# Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

arXiv: https://arxiv.org/abs/2312.01415 · HTML: https://mlsanity.com/paper/2312.01415/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 83 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra](https://mlsanity.com/paper/1705.05907/) (2017)
- [Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials](https://mlsanity.com/paper/2109.07421/) (2021)
- [Fast and Sample-Efficient Interatomic Neural Network Potentials for Molecules and Materials Based on Gaussian Moments](https://mlsanity.com/paper/2109.09569/) (2021)
- [Machine learning enables long time scale molecular photodynamics simulations](https://mlsanity.com/paper/1811.09112/) (2018)

## Abstract (arXiv)

We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm-1 and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.