Metadata-Version: 2.1
Name: rom-operator-inference
Version: 1.2.1
Summary: Operator inference for data-driven, non-intrusive model reduction of dynamical systems.
Home-page: https://github.com/Willcox-Research-Group/rom-operator-inference-Python3
Author: Renee C. Swischuk et al.
Maintainer: Shane A. McQuarrie
Maintainer-email: shanemcq@utexas.edu
License: MIT
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        # Operator Inference in Python
        
        This is a Python implementation of Operator Inference for learning projection-based polynomial reduced-order models of dynamical systems.
        The procedure is **data-driven** and **non-intrusive**, making it a viable candidate for model reduction of "glass-box" systems.
        The methodology was introduced in [\[1\]](#references).
        
        [**See the Wiki**](https://github.com/Willcox-Research-Group/rom-operator-inference-Python3/wiki) for mathematical details and API documentation.
        See [this repository](https://github.com/Willcox-Research-Group/rom-operator-inference-MATLAB) for a MATLAB implementation.
        
        ## Quick Start
        
        ### Installation
        
        Install the package from the command line with the following single command (requires [`pip`](https://pypi.org/project/pip/)).
        ```bash
        $ python3 -m pip install --user rom-operator-inference
        ```
        [**See the wiki**](https://github.com/Willcox-Research-Group/rom-operator-inference-Python3/wiki) for other installation options.
        
        ### Usage
        
        Given a basis matrix `Vr`, snapshot data `X`, and snapshot time derivatives `Xdot`, the following code learns a reduced model for a problem of the form d**x** / dt = **c** + **Ax**(t), then solves the reduced system for 0 ≤ t ≤ 1.
        
        ```python
        import numpy as np
        import rom_operator_inference as roi
        
        # Define a model of the form  dx / dt = c + Ax(t).
        >>> model = roi.InferredContinuousROM(modelform="cA")
        
        # Fit the model to snapshot data X, the time derivatives Xdot,
        # and the linear basis Vr by solving for the operators c_ and A_.
        >>> model.fit(Vr, X, Xdot)
        
        # Simulate the learned model over the time domain [0,1] with 100 timesteps.
        >>> t = np.linspace(0, 1, 100)
        >>> x_ROM = model.predict(X[:,0], t)
        ```
        
        
        ## Examples
        
        The [`examples/`](https://github.com/Willcox-Research-Group/rom-operator-inference-Python3/tree/master/examples) folder contains scripts and notebooks that set up and run several examples:
        - [`examples/tutorial.ipynb`](https://nbviewer.jupyter.org/github/Willcox-Research-Group/rom-operator-inference-Python3/blob/master/examples/tutorial.ipynb): A walkthrough of a very simple heat equation example.
        - [`examples/heat_1D.ipynb`](https://nbviewer.jupyter.org/github/Willcox-Research-Group/rom-operator-inference-Python3/blob/master/examples/heat_1D.ipynb): A more complicated one-dimensional heat equation example [\[1\]](#references).
        - [`examples/data_driven_heat.ipynb`](https://nbviewer.jupyter.org/github/Willcox-Research-Group/rom-operator-inference-Python3/blob/master/examples/data_driven_heat.ipynb): A purely data-driven example using data generated from a one-dimensional heat equation [\[4\]](#references).
        <!-- - `examples/TODO.ipynb`: Burgers' equation [\[1\]](#references). -->
        <!-- - `examples/TODO.ipynb`: Euler equation [\[2\]](#references). -->
        <!-- This example uses MATLAB's Curve Fitting Toolbox to generate the random initial conditions. -->
        
        ---
        
        **Contributors**:
        [Renee Swischuk](https://github.com/swischuk),
        [Shane McQuarrie](https://github.com/shanemcq18),
        [Elizabeth Qian](https://github.com/elizqian),
        [Boris Kramer](http://kramer.ucsd.edu/),
        [Karen Willcox](https://kiwi.oden.utexas.edu/).
        
        
        ## References
        
        These publications introduce, build on, or use Operator Inference.
        Entries are listed chronologically.
        
