A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features
This work offers a more computationally efficient method for predicting local stress fields in structures with microscale features, which is beneficial for engineers and material scientists.
This paper addresses the high computational cost of multiscale computational modeling by replacing traditional microscale solutions with an Encoder-Decoder Convolutional Neural Network. This CNN generates fine-scale stress corrections to coarse predictions around unresolved microscale features, and a Bayesian approach provides credible intervals for uncertainty evaluation.
Multiscale 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.