# Machine-learned Interatomic Potentials for Alloys and Alloy Phase Diagrams

## TL;DR

This paper develops and compares machine-learned interatomic potentials for Ag-Pd alloys, demonstrating high accuracy and transferability, which could advance computational modeling of alloy phase diagrams.

## Contribution

It introduces and evaluates two machine learning approaches, MTP and SOAP-GAP, for modeling alloy energies, showing they rival cluster expansion in accuracy and offer off-lattice modeling capabilities.

## Key findings

- Both models achieve accuracy comparable to cluster expansion.
- SOAP-GAP shows superior transferability between configurations.
- MTP enables efficient calculation of 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.