Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator

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Abstract

A numerical method, based on the design of two artificial neural networks, is presented in order to approximate the viscosity and density features of fluids from the eigenvalues of the Stokes operator. The finite element method is used to solve the direct problem by training a first artificial neural network. A nonlinear map of eigenvalues of the Stokes operator as a function of the viscosity and density of the fluid under study is then obtained. This relationship is later inverted and refined by training a second artificial neural network, solving the aforementioned inverse problem. Numerical examples are presented in order to show the effectiveness and the limitations of this methodology.

Original languageEnglish
Pages (from-to)39-47
Number of pages9
JournalComptes Rendus - Mecanique
Volume346
Issue number1
DOIs
StatePublished - Jan 2018
Externally publishedYes

Keywords

  • Artificial neural network
  • Eigenvalues of the Stokes operator
  • Finite element method
  • Inverse problems
  • Radial basis function
  • Viscosity and density coefficients

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