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Physics-informed learning of governing equations from scarce data

Nature communications, 2021-10, Vol.12 (1), p.6136-6136, Article 6136 [Peer Reviewed Journal]

2021. The Author(s). ;The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;The Author(s) 2021 ;ISSN: 2041-1723 ;EISSN: 2041-1723 ;DOI: 10.1038/s41467-021-26434-1 ;PMID: 34675223

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  • Title:
    Physics-informed learning of governing equations from scarce data
  • Author: Chen, Zhao ; Liu, Yang ; Sun, Hao
  • Subjects: Artificial neural networks ; Boundary conditions ; Complex systems ; Computer applications ; Datasets ; Differential equations ; Embedding ; Learning ; Machine learning ; Mathematical models ; Neural networks ; Nonlinear systems ; Parameter identification ; Partial differential equations ; Physics ; Robustness (mathematics)
  • Is Part Of: Nature communications, 2021-10, Vol.12 (1), p.6136-6136, Article 6136
  • Description: Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.
  • Publisher: England: Nature Publishing Group
  • Language: English
  • Identifier: ISSN: 2041-1723
    EISSN: 2041-1723
    DOI: 10.1038/s41467-021-26434-1
    PMID: 34675223
  • Source: PubMed (Medline)
    ProQuest Central
    DOAJ Directory of Open Access Journals
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