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Operator Inference literature

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Benjamin Peherstorfer edited this page Mar 23, 2024 · 38 revisions

Surveys

BibTeX
@article{Kramer2024,
author= {Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
issn= {0066-4189},
journal= {Annual Review of Fluid Mechanics},
pages= {521-548},
publisher= {Annual Reviews},
title= {Learning nonlinear reduced models from data with operator inference},
volume= {56},
year= {2024},
}
- O. Ghattas, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Learning physics-based models from data: perspectives from inverse problems and model reduction**](https://www.cambridge.org/core/journals/acta-numerica/article/learning-physicsbased-models-from-data-perspectives-from-inverse-problems-and-model-reduction/C072A4B417F8C3873ED75C1D63BBB31D)\Acta Numerica, 2021
BibTeX
@article{Ghattas2021,
author= {Omar Ghattas and Karen Willcox},
issn= {0962-4929},
journal= {Acta Numerica},
pages= {445-554},
publisher= {Cambridge University Press},
title= {Learning physics-based models from data: perspectives from inverse problems and model reduction},
volume= {30},
year= {2021},
}

Operator Inference methodologies

BibTeX
@article{Peherstorfer2016c,
author= {Benjamin Peherstorfer and Karen Willcox},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {196-215},
publisher= {Elsevier},
title= {Data-driven operator inference for nonintrusive projection-based model reduction},
volume= {306},
year= {2016},
}
- [E. Qian](https://scholar.google.com/citations?user=jnHI7wQAAAAJ&hl=en), [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en), and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Lift \& Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems**](https://doi.org/10.1016/j.physd.2020.132401)\Physica D: Nonlinear Phenomena, 2020
BibTeX
@article{Qian2020,
author= {Elizabeth Qian and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
issn= {0167-2789},
journal= {Physica D: Nonlinear Phenomena},
pages= {132401},
publisher= {Elsevier},
title= {Lift \& Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems},
volume= {406},
year= {2020},
}
- S. A. McQuarrie, C. Huang, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process**](https://www.tandfonline.com/doi/full/10.1080/03036758.2020.1863237)\Journal of the Royal Society of New Zealand, 2021
BibTeX
@article{McQuarrie2021a,
author= {Shane A McQuarrie and Cheng Huang and Karen Willcox},
issn= {0303-6758},
journal= {Journal of the Royal Society of New Zealand},
pages= {1-18},
publisher= {Taylor \& Francis},
title= {Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process},
year= {2021},
}
- W. I. T. Uy, and [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en)\ [**Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories**](https://link.springer.com/article/10.1007/s10915-021-01580-2)\Journal of Scientific Computing, 2021
BibTeX
@article{Uy2021,
author= {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
issn= {1573-7691},
issue= {3},
journal= {Journal of Scientific Computing},
pages= {1-31},
publisher= {Springer},
title= {Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories},
volume= {88},
year= {2021},
}
- [E. Qian](https://scholar.google.com/citations?user=jnHI7wQAAAAJ&hl=en), I. Farcas, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Reduced operator inference for nonlinear partial differential equations**](https://doi.org/10.1137/21M1393972)\SIAM Journal on Scientific Computing, 2022
BibTeX
@article{Qian2022,
author= {Elizabeth Qian and Ionut-Gabriel Farcas and Karen Willcox},
issn= {1064-8275},
issue= {4},
journal= {SIAM Journal on Scientific Computing},
pages= {A1934-A1959},
publisher= {SIAM},
title= {Reduced operator inference for nonlinear partial differential equations},
volume= {44},
year= {2022},
}
- S. A. McQuarrie, P. Khodabakhshi, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference**](https://doi.org/10.1137/21M1452810)\SIAM Journal on Scientific Computing, 2023
BibTeX
@article{McQuarrie2023,
author= {Shane A McQuarrie and Parisa Khodabakhshi and Karen Willcox},
issn= {1064-8275},
issue= {4},
journal= {SIAM Journal on Scientific Computing},
pages= {A1917-A1946},
publisher= {SIAM},
title= {Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference},
volume= {45},
year= {2023},
}
- R. Geelen, S. Wright, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Operator inference for non-intrusive model reduction with quadratic manifolds**](https://doi.org/10.1016/j.cma.2022.115717)\Computer Methods in Applied Mechanics and Engineering, 2023
BibTeX
@article{Geelen2023,
author= {Rudy Geelen and Stephen Wright and Karen Willcox},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {115717},
publisher= {Elsevier},
title= {Operator inference for non-intrusive model reduction with quadratic manifolds},
volume= {403},
year= {2023},
}
