Codes

System identification via CUR-factored Hankel approximation

Implements the Eigensystem Realization Algorithm (era.m) from Kung where the Hankel matrix is approximated via CUR-factorization. Example is the same as in the paper. If you are only interested in CUR code, you can use crossApprox.m and maxvol.m

  • Download from GitHub at https://github.com/bokramer/CURERA (Matlab implementation)
  • Reference:
  • [01]
    System identification via CUR-factored Hankel approximation.
    Kramer, B. and Gorodetsky, A.
    SIAM Journal of Scientific Computing, 40(2), 848-866, 2018.
    [BibTeX] [Download]

    Bibtex

    @article{KG18ERA_CUR_Hankel,
    author = {Kramer, B. and Gorodetsky, A.},
    title = {System Identification via {CUR}-Factored {H}ankel Approximation},
    journal = {SIAM Journal on Scientific Computing},
    volume = {40},
    number = {2},
    pages = {A848--A866},
    year = {2018},
    doi = {10.1137/17M1137632}
    }

    Lifting, Transformations, and Operator Inference (OpInf)

    The operator inference frameowork was first established in [01] and we have since combined it with lifting and state transformations to be applicable to a large class of nonlinear non-polynomial systems. Here are some codes for these works:

    • The ROM Operator Inference code is available as a PyPi package: https://pypi.org/project/rom-operator-inference/. This package has some simple test problems, and builds the base for [03], but can also be used for other learning problems.
    • Matlab code of operator inference https://github.com/elizqian/operator-inference (from Elizabeth Qian's GitHub page).
    • Code for [02] at https://github.com/elizqian/transform-and-learn .
    • Code for [03] in python version from https://github.com/Willcox-Research-Group/rom-operator-inference-Python3
    • References:
    [01]
    Data-driven operator inference for non-intrusive projection-based model reduction.
    Peherstorfer, B., and Willcox, K.,
    Computer Methods in Applied Mechanics and Engineering, Vol. 306, 2016, pp. 196–215.
    [BibTeX] [Download]

    Bibtex

    @article{Peherstorfer16DataDriven,
    title = {Data-driven operator inference for nonintrusive projection-based model reduction},
    author = {Peherstorfer, B. and Willcox, K.},
    journal = {Computer Methods in Applied Mechanics and Engineering},
    volume = {306},
    pages = {196-215},
    year = {2016},
    }

    [02]
    Transform & Learn: A data-driven approach to nonlinear model reduction.
    Qian, E., Kramer, B., Marques, A., Willcox, K.
    AIAA Aviation 2019 Forum, June 2019
    [BibTeX] [Download]

    Bibtex

    @inbook{QKMW_2019_transform_and_learn,
    title={Transform & Learn: A data-driven approach to nonlinear model reduction},
    author={Qian, Elizabeth and Kramer, Boris and Marques, Alexandre and Willcox, Karen},
    booktitle = {AIAA Aviation 2019 Forum},
    chapter = {},
    pages = {},
    doi = {10.2514/6.2019-3707},
    URL = {https://doi.org/10.2514/6.2019-3707}
    }

    [03]
    Learning physics-based reduced-order models for a single-injector combustion process.
    Swischuk, R., Kramer, B., Huang, C., Willcox, K.
    AIAA Journal 58:6, 2658-2672, 2020
    [BibTeX] [arxiv] [download]

    Bibtex

    @article{SKHW2020_learning_ROMs_combustor,
    title = {Learning physics-based reduced-order models for a single-injector combustion process},
    author = {Swischuk, R. and Kramer, B. and Huang, C. and Willcox, K.},
    journal = {AIAA Journal},
    volume = {58:6},
    pages = {2658--2672},
    url = {https://doi.org/10.2514/1.J058943},
    year = {2020}
    }