A physics-informed neural network approach to stochastic homogenization of polycrystalline materials

The scattering in the local mechanical properties of polycrystalline materials may have a huge impact on the overall response of micromachines or, generally, of microsystems. Accordingly, Monte Carlo-based stochastic procedures become necessary to assess the scattering in the response, as induced by micromechanical features and by the microfabrication process. Since the prediction of the apparent mechanical properties of heterogeneous polycrystalline materials can be computationally-intensive, data-driven approaches have been recently proposed as a viable alternative. The use of deep learning strategies based on physics-informed artificial neural networks (NNs) can be considered as one of most appealing approaches, due to their capability of feature extraction from large datasets. Moving from our previous results, in this work we discuss the optimization of the architecture of convolutional NN-based models, aiming to predict the scattering in the stiffness of small polysilicon samples, representative of the film morphologies of micro electro-mechanical systems. As the length scale separation principle does not hold true in such cases, a relatively small set of statistical volume elements (SVEs) is digitally generated via regularized Voronoi tessellations. Each microstructure is then associated to a ground-truth label, that is obtained via a numerical homogenization procedure. Once the NN has been trained with these data, the model is employed to upscale the property for any SVE, so that size effects in the apparent properties can be appropriately described