- [P. Benner](https://scholar.google.com/citations?user=6zcRrC4AAAAJ&hl=en), P. Goyal, [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en), and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms**](https://doi.org/10.1016/j.cma.2020.113433)\Computer Methods in Applied Mechanics and Engineering, 2020
BibTeX
@article{Benner2020a,
author= {Peter Benner and Pawan Goyal and Boris Kramer and Benjamin Peherstorfer and Karen Willcox},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {113433},
publisher= {Elsevier},
title= {Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms},
volume= {372},
year= {2020},
}
- M. Guo, S. A. McQuarrie, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Bayesian operator inference for data-driven reduced-order modeling**](https://doi.org/10.1016/j.cma.2022.115336)\Computer Methods in Applied Mechanics and Engineering, 2022
BibTeX
@article{Guo2022,
author= {Mengwu Guo and Shane A McQuarrie and Karen Willcox},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {115336},
publisher= {Elsevier},
title= {Bayesian operator inference for data-driven reduced-order modeling},
volume= {402},
year= {2022},
}
- W. I. T. Uy, Y. Wang, Y. Wen, and [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en)\ [**Active operator inference for learning low-dimensional dynamical-system models from noisy data**](https://doi.org/10.1137/21M1439729)\SIAM Journal on Scientific Computing, 2023
BibTeX
@article{Uy2023,
author= {Wayne Isaac Tan Uy and Yuepeng Wang and Yuxiao Wen and Benjamin Peherstorfer},
issn= {1064-8275},
issue= {4},
journal= {SIAM Journal on Scientific Computing},
pages= {A1462-A1490},
publisher= {SIAM},
title= {Active operator inference for learning low-dimensional dynamical-system models from noisy data},
volume= {45},
year= {2023},
}
- W. I. T. Uy, D. Hartmann, and [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en)\ [**Operator inference with roll outs for learning reduced models from scarce and low-quality data**](https://doi.org/10.1016/j.camwa.2023.06.012)\Computers \& Mathematics with Applications, 2023
BibTeX
@article{Uy2023a,
author= {Wayne Isaac Tan Uy and Dirk Hartmann and Benjamin Peherstorfer},
issn= {0898-1221},
journal= {Computers \& Mathematics with Applications},
pages= {224-239},
publisher= {Elsevier},
title= {Operator inference with roll outs for learning reduced models from scarce and low-quality data},
volume= {145},
year= {2023},
}
- Y. Filanova, I. P. Duff, P. Goyal, and [P. Benner](https://scholar.google.com/citations?user=6zcRrC4AAAAJ&hl=en)\ [**An operator inference oriented approach for linear mechanical systems**](https://doi.org/10.1016/j.ymssp.2023.110620)\Mechanical Systems and Signal Processing, 2023
BibTeX
@article{Filanova2023,
author= {Yevgeniya Filanova and Igor Pontes Duff and Pawan Goyal and Peter Benner},
issn= {0888-3270},
journal= {Mechanical Systems and Signal Processing},
pages= {110620},
publisher= {Elsevier},
title= {An operator inference oriented approach for linear mechanical systems},
volume= {200},
year= {2023},
}
- J. L. d. S. Almeida, A. C. Pires, K. F. V. Cid, and A. C. N. Junior\ [**Non-Intrusive Reduced Models based on Operator Inference for Chaotic Systems**](https://arxiv.org/abs/2206.01604)\arXiv, 2022
BibTeX
@article{Almeida2022,
author= {João Lucas de Sousa Almeida and Arthur Cancellieri Pires and Klaus Feine Vaz Cid and Alberto Costa Nogueira Junior},
journal= {arXiv},
volume= {2206.01604},
title= {Non-Intrusive Reduced Models based on Operator Inference for Chaotic Systems},
year= {2022},
}

Operator Inference Theory

BibTeX
@article{Peherstorfer2020a,
author= {Benjamin Peherstorfer},
issn= {1064-8275},
issue= {5},
journal= {SIAM Journal on Scientific Computing},
pages= {A3489-A3515},
publisher= {SIAM},
title= {Sampling low-dimensional markovian dynamics for preasymptotically recovering reduced models from data with operator inference},
volume= {42},
year= {2020},
}
- [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Stability domains for quadratic-bilinear reduced-order models**](https://doi.org/10.1137/20M1364849)\SIAM Journal on Applied Dynamical Systems, 2021
BibTeX
@article{Kramer2021,
author= {Boris Kramer},
issn= {1536-0040},
issue= {2},
journal= {SIAM Journal on Applied Dynamical Systems},
pages= {981-996},
publisher= {SIAM},
title= {Stability domains for quadratic-bilinear reduced-order models},
volume= {20},
year= {2021},
}
- W. I. T. Uy, and [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en)\ [**Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations**](https://www.esaim-m2an.org/articles/m2an/abs/2021/04/m2an200096/m2an200096.html)\ESAIM: Mathematical Modelling and Numerical Analysis, 2021
BibTeX
@article{Uy2021a,
author= {Wayne Isaac Tan Uy and Benjamin Peherstorfer},
issn= {0764-583X},
issue= {3},
journal= {ESAIM: Mathematical Modelling and Numerical Analysis},
pages= {735-761},
publisher= {EDP Sciences},
title= {Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations},
volume= {55},
year= {2021},
}

