Stochastic Homogenization and Uncertainty Quantification: A Data-Driven Approach

In recent years, machine learning (ML) tools have been applied to the broad majority of scientific fields, computational mechanics being one of them. In this specific field, ML methods have been devised to perform a number of descriptive, predictive and prescriptive tasks, leading to important advantages if compared to classical approaches [1]. Since the prediction of the effective mechanical properties of heterogeneous random media, like e.g. polycrystalline materials, can be computationally-intensive, data-driven approaches represent a viable alternative. In this context, the use of deep learning strategies based on artificial neural networks (NNs) has gained momentum due to their intrinsic capability of automatic feature extraction from large datasets. These algorithms do not require in fact to handle structured input data. In this work, we move from our previous results collected in [2]. By optimizing the architecture of convolutional NN-based models, we aim at predicting the scattering in the overall stiffness of polysilicon microstructures, representative of film morphologies typically found in inertial micro electro-mechanical systems. These microstructures are characterized by a small ratio between the dimension of the polycrystalline aggregate and the representative size of a single grain. As the length scale separation principle does not hold true, the homogenization procedure is to be performed over material representations referred to as statistical volume elements (SVEs). These SVEs are synthetically generated as microstructural images, obtained via regularized Voronoi tessellations, that are used to feed a Monte Carlo procedure to account for the scattering in their morphology. Each microstructure is associated to a ground-truth label, that accounts for the relevant overall stiffness and is obtained via finite element simulations. Having trained the NN with these data, the model is employed to predict the upscaled property of unseen images characterized by a different scale ratio, so that size effects in the apparent properties can be estimated.