  We propose Neural Cellular Automata (NCA) to simulate the microstructure
development during the solidification process in metals. Based on convolutional
neural networks, NCA can learn essential solidification features, such as
preferred growth direction and competitive grain growth, and are up to six
orders of magnitude faster than the conventional Cellular Automata (CA).
Notably, NCA delivers reliable predictions also outside their training range,
which indicates that they learn the physics of the solidification process.
While in this study we employ data produced by CA for training, NCA can be
trained based on any microstructural simulation data, e.g. from phase-field
models.
