Neural Cellular Automata for Curvature-Driven Grain Growth with GPU-Accelerated Training Data Generation

Abstract

Neural Cellular Automata (NCA) offers a promising alternative to manually defined transition rules in classic Cellular Automata (CA) models of microstructure evolution. This concept is applied in the paper to develop a robust model of microstructure evolution driven by grain boundary curvature effects. However, the effectiveness of the NCA approach depends critically on the availability of large, high-quality training datasets. For physically motivated approaches such as the curvature-driven grain boundary migration model, generating such datasets with the available CPU-based CA code at the required size is computationally excessive. Therefore, in this work, a GPU-parallelized CUDA pipeline is developed as a high-throughput data-generation engine for training the NCA model of curvature-driven grain growth. The GPU-based CA grain growth model operates on the Mason formulation, and yields speedups of 20-22× over sequential CPU execution. As a result, it allows the reduction of dataset generation for NCA from a computational bottleneck to a practical pre-processing step. For the developed NCA curvature-driven grain boundary migration model, two approaches are used and tested within the research: a convolutional mask-based NCA, and a ring-based input pre-processing solution that exploits the underlying physics’ isotropic symmetry. The NCA predictions are validated against the ground-truth results from a sequential CA grain growth model. This work demonstrates the capabilities of the two tested approaches and clearly identifies GPU-accelerated data generation as a critical step for scalable NCA-based microstructure modelling. It also provides a foundation for extending the approach to full-field static recrystallization simulations in the presence of coupled physical fields.