Spectral neural network potentials for binary alloys

Abstract

In this work, we present a numerical implementation to compute the atom-centered descriptors introduced by Bartok et al. [Phys. Rev. B 87, 184115 (2013)] based on the harmonic analysis of the atomic neighbor density function. Specifically, we focus on two types of descriptors, the smooth SO(3) power spectrum with the explicit inclusion of a radial basis and the SO(4) bispectrum obtained through mapping the radial component onto a polar angle of a four dimensional hypersphere. With these descriptors, various interatomic potentials for binary Ni–Mo alloys are obtained based on linear and neural network regression models. Numerical experiments suggest that both descriptors produce similar results in terms of accuracy. For linear regression, the smooth SO(3) power spectrum is superior to the SO(4) bispectrum when a large band limit is used. In neural network regression, better accuracy can be achieved with even less number of expansion components for both descriptors. As such, we demonstrate that spectral neural network potentials are feasible choices for large scale atomistic simulations.

Machine learning for high-entropy alloys: Progress, challenges and opportunities

“…Similar to the power spectrum, more complex invariants such as bispectrum can be constructed using the radial distribution function rather than Dirac δ function and map the atomic neighbor density within r c to a sphere in four-dimensional space [153]. The power spectrum and bispectrum in four-dimensional sphere can then be used as descriptors for various regression models, including the linear SNAP [153], quadratic SNAP (qSNAP) [154], and spectral neural network potential [159].…”

PyXtal FF: a Python Library for Automated Force Field Generation

“…In the following, we will introduce four types of atomcentered descriptors in details. The corresponding derivative terms can be found in Appendix A, Appendix B and our recent work [36].…”

“…SIMPLE-NN leverages the capability of Tensorflow platform-a deep learning GPU-accelerated library, and AMP provides several other descriptors such as Zernike and bispectrum components. Our recent works also suggested that NNP can be developed using bispectrum and power spectrum components as the descriptor while training on energy, forces, and stress simultaneously [35,36]. Moreover, DeepPot-SE [37] and SchNetPack [33] packages introduce additional filters to the descriptor such as distance-chemical-species-dependent filter and continuous convolutional filter, respectively, prior to the deep learning model.…”

Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics

“…Compared to GAP, NN is more suitable for large scale simulation due to its better scalability. Very recently, we have developed the NN version of spectral neighbor analysis potential (NN-SNAP) [24][25][26][27] based on the bispectrum coefficient descriptors 15,28 and implemented them to the ML-IAP package inside the LAMMPS software 29 . To train an accurate NN-SNAP model for describing the GaN's B4-B1 transition, we start with the existing dataset from a recent work 16 .…”