Active Δ-learning with universal potentials for global structure optimization

TL;DR

The paper tackles the challenge of locating global minima in complex materials using universal MLIPs, which can require data beyond the initial training set. It implements active Δ-learning by correcting a uMLIP with a Δ-model: $E_{model}(\mathcal{M}) = E_{uMLIP}(\mathcal{M}) + E_{Delta}(\mathcal{M})$, where $E_{Delta}(\mathcal{M})$ is learned as a sparse Gaussian Process Regression over SOAP descriptors. The approach couples this correction to four global-optimization strategies—RSS, BH, GOFEE, and REX—and validates on silver sulfide clusters $[\mathrm{Ag}_2\mathrm{S}]_X$ and sulfur-induced Ag surface reconstructions, using CHGNet, MACE-MP0, and MACE-MPA as uMLIPs. The findings show robust identification of DFT global minima across systems, with REX delivering the fastest practical convergence and pretraining Δ-model data markedly accelerating searches, underscoring the practical potential of combining universal potentials with active-learning corrections.

Abstract

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.

Figures (8)

• Figure 1: Schematic outlining the data collection and progression schemes of RSS, Basin Hopping, GOFEE, and REX. The key highlights the processes represented in the schematic. The conditioned acceptances, Eqs. \ref{['bh_metropolis']} and \ref{['rex_metropolis']}, of rattled and surrogate relaxed structures in Basin Hopping and REX are left out for clarity. The swapping events of REX are shown as walkers interchanging temperatures. In AGOX, this is coded as structures swapping structures.
• Figure 2: Global minimum energy structures in CHGNet, MACE-MP0, MPA, and DFT. The energies (eV) and maximum atomic forces (eV/Å) calculated in DFT are shown underneath. Green ticks and red crosses indicate if the structure identified by the universal potential matches configurationally with the DFT GM structure of the corresponding stoichiometry.
• Figure 3: Depicted are the relative energies of a subsampling of $\left[\mathrm{Ag}_2\mathrm{S}\right]_8$ structures relaxed in CHGNet, MACE-MP0, MACE-MPA and DFT. These energies are relative to the lowest energy obtained in any given potential. Structural diagrams are provided for a selection of structures according to color.
• Figure 4: Global optimization of $\left[\mathrm{Ag}_2\mathrm{S}\right]_{X}$ clusters using active $\Delta$-learning with the MACE-MP0 universal potential and employing the four search methods outlined in Section \ref{['go_methods']}. For each search 25 (100 for RSS) independent repeats were conducted and the success curves report the accumulated share of repeats that have found the GM as a function of elapsed time. The finding of the GM is determined according to a strict spectral graph decomposition.
• Figure 5: Success curves for global optimization of $\left[\mathrm{Ag}_2\mathrm{S}\right]_{X}$ using various combinations of optimization method (left to right) and uMLIP potentials (orange, blue, purple). Included are results using no uMLIP but only a repulsive prior (green) and omitting a surrogate potential altogether (black).