A U-Net-based self-stitching method for generating periodic grain structures

Abstract

When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary simplification. However, the truncated structures leave nonphysical boundaries, which are detrimental to numerical modeling. Here, we propose a self-stitching algorithm for generating periodic structures, demonstrated in a grain structure. The main idea of our algorithm is to artificially add structural information between mismatched boundary pairs, using the hierarchical spatial predictions of the U-Net. The model is trained with 20,000 grain sample pairs simulated from multiphase field simulations, resulting in the successful generation of periodic grain structures as expected. Furthermore, we employ an energy-based metric, the local curvature, to highlight the quality of the generated samples. Through this metric, we determine that the optimum value of the width of the mask is 1/16 of the sample width. The algorithm provides an automatic and unbiased way to obtain periodic boundaries in grain structures and can be applied to porous microstructures in a similar way.