,
    title = {Preserving {L}agrangian structure in data-driven reduced-order modeling of large-scale mechanical systems},
    author = {Harsh Sharma and Boris Kramer},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {462},
    pages = {134128},
    year = {2024},
    doi = {10.1016/j.physd.2024.134128},
}

@article{boef2024stablesparse,
    title = {Stable sparse operator inference for nonlinear structural dynamics},
    author = {Pascal {den Boef} and Diana Manvelyan and Joseph Maubach and Wil Schilders and Nathan {van de Wouw}},
    journal = {arXiv},
    volume = {2407.21672},
    year = {2024},
    doi = {10.48550/arXiv.2407.21672},
}

@article{farcas2024distributed,
    title = {Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    journal = {arXiv},
    volume = {2407.09994},
    year = {2024},
    doi = {10.48550/arXiv.2407.09994},
}

@article{farcas2024domaindecomposition,
    title = {Domain decomposition for data-driven reduced modeling of large-scale systems},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    journal = {AIAA Journal},
    volume = {62},
    number = {11},
    pages = {4071-4086},
    year = {2024},
    doi = {10.2514/1.J063715},
}

@article{geng2024gradient,
    title = {Gradient preserving {O}perator {I}nference: {D}ata-driven reduced-order models for equations with gradient structure},
    author = {Yuwei Geng and Jasdeep Singh and Lili Ju and Boris Kramer and Zhu Wang},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {427},
    pages = {117033},
    year = {2024},
    doi = {10.1016/j.cma.2024.117033},
}

@inproceedings{aretz2024enforcing,
    title = {Enforcing structure in data-driven reduced modeling through nested {O}perator {I}nference},
    author = {Nicole Aretz and Karen Willcox},
    booktitle = {63rd IEEE Conference on Decision and Control (CDC)},
    year = {2024},
    organization = {IEEE},
    doi = {10.1109/CDC56724.2024.10885857},
}

@article{geng2025porthamiltonian,
    title = {Data-driven reduced-order models for port-{H}amiltonian systems with {O}perator {I}nference},
    author = {Yuwei Geng and Lili Ju and Boris Kramer and Zhu Wang},
    journal = {arXiv},
    volume = {2501.02183},
    year = {2025},
    doi = {10.48550/arXiv.2501.02183},
}

@inbook{blonigan2025thermal,
    title = {Operator inference-based model order reduction of thermal protection system finite element simulations},
    author = {Patrick J. Blonigan and John Tencer and Sean Babiniec and Jonathan Murray},
    booktitle = {AIAA SciTech 2025 Forum},
    pages = {2133},
    year = {2025},
    doi = {10.2514/6.2025-2133},
}

@inbook{farcas2025parallel,
    title = {A parallel implementation of reduced-order modeling of large-scale systems},
    author = {Ionut-Gabriel Farcas and Rayomand P. Gundevia and Ramakanth Munipalli and Karen E. Willcox},
    booktitle = {AIAA SciTech 2025 Forum},
    pages = {1170},
    year = {2025},
    doi = {10.2514/6.2025-1170},
}

@article{gkimisis2025spatiallylocal,
    title = {Non-intrusive reduced-order modeling for dynamical systems with spatially localized features},
    author = {Leonidas Gkimisis and Nicole Aretz and Marco Tezzele and Thomas Richter and Peter Benner and Karen E. Willcox},
    journal = {arXiv},
    volume = {2501.04400},
    year = {2025},
    doi = {10.48550/arXiv.2501.04400},
}

@article{gruber2025variational,
    author = {Anthony Gruber and Irina Tezaur},
    title = {Variationally consistent {H}amiltonian model reduction},
    journal = {SIAM Journal on Applied Dynamical Systems},
    volume = {24},
    number = {1},
    pages = {376-414},
    year = {2025},
    doi = {10.1137/24M1652490},
}

@article{mcquarrie2025gpbayesopinf,
    title = {Bayesian learning with {G}aussian processes for low-dimensional representations of time-dependent nonlinear systems},
    author = {Shane A. McQuarrie and Anirban Chaudhuri and Karen E. Willcox and Mengwu Guo},
    journal = {Physica D: Nonlinear Phenomena},
    volume = {475},
    pages = {134572},
    year = {2025},
    doi = {10.1016/j.physd.2025.134572},
}

@article{kim2025stateconstraints,
    title = {Physically consistent predictive reduced-order modeling by enhancing {O}perator {I}nference with state constraints},
    author = {Hyeonghun Kim and Boris Kramer},
    journal = {arXiv},
    volume = {2502.03672},
    year = {2025},
    doi = {10.48550/arXiv.2502.03672},
}

@article{vijaywargiya2025tensoropinf,
    title = {Tensor parametric {H}amiltonian operator inference},
    author = {Arjun Vijaywargiya and Shane A. McQuarrie and Anthony Gruber},
    journal = {arXiv},
    volume = {2502.10888},
    year = {2025},
    doi = {10.48550/arXiv.2502.10888},
}

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