main.bib

@book{brunton2022data,
  title={Data-driven science and engineering: Machine learning, dynamical systems, and control},
  author={Brunton, Steven L and Kutz, J Nathan},
  year={2022},
  publisher={Cambridge University Press}
}
@book{kutz2016dynamic,
  title={Dynamic mode decomposition: data-driven modeling of complex systems},
  author={Kutz, J Nathan and Brunton, Steven L and Brunton, Bingni W and Proctor, Joshua L},
  year={2016},
  publisher={SIAM}
}

@article{jonker2020efficient,
  title={Efficient robust parameter identification in generalized kalman smoothing models},
  author={Jonker, Jonathan and Zheng, Peng and Aravkin, Aleksandr Y},
  journal={IEEE Transactions on Automatic Control},
  volume={66},
  number={10},
  pages={4852--4857},
  year={2020},
  publisher={IEEE}
}
@article{aravkin2012robust,
  title={Robust and Trend-following Kalman Smoothers using Student's t},
  author={Aravkin, Aleksandr and Burke, James V and Pillonetto, Gianluigi},
  journal={IFAC Proceedings Volumes},
  volume={45},
  number={16},
  pages={1215--1220},
  year={2012},
  publisher={Elsevier}
}
@article{jonker2019fast,
  title={Fast robust methods for singular state-space models},
  author={Jonker, Jonathan and Aravkin, Aleksandr and Burke, James V and Pillonetto, Gianluigi and Webster, Sarah},
  journal={Automatica},
  volume={105},
  pages={399--405},
  year={2019},
  publisher={Elsevier}
}
@article{zheng2018unified,
  title={A unified framework for sparse relaxed regularized regression: SR3},
  author={Zheng, Peng and Askham, Travis and Brunton, Steven L and Kutz, J Nathan and Aravkin, Aleksandr Y},
  journal={IEEE Access},
  volume={7},
  pages={1404--1423},
  year={2018},
  publisher={IEEE}
}
@misc{ichinaga2024pydmd,
      title={PyDMD: A Python package for robust dynamic mode decomposition},
      author={Sara M. Ichinaga and Francesco Andreuzzi and Nicola Demo and Marco Tezzele and Karl Lapo and Gianluigi Rozza and Steven L. Brunton and J. Nathan Kutz},
      year={2024},
      eprint={2402.07463},
      archivePrefix={arXiv},
      primaryClass={stat.CO}
}
@article{Schaeffer2017,
   author = {Hayden Schaeffer and Scott G Mccalla},
   doi = {10.1103/PhysRevE.96.023302},
   journal = {PHYSICAL REVIEW E},
   pages = {23302},
   title = {Sparse model selection via integral terms},
   volume = {96},
   year = {2017},
}
@article{gao2022bayesian,
  title={Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants},
  author={Gao, L and Kutz, J Nathan},
  journal={arXiv preprint arXiv:2211.10575},
  year={2022}
}
@article{gao2023convergence,
  title={Convergence of uncertainty estimates in ensemble and Bayesian sparse model discovery},
  author={Gao, L and Fasel, Urban and Brunton, Steven L and Kutz, J Nathan},
  journal={arXiv preprint arXiv:2301.12649},
  year={2023}
}
@article{cranmer2020discovering,
   author = {Miles Cranmer and Alvaro Sanchez-Gonzalez and Peter Battaglia and Rui Xu and Kyle Cranmer and David Spergel and Shirley Ho},
   journal = { Advances in Neural Information Processing Systems 33},
   title = {Discovering Symbolic Models from Deep Learning with Inductive Biases},
   url = {https://github.com/MilesCranmer/symbolic\_},
   year = {2020},
}
@software{pysindy-experiments-2024,
author = {Stevens-Haas, Jacob and Bhangale, Yash},
license = {MIT},
month = apr,
title = {{pysindy-experiments}},
url = {https://github.com/Jacob-Stevens-Haas/gen-experiments},
version = {0.1.1},
year = {2024}
}
@article{Long2019,
   author = {Zichao Long and Yiping Lu and Bin Dong},
   doi = {10.1016/j.jcp.2019.108925},
   isbn = {2019.108925},
   journal = {Journal of Computational Physics},
   keywords = {Convolutional neural network,Dynamic system,Partial differential equations,Symbolic neural network},
   pages = {108925},
   title = {PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network},
   volume = {399},
   url = {www.elsevier.com/locate/jcp},
   year = {2019},
}
@inproceedings{Long2018,
   author = {Zichao Long and Yiping Lu and Xianzhong Ma and Bin Dong},
   booktitle = {Proceedings of the International Conference on Machine Learning},
   title = {PDE-Net: Learning PDEs from Data},
   year = {2018},
}