Operator Inference with structure

BibTeX
@inproceedings{Koike2024,
author= {Tomoki Koike and Elizabeth Qian},
journal= {AIAA SCITECH 2024 Forum},
pages= {1012},
title= {Energy-Preserving Reduced Operator Inference for Efficient Design and Control},
year= {2024},
}
- A. Bychkov, O. Issan, G. Pogudin, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems**](https://arxiv.org/abs/2303.10285)\arXiv, 2023
BibTeX
@article{Bychkov2023,
author= {Andrey Bychkov and Opal Issan and Gleb Pogudin and Boris Kramer},
journal= {arXiv},
title= {Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems},
volume= {2303.10285},
year= {2023},
}
- H. Sharma, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems**](https://arxiv.org/abs/2203.06361)\arXiv, 2022
BibTeX
@article{Sharma2022a,
author= {Harsh Sharma and Boris Kramer},
journal= {arXiv},
title= {Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems},
volume= {2203.06361},
year= {2022},
}
- N. Sawant, [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), and [B. Peherstorfer](https://scholar.google.com/citations?user=C81WhlkAAAAJ&hl=en)\ [**Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference**](https://doi.org/10.1016/j.cma.2022.115836)\Computer Methods in Applied Mechanics and Engineering, 2023
BibTeX
@article{Sawant2023,
author= {Nihar Sawant and Boris Kramer and Benjamin Peherstorfer},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {115836},
publisher= {Elsevier},
title= {Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference},
volume= {404},
year= {2023},
}
- P. Goyal, I. P. Duff, and [P. Benner](https://scholar.google.com/citations?user=6zcRrC4AAAAJ&hl=en)\ [**Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference**](https://arxiv.org/abs/2308.13819)\arXiv, 2023
BibTeX
@article{Goyal2023,
author= {Pawan Goyal and Igor Pontes Duff and Peter Benner},
journal= {arXiv},
volume= {arXiv:2308.13819},
title= {Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference},
year= {2023},
}
- H. Sharma, Z. Wang, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems**](https://doi.org/10.1016/j.physd.2021.133122)\Physica D: Nonlinear Phenomena, 2022
BibTeX
@article{Sharma2022,
author= {Harsh Sharma and Zhu Wang and Boris Kramer},
issn= {0167-2789},
journal= {Physica D: Nonlinear Phenomena},
pages= {133122},
publisher= {Elsevier},
title= {Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems},
volume= {431},
year= {2022},
}
- A. Gruber, and I. Tezaur\ [**Canonical and Noncanonical Hamiltonian Operator Inference**](https://doi.org/10.1016/j.cma.2023.116334)\Computer Methods in Applied Mechanics and Engineering, 2023
BibTeX
@article{Gruber2023,
author= {Anthony Gruber and Irina Tezaur},
journal= {Computer Methods in Applied Mechanics and Engineering},
volume= {416},
title= {Canonical and Noncanonical Hamiltonian Operator Inference},
year= {2023},
}
- H. Sharma, D. A. Najera-Flores, M. D. Todd, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems**](https://doi.org/10.1016/j.cma.2024.116865)\Computer Methods in Applied Mechanics and Engineering, 2024
BibTeX
@article{Sharma2024,
author= {Harsh Sharma and David A Najera-Flores and Michael D Todd and Boris Kramer},
issn= {0045-7825},
journal= {Computer Methods in Applied Mechanics and Engineering},
pages= {116865},
publisher= {Elsevier},
title= {Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems},
volume= {423},
year= {2024},
}
- Y. Geng, J. Singh, L. Ju, [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), and Z. Wang\ [**Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure**](https://arxiv.org/abs/2401.12138)\arXiv, 2024
BibTeX
@article{Geng2024,
author= {Yuwei Geng and Jasdeep Singh and Lili Ju and Boris Kramer and Zhu Wang},
journal= {arXiv},
volume= {2401.12138},
title= {Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure},
year= {2024},
}

