Active Δ-learning with universal potentials for global structure optimization

Universal machine learning interatomic potentials (uMLIPs) have recently been formulated and shown to generalize well. When applied out-of-sample, further data collection for improvement of the uMLIPs may, however, be required. In this work we demonstrate that, whenever the envisaged use of the MLIPs is global optimization, the data acquisition can follow an active learning scheme in which a gradually updated uMLIP directs the finding of new structures, which are subsequently evaluated at the density functional theory (DFT) level. In the scheme, we augment foundation models using a Δ-model based on this new data using local SOAP-descriptors, Gaussian kernels, and a sparse Gaussian process regression model. We compare the efficacy of the approach with different global optimization algorithms, random structure search, basin hopping, a Bayesian approach with competitive candidates (GOFEE), and a replica exchange formulation (REX). We further compare several foundation models, CHGNet, MACE-MP0, and MACE-MPA. The test systems are silver-sulfur clusters and sulfur-induced surface reconstructions on Ag(111) and Ag(100). Judged by the fidelity of identifying global minima, active learning with GPR-based Δ-models appears to be a robust approach. Judged by the total CPU time spent, the REX approach stands out as being the most efficient.