A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features

TL;DR

This paper introduces a Bayesian multiscale CNN framework that predicts local stress fields in structures with microscale features, reducing computational costs and providing uncertainty quantification for improved multiscale modeling.

Contribution

It replaces traditional microscale simulations with a CNN-based surrogate that predicts stress corrections, incorporating Bayesian methods for uncertainty estimation.

Findings

Accurately predicts stress fields in porous structures

Provides credible intervals for uncertainty quantification

Demonstrates efficiency over direct numerical simulations

Abstract

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.