@article{Kaptanoglu2022,
   author = {Alan Kaptanoglu and Brian de Silva and Urban Fasel and Kadierdan Kaheman and Andy Goldschmidt and Jared Callaham and Charles Delahunt and Zachary Nicolaou and Kathleen Champion and Jean-Christophe Loiseau and J. Kutz and Steven Brunton},
   doi = {10.21105/JOSS.03994},
   issue = {69},
   journal = {Journal of Open Source Software},
   month = {1},
   note = {A summary of variants to SINDy as of late 2021. Addition of PDEs, ensembling, and a few optimizers (Trapping, FROLS, PI)},
   pages = {3994},
   publisher = {The Open Journal},
   title = {PySINDy: A comprehensive Python package for robust sparse system identification},
   volume = {7},
   year = {2022},
}
@article{messenger2021weak,
   author = {Daniel A. Messenger and David M. Bortz},
   doi = {10.1137/20M1343166},
   issn = {15403467},
   issue = {3},
   journal = {Multiscale Modeling and Simulation},
   keywords = {Adaptive grid,Data-driven model selection,Galerkin method,Generalized least squares,Nonlinear dynamics,Sparse recovery,generalized least squares,nonlinear dynamics,sparse recovery},
   pages = {1474-1497},
   publisher = {Society for Industrial and Applied Mathematics Publications},
   title = {Weak SINDy: Galerkin-based data-driven model selection},
   volume = {19},
   url = {https://doi.org/10.1137/20M1343166},
   year = {2021},
}
@article{messenger2021bweak,
   author = {Daniel A. Messenger and David M. Bortz},
   doi = {10.1016/J.JCP.2021.110525},
   issn = {10902716},
   journal = {Journal of Computational Physics},
   keywords = {Convolution,Data-driven model selection,Galerkin method,Partial differential equations,Sparse recovery,Weak solutions},
   month = {10},
   publisher = {Academic Press Inc.},
   title = {Weak SINDy for partial differential equations},
   volume = {443},
   year = {2021},
}
@article{cuomo2022scientific,
  title={Scientific machine learning through physics--informed neural networks: Where we are and what's next},
  author={Cuomo, Salvatore and Di Cola, Vincenzo Schiano and Giampaolo, Fabio and Rozza, Gianluigi and Raissi, Maziar and Piccialli, Francesco},
  journal={Journal of Scientific Computing},
  volume={92},
  number={3},
  pages={88},
  year={2022},
  publisher={Springer}
}
@article{Raissi2019,
   author = {M Raissi and P Perdikaris and G E Karniadakis},
   doi = {10.1016/j.jcp.2018.10.045},
   journal = {Journal of Computational Physics},
   keywords = {Data-driven scientific computing,Kutta methods,Machine learning,Nonlinear dynamics,Predictive modeling,Runge-},
   pages = {686-707},
   title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
   volume = {378},
   url = {www.elsevier.com/locate/jcp},
   year = {2019},
}
@article{Rudy2017,
   author = {Samuel H Rudy and Steven L Brunton and Joshua L Proctor and J Nathan Kutz},
   issue = {e1602614},
   journal = {Science Advances},
   title = {Data-driven discovery of partial differential equations},
   volume = {3},
   url = {https://www.science.org},
   year = {2017},
}

