Operator Inference literature

Operator Inference methodologies

• B. Peherstorfer, and K. Willcox
  Data-driven operator inference for nonintrusive projection-based model reduction
  Computer Methods in Applied Mechanics and Engineering, 2016
  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, B. Kramer, B. Peherstorfer, and K. Willcox
  Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
  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},
  }

• P. Benner, P. Goyal, B. Kramer, B. Peherstorfer, and K. Willcox
  Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
  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},
  }

• W. I. T. Uy, and B. Peherstorfer
  Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories
  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},
  }

• S. Yıldız, P. Goyal, P. Benner, and B. Karasözen
  Learning reduced‐order dynamics for parametrized shallow water equations from data
  International Journal for Numerical Methods in Fluids, 2021
  BibTeX

  @article{Suleyman2021,
  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},
  }

• S. A. McQuarrie, C. Huang, and K. Willcox
  Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process
  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},
  }

• P. Goyal, and P. Benner
  LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes
  arXiv, 2021
  BibTeX

  @article{goyal2021lqresnet,
  title= {LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes},
  author= {Pawan Goyal and Peter Benner},
  year= {2021},
  volume= {2103.02249},
  journal= {arXiv},
  }

• P. Benner, P. Goyal, J. Heiland, and I. P. Duff
  Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
  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},
  }

• E. Qian, I. Farcas, and K. Willcox
  Reduced operator inference for nonlinear partial differential equations
  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},
  }

• M. Guo, S. A. McQuarrie, and K. Willcox
  Bayesian operator inference for data-driven reduced-order modeling
  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},
  }

• 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
  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},
  }

• O. Issan, and B. Kramer
  Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference
  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},
  }

• S. A. McQuarrie, P. Khodabakhshi, and K. Willcox
  Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference
  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
  Operator inference for non-intrusive model reduction with quadratic manifolds
  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},
  }

• W. I. T. Uy, Y. Wang, Y. Wen, and B. Peherstorfer
  Active operator inference for learning low-dimensional dynamical-system models from noisy data
  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
  Operator inference with roll outs for learning reduced models from scarce and low-quality data
  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},
  }

• P. Benner, P. Goyal, J. Heiland, and I. P. Duff
  A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
  PAMM, 2023
  BibTeX

  @article{https://doi.org/10.1002/pamm.202200049,
  author= {Peter Benner and Pawan Goyal and Jan Heiland and Igor Pontes Duff},
  title= {A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems},
  journal= {PAMM},
  volume= {23},
  number= {1},
  year= {2023},
  }

Operator Inference theory

• B. Peherstorfer
  Sampling low-dimensional Markovian dynamics for preasymptotically recovering reduced models from data with operator inference
  SIAM Journal on Scientific Computing, 2020
  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
  Stability domains for quadratic-bilinear reduced-order models
  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
  Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
  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

• H. Sharma, Z. Wang, and B. Kramer
  Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems
  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},
  }

• Y. Filanova, I. P. Duff, P. Goyal, and P. Benner
  An operator inference oriented approach for linear mechanical systems
  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},
  }

• N. Sawant, B. Kramer, and B. Peherstorfer
  Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference
  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
  Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference
  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},
  }

• A. Gruber, and I. Tezaur
  Canonical and Noncanonical Hamiltonian Operator Inference
  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},
  }

• T. Koike, and E. Qian
  Energy-Preserving Reduced Operator Inference for Efficient Design and Control
  AIAA SCITECH 2024 Forum, 2024
  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
  Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems
  SIAM Journal of Applied Dynamical Systems, 2024
  BibTeX

  @article{Bychkov2023,
  author= {Andrey Bychkov and Opal Issan and Gleb Pogudin and Boris Kramer},
  title= {Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems},
  journal= {SIAM Journal of Applied Dynamical Systems},
  volume= {},
  pages= {},
  year= {2024},
  }

• H. Sharma, and B. Kramer
  Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems
  Physica D: Nonlinear Phenomena, 2024
  BibTeX

  @article{Sharma2022a,
  author= {Harsh Sharma and Boris Kramer},
  journal= {Physica D: Nonlinear Phenomena},
  volume= {},
  pages= {134128},
  year= {2024},
  title= {Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems},
  }

• H. Sharma, D. A. Najera-Flores, M. D. Todd, and B. Kramer
  Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems
  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, and Z. Wang
  Gradient Preserving Operator Inference: Data-Driven Reduced-Order Models for Equations with Gradient Structure
  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

• R. Swischuk, B. Kramer, C. Huang, and K. Willcox
  Learning physics-based reduced-order models for a single-injector combustion process
  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. Jain, S. McQuarrie, and B. Kramer
  Performance comparison of data-driven reduced models for a single-injector combustion process
  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},
  }

• I. Adibnazari, H. Sharma, J. C. Torralba, B. Kramer, and M. T. Tolley
  Full-Body Optimal Control of a Swimming Soft Robot Enabled by Data-Driven Model Reduction
  2023 Southern California Robotics (SCR) Symposium, 2023
  BibTeX

  @article{AdiShaTorKraTol_Soft_Robot_DDROM_SCR2023,
  author= {I. Adibnazari and H. Sharma and J. Cervera Torralba and B. Kramer and M. T. Tolley},
  journal= {2023 Southern California Robotics (SCR) Symposium},
  title= {Full-Body Optimal Control of a Swimming Soft Robot Enabled by Data-Driven Model Reduction},
  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
  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, A. S. Ashley, and M. C. Henson
  Data-driven Model Reduction via Operator Inference for Coupled Aeroelastic Flutter
  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},
  }

Surveys

• O. Ghattas, and K. Willcox
  Learning physics-based models from data: perspectives from inverse problems and model reduction
  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},
  }

• B. Kramer, B. Peherstorfer, and K. Willcox
  Learning nonlinear reduced models from data with operator inference
  Annual Review of Fluid Mechanics, 2024
  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},
  }