Applications

BibTeX
@article{,
author= {Süleyman Yıldız and Pawan Goyal and Peter Benner and Bülent Karasözen},
issn= {0271-2091},
issue= {8},
journal= {International Journal for Numerical Methods in Fluids},
pages= {2803-2821},
publisher= {Wiley Online Library},
title= {Learning reduced‐order dynamics for parametrized shallow water equations from data},
volume= {93},
year= {2021},
}
- P. Jain, S. McQuarrie, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Performance comparison of data-driven reduced models for a single-injector combustion process**](https://arc.aiaa.org/doi/10.2514/6.2021-3633)\AIAA Propulsion and Energy 2021 Forum, 2021
BibTeX
@inproceedings{Jain2021,
author= {Parikshit Jain and Shane McQuarrie and Boris Kramer},
journal= {AIAA Propulsion and Energy 2021 Forum},
pages= {3633},
title= {Performance comparison of data-driven reduced models for a single-injector combustion process},
year= {2021},
}
- R. Swischuk, [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao), C. Huang, and [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en)\ [**Learning physics-based reduced-order models for a single-injector combustion process**](https://arc.aiaa.org/doi/10.2514/1.J058943)\AIAA Journal, 2020
BibTeX
@article{Swischuk2020,
author= {Renee Swischuk and Boris Kramer and Cheng Huang and Karen Willcox},
issn= {1533-385X},
issue= {6},
journal= {AIAA Journal},
pages= {2658-2672},
publisher= {American Institute of Aeronautics and Astronautics},
title= {Learning physics-based reduced-order models for a single-injector combustion process},
volume= {58},
year= {2020},
}
- [P. Benner](https://scholar.google.com/citations?user=6zcRrC4AAAAJ&hl=en), P. Goyal, J. Heiland, and I. P. Duff\ [**Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows**](https://etna.math.kent.edu/vol.56.2022/pp28-51.dir/pp28-51.pdf)\Electronic Transactions on Numerical Analysis, 2022
BibTeX
@article{Benner2020,
author= {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
journal= {Electronic Transactions on Numerical Analysis},
volume= {56},
title= {Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows},
year= {2022},
}
- O. Issan, and [B. Kramer](https://scholar.google.com/citations?user=yfmbPNoAAAAJ&hl=en&oi=ao)\ [**Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference**](https://doi.org/10.1016/j.jcp.2022.111689)\Journal of Computational Physics, 2023
BibTeX
@article{Issan2023,
author= {Opal Issan and Boris Kramer},
issn= {0021-9991},
journal= {Journal of Computational Physics},
pages= {111689},
publisher= {Elsevier},
title= {Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference},
volume= {473},
year= {2023},
}
- P. R. B. Rocha, J. L. d. S. Almeida, M. S. d. P. Gomes, and A. C. N. Junior\ [**Reduced-order modeling of the two-dimensional Rayleigh–Bénard convection flow through a non-intrusive operator inference**](https://doi.org/10.1016/j.engappai.2023.106923)\Engineering Applications of Artificial Intelligence, 2023
BibTeX
@article{Rocha2023,
author= {Pedro Roberto Barbosa Rocha and João Lucas de Sousa Almeida and Marcos Sebastião de Paula Gomes and Alberto Costa Nogueira Junior},
issn= {0952-1976},
journal= {Engineering Applications of Artificial Intelligence},
pages= {106923},
publisher= {Elsevier},
title= {Reduced-order modeling of the two-dimensional Rayleigh–Bénard convection flow through a non-intrusive operator inference},
volume= {126},
year= {2023},
}
- B. G. Zastrow, A. Chaudhuri, [K. Willcox](https://scholar.google.com/citations?user=axvGyXoAAAAJ&hl=en), A. S. Ashley, and M. C. Henson\ [**Data-driven Model Reduction via Operator Inference for Coupled Aeroelastic Flutter**](https://arc.aiaa.org/doi/10.2514/6.2023-0330)\AIAA Scitech 2023 Forum, 2023
BibTeX
@inproceedings{Zastrow2023,
author= {Benjamin G Zastrow and Anirban Chaudhuri and Karen Willcox and Anthony S Ashley and Michael C Henson},
journal= {AIAA Scitech 2023 Forum},
pages= {0330},
title= {Data-driven Model Reduction via Operator Inference for Coupled Aeroelastic Flutter},
year= {2023},
}

Other

Back to Willcox-Research-Group/rom-operator-inference-Python3

Operator Inference: a brief mathematical summary of Operator Inference and some of its extensions.

Installation: getting set up with pip and/or git.

API Reference: complete rom_operator_inference documentation.

Index of Notation: list of notation used in the package and the documentation.

References: list of publications that use or build on Operator Inference.

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