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A finite element reduced‐order model based on adaptive mesh refinement and artificial neural networks
Author(s) -
Baiges Joan,
Codina Ramon,
Castañar Inocencio,
Castillo Ernesto
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6235
Subject(s) - finite element method , polygon mesh , artificial neural network , computer science , mesh generation , nonlinear system , mixed finite element method , forcing (mathematics) , term (time) , mathematics , algorithm , structural engineering , artificial intelligence , engineering , mathematical analysis , physics , computer graphics (images) , quantum mechanics
Summary In this work, a reduced‐order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN‐ROM) is presented. The idea is to run a high‐fidelity simulation by using an adaptively refined finite element mesh and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced‐order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to nonlinear solid mechanics problems, transient quasi‐incompressible flows, and a fluid‐structure interaction problem. The results of the numerical examples show that the FAN‐ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.