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.
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@article{CRMECA_2018__346_1_39_0,
author = {Sebasti\'an Ossand\'on and Mauricio Barrientos and Camilo Reyes},
title = {Neural network solution to an inverse problem associated with the eigenvalues of the {Stokes} operator},
journal = {Comptes Rendus. M\'ecanique},
pages = {39--47},
publisher = {Elsevier},
volume = {346},
number = {1},
year = {2018},
doi = {10.1016/j.crme.2017.11.006},
language = {en},
}
TY - JOUR AU - Sebastián Ossandón AU - Mauricio Barrientos AU - Camilo Reyes TI - Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator JO - Comptes Rendus. Mécanique PY - 2018 SP - 39 EP - 47 VL - 346 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2017.11.006 LA - en ID - CRMECA_2018__346_1_39_0 ER -
%0 Journal Article %A Sebastián Ossandón %A Mauricio Barrientos %A Camilo Reyes %T Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator %J Comptes Rendus. Mécanique %D 2018 %P 39-47 %V 346 %N 1 %I Elsevier %R 10.1016/j.crme.2017.11.006 %G en %F CRMECA_2018__346_1_39_0
Sebastián Ossandón; Mauricio Barrientos; Camilo Reyes. Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator. Comptes Rendus. Mécanique, Volume 346 (2018) no. 1, pp. 39-47. doi : 10.1016/j.crme.2017.11.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.11.006/
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Sebastián Ossandón; Camilo Reyes
C. R. Méca (2016)