Abstract
AbstractMultiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale methods use the solution of cheaper macroscale surrogates as boundary conditions to microscale sliding windows. The microscale problems remain a numerically challenging operation both in terms of implementation and cost. In this work we propose to replace the local microscale solution by an Encoder-Decoder Convolutional Neural Network that will generate fine-scale stress corrections to coarse predictions around unresolved microscale features, without prior parametrisation of local microscale problems. We deploy a Bayesian approach providing credible intervals to evaluate the uncertainty of the predictions, which is then used to investigate the merits of a selective learning framework. We will demonstrate the capability of the approach to predict equivalent stress fields in porous structures using linearised and finite strain elasticity theories.
Funder
Fonds National de la Recherche Luxembourg
H2020 European Institute of Innovation and Technology; TWINNING Project DRIVEN
H2020 Marie Sklodowska-Curie Actions
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Mechanical Engineering,Ocean Engineering,Computational Mechanics
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