  Surrogate models driven by sizeable datasets and scientific machine-learning
methods have emerged as an attractive microstructure simulation tool with the
potential to deliver predictive microstructure evolution dynamics with huge
savings in computational costs. Taking 2D and 3D grain growth simulations as an
example, we present a completely overhauled computational framework based on
graph neural networks with not only excellent agreement to both the ground
truth phase-field methods and theoretical predictions, but enhanced accuracy
and efficiency compared to previous works based on convolutional neural
networks. These improvements can be attributed to the graph representation,
both improved predictive power and a more flexible data structure amenable to
adaptive mesh refinement. As the simulated microstructures coarsen, our method
can adaptively adopt remeshed grids and larger timesteps to achieve further
speedup. The data-to-model pipeline with training procedures together with the
source codes are provided.
