Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant
  Magnets
Yu Miyazaki
I present a novel equivariant neural network architecture for the large-scale
spin dynamics simulation of the Kondo lattice model. This neural network mainly
consists of tensor-product-based convolution layers and ensures two
equivariances: translations of the lattice and rotations of the spins. I
implement equivariant neural networks for two Kondo lattice models on
two-dimensional square and triangular lattices, and perform training and
validation. In the equivariant model for the square lattice, the validation
error (based on root mean squared error) is reduced to less than one-third
compared to a model using invariant descriptors as inputs. Furthermore, I
demonstrate the ability to reproduce phase transitions of skyrmion crystals in
the triangular lattice, by performing dynamics simulations using the trained
model.