Machine-learned Interatomic Potentials for Alloys and Alloy Phase Diagrams

Abstract

We introduce machine-learned potentials for Ag-Pd to describe the energy of alloy configurations over a wide range of compositions. We compare two different approaches. Moment tensor potentials (MTP) are polynomial-like functions of interatomic distances and angles. The Gaussian Approximation Potential (GAP) framework uses kernel regression, and we use the Smooth Overlap of Atomic Positions (SOAP) representation of atomic neighbourhoods that consists of a complete set of rotational and permutational invariants provided by the power spectrum of the spherical Fourier transform of the neighbour density. Both types of potentials give excellent accuracy for a wide range of compositions and rival the accuracy of cluster expansion, a benchmark for this system. While both models are able to describe small deformations away from the lattice positions, SOAP-GAP excels at transferability as shown by sensible transformation paths between configurations, and MTP allows, due to its lower computational cost, the calculation of compositional phase diagrams. Given the fact that both methods perform as well as cluster expansion would but yield off-lattice models, we expect them to open new avenues in computational materials modeling for alloys.

Free energy of (CoxMn1-x)3O4 mixed phases from machine-learning-enhanced ab initio calculations

“…For this, various learning algorithms and various representations for the atomic configurations (or 'descriptors') exist which take into account rotational and translational invariance [18][19][20][21][22]. Comparisons of some of these methods can be found, highlighting their differing predictive capabilities and computational cost [23,24].…”

Rapid generation of optimal generalized Monkhorst-Pack grids

“…In the years since our previous work was published there has been increasing interest in the generation and use of generalized k-point grids [6,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Of particular note, Hart and co-workers have recently developed algorithms and released an open-source software package (GRkgridgen) for generating generalized k-point grids on the fly [27,28].…”

Efficient implementation of atom-density representations

“…Supervised and unsupervised machine learning (ML) methods are gaining increasing importance in the field of atomistic materials modeling. Supervised ML methods -in particular, those used to construct interatomic potentials (MLIPs) [1][2][3][4][5][6][7][8] , find structure-property mappings across chemical compound space [9][10][11][12] , and model the dependence on configuration and composition of experimentally relevant quantities like the dipole moment [13][14][15][16] , polarizability 17 , band structure 18,19 , and charge distribution [20][21][22] -are useful tools in the quest for predictive materials modelling, specifically the use of large, complex, quantum-accurate simulations to access experimental length and time scales [23][24][25][26][27][28][29][30][31] . Furthermore, unsupervised ML methods are gaining prominence as a way to interpret simulations of ever-increasing complexity [32][33][34][35][36][37][38] .…”

“…In some cases, different frameworks have been shown to yield comparable errors 50 , while other studies have suggested a trade-off between accuracy and computational cost, with the combination of SOAP features and Gaussian process regression (hereafter termed just SOAP-GAP) emerging as the most accurate, but also the most computationally demanding method. 29,51 In fact, the evaluation of SOAP features and their gradients can take anywhere from 10 % to 90 % (depending on the system and the parameters chosen) of the total computational cost of the energy and force evaluation in a typical molecular dynamics (MD) simulation with the SOAP-GAP method; almost all of the remaining cost is taken up by the evaluation of kernel (and its gradients) required to compute the GAP energy and forces. We therefore discuss optimization strategies aimed at reducing the computational cost of these two critical components.…”