Interpolation and differentiation of alchemical degrees of freedom in machine learning interatomic potentials

TL;DR

This paper introduces a differentiable approach to interpolate and differentiate alchemical degrees of freedom in machine learning interatomic potentials, enabling efficient compositional optimization and phase stability analysis in complex materials.

Contribution

It presents a novel method to incorporate continuous alchemical variables into MLIPs, allowing smooth interpolation, gradient-based optimization, and enhanced modeling of disordered and multicomponent systems.

Findings

Enables efficient gradient calculation for compositional changes.

Allows optimization of solid solutions towards target properties.

Facilitates free energy calculations for vacancies and composition variations.

Abstract

Machine learning interatomic potentials (MLIPs) have become a workhorse of modern atomistic simulations, and recently published universal MLIPs, pre-trained on large datasets, have demonstrated remarkable accuracy and generalizability. However, the computational cost of MLIPs limits their applicability to chemically disordered systems requiring large simulation cells or to sample-intensive statistical methods. Here, we report the use of continuous and differentiable alchemical degrees of freedom in atomistic materials simulations, exploiting the fact that graph neural network MLIPs represent discrete elements as real-valued tensors. The proposed method introduces alchemical atoms with corresponding weights into the input graph, alongside modifications to the message-passing and readout mechanisms of MLIPs, and allows smooth interpolation between the compositional states of materials. The end-to-end differentiability of MLIPs enables efficient calculation of the gradient of energy with respect to the compositional weights. With this modification, we propose methodologies for optimizing the composition of solid solutions towards target macroscopic properties, characterizing order and disorder in multicomponent oxides, and conducting alchemical free energy simulations to quantify the free energy of vacancy formation and composition changes. The approach offers an avenue for extending the capabilities of universal MLIPs in the modeling of compositional disorder and characterizing the phase stability of complex materials systems.