TY - JOUR

T1 - Neural network solution to an inverse problem associated with the eigenvalues of the Stokes operator

AU - Ossandón, Sebastián

AU - Barrientos, Mauricio

AU - Reyes, Camilo

N1 - Funding Information:
Sebastián Ossandón acknowledges support from the European Union's Horizon 2020 , research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 644202 : Geophysical Exploration using Advanced Galerkin Methods (GEAGAM); C. Reyes thanks a partial support from Project Innova-Chile CORFO No. 10CEII-9007 : “CSIRO-CHILE International Centre of Excellence in Mining and Mineral Processing”, Program 3-Project 1.
Publisher Copyright:
© 2017 Académie des sciences

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

KW - Artificial neural network

KW - Eigenvalues of the Stokes operator

KW - Finite element method

KW - Inverse problems

KW - Radial basis function

KW - Viscosity and density coefficients

UR - http://www.scopus.com/inward/record.url?scp=85036528226&partnerID=8YFLogxK

U2 - 10.1016/j.crme.2017.11.006

DO - 10.1016/j.crme.2017.11.006

M3 - Article

AN - SCOPUS:85036528226

VL - 346

SP - 39

EP - 47

JO - Comptes Rendus - Mecanique

JF - Comptes Rendus - Mecanique

SN - 1631-0721

IS - 1

ER -