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A Review of Data‐Driven Discovery for Dynamic Systems

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  • Joshua S. North
  • Christopher K. Wikle
  • Erin M. Schliep

Abstract

Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work.

Suggested Citation

  • Joshua S. North & Christopher K. Wikle & Erin M. Schliep, 2023. "A Review of Data‐Driven Discovery for Dynamic Systems," International Statistical Review, International Statistical Institute, vol. 91(3), pages 464-492, December.
    • Handle: RePEc:bla:istatr:v:91:y:2023:i:3:p:464-492
    DOI: 10.1111/insr.12554
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    References listed on IDEAS

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    1. Wei, Baolei, 2022. "Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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    5. Christopher K. Wikle & Scott H. Holan, 2011. "Polynomial nonlinear spatio‐temporal integro‐difference equation models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 339-350, July.
    6. Andrew Zammit-Mangion & Tin Lok James Ng & Quan Vu & Maurizio Filippone, 2022. "Deep Compositional Spatial Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1787-1808, October.
    7. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    8. Petra Kuhnert & D.W. Gladish & C.K. Wikle, 2014. "Physically motivated scale interaction parameterization in reduced rank quadratic nonlinear dynamic spatio‐temporal models," Environmetrics, John Wiley & Sons, Ltd., vol. 25(4), pages 230-244, June.
    9. Andreas Mardt & Luca Pasquali & Hao Wu & Frank Noé, 2018. "Author Correction: VAMPnets for deep learning of molecular kinetics," Nature Communications, Nature, vol. 9(1), pages 1-1, December.
    10. Andreas Mardt & Luca Pasquali & Hao Wu & Frank Noé, 2018. "VAMPnets for deep learning of molecular kinetics," Nature Communications, Nature, vol. 9(1), pages 1-11, December.
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