# Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets

arXiv: https://arxiv.org/abs/2305.03804 · HTML: https://mlsanity.com/paper/2305.03804/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)

## Built on by (most cited first, 1 of 1)

- [Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems](https://mlsanity.com/paper/2604.11513/) (2026)

## Abstract (arXiv)

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.