  We propose GrainGNN, a surrogate model for the evolution of polycrystalline
grain structure under rapid solidification conditions in metal additive
manufacturing. High fidelity simulations of solidification microstructures are
typically performed using multicomponent partial differential equations (PDEs)
with moving interfaces. The inherent randomness of the PDE initial conditions
(grain seeds) necessitates ensemble simulations to predict microstructure
statistics, e.g., grain size, aspect ratio, and crystallographic orientation.
Currently such ensemble simulations are prohibitively expensive and surrogates
are necessary.
  In GrainGNN, we use a dynamic graph to represent interface motion and
topological changes due to grain coarsening. We use a reduced representation of
the microstructure using hand-crafted features; we combine pattern finding and
altering graph algorithms with two neural networks, a classifier (for
topological changes) and a regressor (for interface motion). Both networks have
an encoder-decoder architecture; the encoder has a multi-layer transformer
long-short-term-memory architecture; the decoder is a single layer perceptron.
  We evaluate GrainGNN by comparing it to high-fidelity phase field simulations
for in-distribution and out-of-distribution grain configurations for
solidification under laser power bed fusion conditions. GrainGNN results in
80\%--90\% pointwise accuracy; and nearly identical distributions of scalar
quantities of interest (QoI) between phase field and GrainGNN simulations
compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch
on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a
single NVIDIA A100 GPU) is 150$\times$--2000$\times$ for 100-initial grain
problem. Further, using GrainGNN, we model the formation of 11,600 grains in
220 seconds on a single CPU core.