@article{Boninsegna2018,
   author = {Lorenzo Boninsegna and Feliks Nüske and Cecilia Clementi},
   doi = {10.1063/1.5018409},
   issn = {00219606},
   issue = {24},
   journal = {Journal of Chemical Physics},
   month = {6},
   pmid = {29960307},
   publisher = {American Institute of Physics Inc.},
   title = {Sparse learning of stochastic dynamical equations},
   volume = {148},
   year = {2018},
}
@article{Messenger2021,
   author = {Daniel A. Messenger and David M. Bortz},
   doi = {10.1137/20M1343166},
   issn = {15403467},
   issue = {3},
   journal = {Multiscale Modeling and Simulation},
   keywords = {Adaptive grid,Data-driven model selection,Galerkin method,Generalized least squares,Nonlinear dynamics,Sparse recovery,generalized least squares,nonlinear dynamics,sparse recovery},
   pages = {1474-1497},
   publisher = {Society for Industrial and Applied Mathematics Publications},
   title = {Weak SINDy: Galerkin-based data-driven model selection},
   volume = {19},
   url = {https://doi.org/10.1137/20M1343166},
   year = {2021},
}
@article{Kaptanoglu2023,
   author = {Alan A Kaptanoglu and Lanyue Zhang and Zachary G Nicolaou and Urban Fasel and Steven L Brunton},
   keywords = {SINDy,chaos,dynamical systems,nonlinear systems,sparse regression,system identification},
   title = {Benchmarking sparse system identification with low-dimensional chaos},
}
@article{VanBreugel2020,
   doi={10.1109/ACCESS.2020.3034077},
   author={F. {van Breugel} and J. {Nathan Kutz} and B. W. {Brunton}},
   journal={IEEE Access},
   title={Numerical differentiation of noisy data: A unifying multi-objective optimization framework},
   year={2020}
}
@article{cranmer2019learning,
   author = {Miles D Cranmer and Rui Xu and Peter Battaglia and Shirley Ho},
   journal = {33rd annual conference on Neural Information Processing Systems},
   title = {Learning Symbolic Physics with Graph Networks},
   url = {https://ml4physicalsciences.github.io/2019/files/NeurIPS\_ML4PS\_2019\_15.pdf},
   year = {2019},
}
@book{Eaton2007,
   author = {Morris L. Eaton},
   doi = {10.1214/LNMS/1196285102},
   isbn = {9780940600690},
   journal = {Lecture Notes - Monograph Series},
   publisher = {Institute of Mathematical Statistics},
   title = {Multivariate Statistics: A Vector Space Approach},
   volume = {53},
   url = {https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Multivariate-Statistics/toc/10.1214/lnms/1196285102},
   year = {2007},
   pages = {116,117},
}
@software{pysindy-experiments,
author = {Stevens-Haas, Jacob and Bhangale, Yash},
doi = {\red{tbd}},
month = feb,
title = {{Pysindy Experiments}},
url = {https://github.com/Jacob-Stevens-Haas/gen\_experiments},
version = {\red{tbd}},
year = {2024}
}

@misc{atkinson2020bayesian,
   author = {Steven Atkinson},
   title = {Bayesian Hidden Physics Models: Uncertainty Quantification for Discovery of Nonlinear Partial Differential Operators from Data},
   url = {https://arxiv.org/abs/2006.04228},
   year = {2020},
}
@article{pysindy2020joss,
   author = {Brian de Silva and Kathleen Champion and Markus Quade and Jean-Christophe Loiseau and J. Kutz and Steven Brunton},
   doi = {10.21105/JOSS.02104},
   issue = {49},
   journal = {Journal of Open Source Software},
   month = {5},
   note = {chemical reaction dynamics (Hoffmann, Fröhner, & Noé, 2019),nonlinear optics (Sorokina,thermal fluids (Loiseau, 2019),plasma convection (Dam, Brøns, Juul Rasmussen, Naulin, & Hesthaven, 2017),numerical algorithms (Thaler, Paehler, & Adams, 2019),structural modeling (Lai & Nagarajaiah, 2019)physical constraints (Loiseau & Brunton, 2018)stochastic systems (Boninsegna, Nüske, & Clementi, 2018)},
   pages = {2104},
   publisher = {The Open Journal},
   title = {PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data},
   volume = {5},
   year = {2020},
}
@article{pysindy2021joss,
   author = {Alan Kaptanoglu and Brian de Silva and Urban Fasel and Kadierdan Kaheman and Andy Goldschmidt and Jared Callaham and Charles Delahunt and Zachary Nicolaou and Kathleen Champion and Jean-Christophe Loiseau and J. Kutz and Steven Brunton},
   doi = {10.21105/JOSS.03994},
   issue = {69},
   journal = {Journal of Open Source Software},
   month = {1},
   note = {A summary of variants to SINDy as of late 2021. Addition of PDEs, ensembling, and a few optimizers (Trapping, FROLS, PI)},
   pages = {3994},
   publisher = {The Open Journal},
   title = {PySINDy: A comprehensive Python package for robust sparse system identification},
   volume = {7},
   year = {2022},
}

@InProceedings{sanchez2020learning,
  title = 	 {Learning to Simulate Complex Physics with Graph Networks},
  author =       {Sanchez-Gonzalez, Alvaro and Godwin, Jonathan and Pfaff, Tobias and Ying, Rex and Leskovec, Jure and Battaglia, Peter},
  booktitle = 	 {Proceedings of the 37th International Conference on Machine Learning},
  pages = 	 {8459--8468},
  year = 	 {2020},
  editor = 	 {III, Hal Daumé and Singh, Aarti},
  volume = 	 {119},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--18 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v119/sanchez-gonzalez20a/sanchez-gonzalez20a.pdf},
  url = 	 {https://proceedings.mlr.press/v119/sanchez-gonzalez20a.html},
}