        - \[1\] [Peherstorfer, B.](https://scholar.google.com/citations?user=C81WhlkAAAAJ) and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Data-driven operator inference for non-intrusive projection-based model reduction.**](https://www.sciencedirect.com/science/article/pii/S0045782516301104)
        _Computer Methods in Applied Mechanics and Engineering_, Vol. 306, pp. 196-215, 2016.
        ([Download](https://kiwi.oden.utexas.edu/papers/Non-intrusive-model-reduction-Peherstorfer-Willcox.pdf))<details><summary>BibTeX</summary><pre>
        @article{PW2016OperatorInference,
            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},
            publisher = {Elsevier}
        }</pre></details>
        
        - \[2\] [Qian, E.](https://scholar.google.com/citations?user=jnHI7wQAAAAJ), [Kramer, B.](http://kramer.ucsd.edu/), [Marques, A.](https://scholar.google.com/citations?user=d4tBWWwAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Transform & Learn: A data-driven approach to nonlinear model reduction**](https://arc.aiaa.org/doi/10.2514/6.2019-3707).
        In the AIAA Aviation 2019 Forum & Exhibition, Dallas, TX, June 2019. Paper AIAA-2019-3707.
        ([Download](https://kiwi.oden.utexas.edu/papers/learn-data-driven-nonlinear-reduced-model-Qian-Willcox.pdf))<details><summary>BibTeX</summary><pre>
        @inbook{QKMW2019TransformAndLearn,
            title     = {Transform \\& Learn: A data-driven approach to nonlinear model reduction},
            author    = {Qian, E. and Kramer, B. and Marques, A. N. and Willcox, K. E.},
            booktitle = {AIAA Aviation 2019 Forum},
            year      = {2018},
            address   = {Dallas, TX},
            note      = {Paper AIAA-2019-3707},
            doi       = {10.2514/6.2019-3707},
            URL       = {https://arc.aiaa.org/doi/abs/10.2514/6.2019-3707},
            eprint    = {https://arc.aiaa.org/doi/pdf/10.2514/6.2019-3707}
        }</pre></details>
        
        - \[3\] [Swischuk, R.](https://scholar.google.com/citations?user=L9D0LBsAAAAJ), [Mainini, L.](https://scholar.google.com/citations?user=1mo8GgkAAAAJ), [Peherstorfer, B.](https://scholar.google.com/citations?user=C81WhlkAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Projection-based model reduction: Formulations for physics-based machine learning.**](https://www.sciencedirect.com/science/article/pii/S0045793018304250)
        _Computers & Fluids_, Vol. 179, pp. 704-717, 2019.
        ([Download](https://kiwi.oden.utexas.edu/papers/Physics-based-machine-learning-swischuk-willcox.pdf))<details><summary>BibTeX</summary><pre>
        @article{SMPW2019PhysicsbasedML,
            title     = {Projection-based model reduction: Formulations for physics-based machine learning},
            author    = {Swischuk, R. and Mainini, L. and Peherstorfer, B. and Willcox, K.},
            journal   = {Computers \\& Fluids},
            volume    = {179},
            pages     = {704--717},
            year      = {2019},
            publisher = {Elsevier}
        }</pre></details>
        
        - \[4\] [Swischuk, R.](https://scholar.google.com/citations?user=L9D0LBsAAAAJ),
        [**Physics-based machine learning and data-driven reduced-order modeling**](https://dspace.mit.edu/handle/1721.1/122682).
        Master's thesis, Massachusetts Institute of Technology, 2019.
        ([Download](https://dspace.mit.edu/bitstream/handle/1721.1/122682/1123218324-MIT.pdf))<details><summary>BibTeX</summary><pre>
        @phdthesis{swischuk2019MLandDDROM,
            title  = {Physics-based machine learning and data-driven reduced-order modeling},
            author = {Swischuk, Renee},
            year   = {2019},
            school = {Massachusetts Institute of Technology}
        }</pre></details>
        
        - \[5\] [Peherstorfer, B.](https://scholar.google.com/citations?user=C81WhlkAAAAJ)
        [**Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference**](https://arxiv.org/abs/1908.11233).
        arXiv:1908.11233.
        ([Download](https://arxiv.org/pdf/1908.11233.pdf))<details><summary>BibTeX</summary><pre>
        @article{peherstorfer2019samplingMarkovian,
            title   = {Sampling low-dimensional Markovian dynamics for pre-asymptotically recovering reduced models from data with operator inference},
            author  = {Peherstorfer, Benjamin},
            journal = {arXiv preprint arXiv:1908.11233},
            year    = {2019}
        }</pre></details>
        
