Fine-tuning of universal machine-learning interatomic potentials for 2D high-entropy alloys

Abstract

High-entropy alloys (HEAs) and their two-dimensional counterparts (2D-HEAs) have recently attracted attention due to their tunable properties and catalytic potential, yet their chemical complexity makes direct density functional theory (DFT) calculations computationally prohibitive. The complexity also makes training of machine-learning interatomic potentials (MLIPs) challenging, but this could possibly be overcome by employing universal MLIPs as starting point. In this work, we investigate the applicability of universal MLIP models for 2D transition metal sulfide HEAs and develop effective fine-tuning strategies. Training structures are systematically generated and selected, and the performance of universal and fine-tuned models are benchmarked against DFT. We find that all universal MLIPs employed in this work yield unsatisfactory mixing energies without fine-tuning. Applied to the experimentally synthesized (Mo,Ta,Nb,W,V)S$_2$ system, fine-tuned models based on enumerated structures can achieve near-DFT accuracy in predicting mixing energies while enabling Monte-Carlo simulations and random structure sampling at scales inaccessible to DFT.

Figures (6)

• Figure 1: Illustration of TMDC HEA structure and energetics. (a) Atomic structure of a random $10 \times 10$ supercell of (Mo,Ta,Nb,W,V)$_{0.2}$S$_2$. (b) The mixing energy as a function of concentration for all (10) possible binary alloys. (c) Mixing energy of 2-, 3-, 4-, and 5-component systems with random concentrations and configurations. The white dots and orange diamonds indicate the median values and outliers, respectively. The thick black bars represent the interquartile ranges (IQR), and the thin black lines denote the whiskers, corresponding to $1.5 \times \mathrm{IQR}$. (d) Table of the number of enumerated structures as a function of the supercell size (number of unit cells in the supercell) and the number of alloy components. The values are for single combination of elements and the numbers in parentheses refer to the number of possible element combinations [e.g., there are 10 binary combinations, as shown in panel (b)]. Bold values on the diagonal indicate equimolar structures with minimal supercell size for n-component alloy.
• Figure 2: uMLIPs (MACE, MatterSim, CHGNet) applied to benchmark databases. (a) Bar plot with MAE values of energy and (b) mixing energy for all three databases and five foundation models. (c,d) The corresponding correlation plots of energy and mixing energy.
• Figure 3: Comparison of random and enumerated models in the (Mo,Ta)S$_2$ system with gradually increasing training set size. (a) Bar plots with MAE values of energy and (b) mixing energy for a series of models on random and enumerated databases, respectively. See text for explanation of model labeling. (c) Correlation plots of mixing energy. R/E(M) refer to random/enumerated model and R/E(D) to random/enumerated database. All random/enumerated models are plotted in each panel, with the same color coding as in panels (a,b).
• Figure 4: (a) 16 fine-tuned models applied to random 2-, 3-, 4-, and 5-component alloys (Database 2). The labels on the x-axis indicate the model ID and the number of configurations in the training file. (b) Table describing the composition of training data used in fine-tuning these models. The numbers outside parentheses denote the number of alloy elements, while the numbers in the parentheses indicate the supercell sizes. (c) Illustration of the stochastic effects observed in Model 4 and its Monte Carlo annealing counterpart.
• Figure 5: Fine-tuned models applied to databases. (a) Bar plot with MAE values of energy and (b) mixing energy of 8 models (5 enumerated, 3 random) on 3 databases. (b) Correlation plots of mixing energy.