@article{Kaptanoglu2021,
   author = {Alan A Kaptanoglu and Jared L Callaham and Aleksandr Aravkin and Christopher J Hansen and Steven L Brunton},
   doi = {10.1103/PhysRevFluids.6.094401},
   journal = {PHYSICAL REVIEW FLUIDS},
   keywords = {doi:10.1103/PhysRevFluids.6.094401 url:https://doi.org/10.1103/PhysRevFluids.6.094401},
   pages = {94401},
   title = {Promoting global stability in data-driven models of quadratic nonlinear dynamics},
   volume = {6},
   year = {2021},
}
@article{Hirsh2022,
   author = {Seth M. Hirsh and David A. Barajas-Solano and J. Nathan Kutz},
   doi = {10.1098/RSOS.211823},
   issn = {20545703},
   issue = {2},
   journal = {Royal Society Open Science},
   keywords = {Bayesian inference,model discovery,uncertainty quantification},
   publisher = {Royal Society Publishing},
   title = {Sparsifying priors for Bayesian uncertainty quantification in model discovery},
   volume = {9},
   url = {https://doi.org/10.1098/rsos.211823},
   year = {2022},
}
@article{Chartrand2011,
   author = {Rick Chartrand and L Marin and D Xiao},
   doi = {10.5402/2011/164564},
   journal = {International Scholarly Research Network ISRN Applied Mathematics},
   pages = {11},
   title = {Numerical Differentiation of Noisy,  Nonsmooth Data},
   volume = {2011},
   year = {2011},
}

@article{Callaham2021,
   author = {J. L. Callaham and J. C. Loiseau and G. Rigas and S. L. Brunton},
   doi = {10.1098/RSPA.2021.0092},
   issn = {14712946},
   issue = {2250},
   journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
   keywords = {Fokker-Planck equation,Langevin equation,data-driven modelling,sparse regression,statistical physics Keywords: system identificatio,stochastic modelling,system identification},
   month = {6},
   publisher = {Royal Society Publishing},
   title = {Nonlinear stochastic modelling with Langevin regression},
   volume = {477},
   year = {2021},
}

@book{welch1995introduction,
  title={An introduction to the Kalman filter},
  author={Welch, Greg and Bishop, Gary and others},
  year={1995},
  publisher={Chapel Hill, NC, USA}
}

@article{aravkin2017generalized,
  title={Generalized Kalman smoothing: Modeling and algorithms},
  author={Aravkin, Aleksandr and Burke, James V and Ljung, Lennart and Lozano, Aurelie and Pillonetto, Gianluigi},
  journal={Automatica},
  volume={86},
  pages={63--86},
  year={2017},
  publisher={Elsevier}
}
@article{kalman,
   author = {Kalman, R E},
   journal = {Transactions of the AMSE - Journal of Basic Engineering},
   number = {D},
   pages = {35--45},
   title = {{A New Approach to Linear Filtering and Prediction Problems}},
   volume = {82},
   year = {1960}
}
@article{north2023review,
  title={A Review of Data-Driven Discovery for Dynamic Systems},
  author={North, Joshua S and Wikle, Christopher K and Schliep, Erin M},
  journal={International Statistical Review},
  volume={91},
  number={3},
  pages={464--492},
  year={2023},
  publisher={Wiley Online Library}
}

