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Data-driven discovery of partial differential equations

Science advances, 2017-04, Vol.3 (4), p.e1602614-e1602614 [Peer Reviewed Journal]

Copyright © 2017, The Authors 2017 The Authors ;ISSN: 2375-2548 ;EISSN: 2375-2548 ;DOI: 10.1126/sciadv.1602614 ;PMID: 28508044

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  • Title:
    Data-driven discovery of partial differential equations
  • Author: Rudy, Samuel H ; Brunton, Steven L ; Proctor, Joshua L ; Kutz, J Nathan
  • Subjects: Applied Mathematics ; SciAdv r-articles
  • Is Part Of: Science advances, 2017-04, Vol.3 (4), p.e1602614-e1602614
  • Description: We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.
  • Publisher: United States: American Association for the Advancement of Science
  • Language: English
  • Identifier: ISSN: 2375-2548
    EISSN: 2375-2548
    DOI: 10.1126/sciadv.1602614
    PMID: 28508044
  • Source: PubMed Central
    DOAJ Directory of Open Access Journals
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