        - \[6\] [Swischuk, R.](https://scholar.google.com/citations?user=L9D0LBsAAAAJ), [Kramer, B.](http://kramer.ucsd.edu/), [Huang, C.](https://scholar.google.com/citations?user=lUXijaQAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Learning physics-based reduced-order models for a single-injector combustion process**](https://arc.aiaa.org/doi/10.2514/1.J058943).
        _AIAA Journal_, Vol. 58:6, pp. 2658-2672, 2020.
        Also in Proceedings of 2020 AIAA SciTech Forum & Exhibition, Orlando FL, January, 2020. Paper AIAA-2020-1411.
        Also Oden Institute Report 19-13.
        ([Download](https://kiwi.oden.utexas.edu/papers/learning-reduced-model-combustion-Swischuk-Kramer-Huang-Willcox.pdf))<details><summary>BibTeX</summary><pre>
        @article{SKHW2020ROMCombustion,
            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},
            number    = {6},
            pages     = {2658--2672},
            year      = {2020},
            publisher = {American Institute of Aeronautics and Astronautics}
        }</pre></details>
        
        - \[7\] [Qian, E.](https://scholar.google.com/citations?user=jnHI7wQAAAAJ), [Kramer, B.](http://kramer.ucsd.edu/), [Peherstorfer, B.](https://scholar.google.com/citations?user=C81WhlkAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems**](https://www.sciencedirect.com/science/article/abs/pii/S0167278919307651).
        _Physica D: Nonlinear Phenomena_, Vol. 406, May 2020, 132401.
        ([Download](https://kiwi.oden.utexas.edu/papers/lift-learn-scientific-machine-learning-Qian-Willcox.pdf))<details><summary>BibTeX</summary><pre>
        @article{QKPW2020LiftAndLearn,
            title   = {Lift \\& Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems.},
            author  = {Qian, E. and Kramer, B. and Peherstorfer, B. and Willcox, K.},
            journal = {Physica {D}: {N}onlinear {P}henomena},
            volume  = {406},
            pages   = {132401},
            url     = {https://doi.org/10.1016/j.physd.2020.132401},
            year    = {2020}
        }</pre></details>
        
        - \[8\] [Benner, P.](https://scholar.google.com/citations?user=6zcRrC4AAAAJ), [Goyal, P.](https://scholar.google.com/citations?user=9rEfaRwAAAAJ), [Kramer, B.](http://kramer.ucsd.edu/), [Peherstorfer, B.](https://scholar.google.com/citations?user=C81WhlkAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms**](https://arxiv.org/abs/2002.09726).
        arXiv:2002.09726. Also Oden Institute Report 20-04.
        ([Download](https://kiwi.oden.utexas.edu/papers/Non-intrusive-nonlinear-model-reduction-Benner-Goyal-Kramer-Peherstorfer-Willcox.pdf))<details><summary>BibTeX</summary><pre>
        @article{BGKPW2020OpInfNonPoly,
            title   = {Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms},
            author  = {Benner, P. and Goyal, P. and Kramer, B. and Peherstorfer, B. and Willcox, K.},
            journal = {arXiv preprint arXiv:2002.09726},
            year    = {2020}
        }</pre></details>
        
        - \[9\] [Yıldız, S.](https://scholar.google.com/citations?user=UVPD79MAAAAJ), [Goyal, P.](https://scholar.google.com/citations?user=9rEfaRwAAAAJ), [Benner, P.](https://scholar.google.com/citations?user=6zcRrC4AAAAJ), and [Karasözen, B.](https://scholar.google.com/citations?user=R906kj0AAAAJ),
        [**Data-driven learning of reduced-order dynamics for a parametrized shallow water equation**](https://arxiv.org/abs/2007.14079).
        arXiv:2007.14079.
        ([Download](https://arxiv.org/pdf/2007.14079.pdf))<details><summary>BibTeX</summary><pre>
        @article{SGBK2020OpInfAffine,
            title   = {Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation},
            author  = {Y{\i}ld{\i}z, S. and Goyal, P. and Benner, P. and Karas{\\"o}zen, B.},
            journal = {arXiv preprint arXiv:2007.14079},
            year    = {2020}
        }</pre></details>
        
        - \[10\] [McQuarrie, S. A.](https://scholar.google.com/citations?user=qQ6JDJ4AAAAJ), [Huang, C.](https://scholar.google.com/citations?user=lUXijaQAAAAJ), and [Willcox, K.](https://kiwi.oden.utexas.edu/),
        [**Data-driven reduced-order models via regularized operator inference for a single-injector combustion process**](https://arxiv.org/abs/2008.02862).
        arXiv:2008.02862.
        ([Download](https://arxiv.org/pdf/2008.02862.pdf))<details><summary>BibTeX</summary><pre>
        @article{MHW2020regOpInfCombustion,
            title   = {Data-driven reduced-order models via regularized operator inference for a single-injector combustion process},
            author  = {McQuarrie, S. A. and Huang, C. and Willcox, K.},
            journal = {arXiv preprint arXiv:2008.02862},
            year    = {2020}
        }</pre></details>
        
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