@article{KalBuc,
   author = {Kalman, R E and Bucy, R S},
   journal = {Trans. ASME J. Basic Eng},
   keywords = {RTS smoother},
   pages = {95--108},
   title = {{New results in linear filtering and prediction theory}},
   volume = {83},
   year = {1961}
}
@INPROCEEDINGS{Barratt2020,
  author={Barratt, Shane T. and Boyd, Stephen P.},
  booktitle={2020 American Control Conference (ACC)},
  title={Fitting a Kalman Smoother to Data},
  year={2020},
  pages={1526-1531},
  keywords={Kalman filters;Covariance matrices;Smoothing methods;Tuning;Optimization;Trajectory;Measurement uncertainty},
  doi={10.23919/ACC45564.2020.9147485}}
@article{Champion2020,
   author = {Kathleen Champion and Peng Zheng and Aleksandr Y. Aravkin and Steven L. Brunton and J. Nathan Kutz},
   doi = {10.1109/ACCESS.2020.3023625},
   issn = {21693536},
   journal = {IEEE Access},
   keywords = {Nonconvex optimization,Outlier removal,Sparse regression,Systems identification},
   pages = {169259-169271},
   title = {A unified sparse optimization framework to learn parsimonious physics-informed models from data},
   volume = {8},
   year = {2020},
}
@article{Brunton2016,
   author = {Steven L Brunton and Joshua L Proctor and J Nathan Kutz},
   doi = {10.1073/pnas.1517384113},
   issue = {15},
   journal = {Proceedings of the National Academy of Sciences},
   title = {Discovering governing equations from data by sparse identification of nonlinear dynamical systems},
   volume = {113},
   year = {2016},
}
@article{Hoffmann2019,
   author = {Moritz Hoffmann and Christoph Fröhner and Frank Noé},
   doi = {10.1063/1.5066099},
   issn = {00219606},
   issue = {2},
   journal = {Journal of Chemical Physics},
   month = {1},
   pmid = {30646700},
   publisher = {American Institute of Physics Inc.},
   title = {Reactive SINDy: Discovering governing reactions from concentration data},
   volume = {150},
   year = {2019},
}
@article{Rudy2019,
   author = {Samuel H Rudy and Steven L Brunton and J Nathan Kutz},
   doi = {10.1016/j.jcp.2019.108860},
   isbn = {2019.108860},
   journal = {Journal of Computational Physics},
   keywords = {Data assimilation,Denoising,Dynamical systems,Parameter estimation},
   pages = {108860},
   title = {Smoothing and parameter estimation by soft-adherence to governing equations},
   volume = {398},
   url = {www.elsevier.com/locate/jcp},
   year = {2019},
}
@article{Guan2021,
   author = {Yifei Guan and Steven L. Brunton and Igor Novosselov},
   doi = {10.1098/rsos.202367},
   issn = {20545703},
   issue = {8},
   journal = {Royal Society Open Science},
   keywords = {Data-driven modelling,Electrohydrodynamics,Proper orthogonal decomposition,Reduced-order modelling,Sparse identification of nonlinear dynamics},
   month = {8},
   publisher = {Royal Society Publishing},
   title = {Sparse nonlinear models of chaotic electroconvection},
   volume = {8},
   year = {2021},
}
@article{Bertsimas2023,
   author = {Dimitris Bertsimas and Wes Gurnee},
   doi = {10.1007/s11071-022-08178-9},
   issn = {1573269X},
   issue = {7},
   journal = {Nonlinear Dynamics},
   keywords = {Optimization,Sparse regression,System identification},
   month = {4},
   pages = {6585-6604},
   publisher = {Springer Science and Business Media B.V.},
   title = {Learning sparse nonlinear dynamics via mixed-integer optimization},
   volume = {111},
   year = {2023},
}
@article{Fasel2022,
   author = {U. Fasel and J. N. Kutz and B. W. Brunton and S. L. Brunton},
   doi = {10.1098/RSPA.2021.0904},
   issn = {14712946},
   issue = {2260},
   journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
   keywords = {active learning,ensemble methods,model discovery,nonlinear dynamics,probabilistic forecasting,sparse regression},
   publisher = {Royal Society Publishing},
   title = {Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control},
   volume = {478},
   year = {2022},
}
@misc{Gilpin2023,
   author = {William Gilpin},
   institution = {35th Conference on Neural Information Processing Systems (NeurIPS 2021) Track on Datasets and Benchmarks},
   title = {Chaos as an interpretable benchmark for forecasting and data-driven modelling},
   url = {https://github.com/williamgilpin/dysts},
   year = {2023},
}
@misc{Stevens-Haas2022,
      title={Theoretical Advances in Current Estimation and Navigation from a Glider-Based Acoustic Doppler Current Profiler (ADCP)},
      author={Jacob Stevens-Haas and Sarah E. Webster and Aleksandr Aravkin},
      year={2022},
      month={10},
      eprint={2110.10199},
      archivePrefix={arXiv},
      primaryClass={math.OC}
}
@software{Stevens-Haas_mitosis,
   author = {Stevens-Haas, Jacob},
   license = {MIT},
   month = apr,
   title = {{mitosis}},
   url = {https://github.com/Jacob-Stevens-Haas/mitosis},
   version = {0.5.1},
   year = {2024}
}
@article{Kaptanoglu2023weak,
   author = {Alan A. Kaptanoglu and Lanyue Zhang and Zachary G. Nicolaou and Urban Fasel and Steven L. Brunton},
   doi = {10.1007/s11071-023-08525-4},
   issn = {1573269X},
   issue = {14},
   journal = {Nonlinear Dynamics},
   keywords = {Chaos,Dynamical systems,Nonlinear systems,SINDy,Sparse regression,System identification},
   month = {2},
   pages = {13143-13164},
   publisher = {Springer Science and Business Media B.V.},
   title = {Benchmarking sparse system identification with low-dimensional chaos},
   volume = {111},
   url = {https://arxiv.org/abs/2302.10787v1},
   year = {2023},
}