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Cited by 1,557Model Reduction and Neural NetworksControl Systems and IdentificationNumerical methods for differential equations

Data-driven discovery of partial differential equations

Open access
Rudy, Samuel H., Brunton, Steven L., Proctor, Joshua L., Kutz, J. Nathan·2017·Science Advances
DOI 10.1126/sciadv.1602614PMC PMC5406137
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Abstract

Researchers propose sparse regression for identifying governing partial differential equations for spatiotemporal systems.

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Crossref · 10.1126/sciadv.1602614

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  • Variational System Identification has been applied to identify governing equations for the evolution of materials, the spatiotemporal spread of COVID-19, and constitutive models of soft materials.

    “Variational System Identification has been applied to identify governing equations for the evolution of materials17,20,19, the spatiotemporal spread of COVID-1921,18, as well as constitutive models of soft materials22,23.”

    From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [21]

    The Introduction and Materials and Methods describe discovering governing PDEs through sparse regression, not applications of Variational System Identification to materials, COVID-19, or soft-material constitutive models. Searches for those applications found no passage addressing them in our copy (page numbers unavailable). (LLM, conf=0.76)

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Cites

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Research works printed but not linked: 26

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  11. [17]Mangan N. M., Brunton S. L., Proctor J. L., Kutz J. N., Inferring biological networks by sparse identification of nonlinear dynamics. IEEE Trans. Mol. Biol. Multi-Scale Commun. 2, 52– 63 (2016).
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  14. [25]Brunton S. L., Brunton B. W., Proctor J. L., Kaiser E., Kutz J. N., Chaos as an intermittently forced linear system. arXiv:1608.05306 (2016). PMC5449398 28559566 · arXiv
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Cited by

Sorted by citations

Authors
Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N.
Affiliations
  • University of Washington (US)
  • Institute for Disease Modeling (US)
Corresponding author
Rudy, Samuel H.
ORCID
Venue
Science Advances
Publisher
American Association for the Advancement of Science (AAAS)
Published
2017-04-07
Volume
3
Issue
4
Pages
e1602614-e1602614
ISSN
2375-2548 (ISSN-L)
DOI
10.1126/sciadv.1602614
PMC
PMC5406137
OpenAlex
W2525748878
Cited by
1,557
References
3
Citations by year
2026: 167 · 2025: 221 · 2024: 214 · 2023: 218 · 2022: 223 · 2021: 205 · 2020: 167 · 2019: 106 · 2018: 27 · 2017: 8
FWCI
43.84
Type
journal article
Language
en
Open access
Licence
cc-by-nc
Locations
  • Science Advances (publishedVersion, cc-by-nc)
  • PubMed Central (publishedVersion, cc-by-nc)
  • PubMed (publishedVersion)
Funders
  • Air Force Office of Scientific Research (ID0EXLBG14923, FA9550-15-1-0385)
  • Defense Advanced Research Projects Agency (ID0EARBG14924, DARPA contract HR0011-16-C-0016, ID0EJWBG14925)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
Keywords
sparse regression, governing equations, time-series measurements, Pareto analysis, model complexity, Navier-Stokes equations, quantum harmonic oscillator, diffusion equation, Korteweg-de Vries equation, traveling waves, inverse problems

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