Towards Computational Microscope of Chemical Order-Disorder via ML-Accelerated Monte Carlo Simulation

Abstract

Tailoring the performance of next-generation high entropy materials requires a deep understanding of the competition between entropy-driven random solid solution and enthalpy-driven chemical ordering. Investigating such order and disorder complexity demands atomistic simulations that achieve high accuracy, efficiency, and generalizability across vast spatial, temporal, and especially chemical scales. While machine learning (ML) interatomic potentials have transformed molecular dynamics, they remain limited in capturing diffusion-driven chemical evolution over long timescales. The recently introduced SMC-X method brings exciting opportunities. Realizing its full potential requires a comprehensive study, which is the focus of this work. To assess model performance, we systematically benchmark invariant and equivariant architectures using a density functional theory dataset of more than 10,000 configurations spanning seven elements: Fe, Co, Ni, Al, Ti, Ta, and V. To understand the roles of pairwise and higher-order interactions, we decouple their contributions across chemical space using an explainable machine learning approach. We also examine the impact of lattice relaxation by comparing models trained on datasets with and without structural relaxation. Our results clarify how to choose ML surrogate models for Monte Carlo simulations, bridge the gap between theory and experiment, and lay a foundation for establishing ML-accelerated Monte Carlo as a computational microscope for chemical complexity.

Figures (9)

• Figure 1: Schematics to illustrate the main topics of this work. (a) Various chemical complexities. (b) The AGE metrics for the performance of MLIP models. (c) The simulation scales as measured in terms of spatial, temporal, and chemical space. (d) A schematic of using ML-accelerated MC as a computational microscope for direct comparison with experiment, particularly atom probe tomography (APT).
• Figure 2: Parity plots of the predicted vs. DFT-calculated configurational energies for seven HEA systems using the baseline model EPI-BRR. The solid diagonal red line represents perfect agreement ($\rm{y=x}$).
• Figure 3: Heat maps of RMSE (a) and $\rm{1-R^2}$ (b) for eight different models, over different datasets. Mixing refers to combining all seven materials for training, evaluation, and testing. OOD refers to out-of-distribution test, which uses the model trained over the seven materials to test on new materials with unseen chemical compositions.
• Figure 4: Hierarchical feature importance analysis of four HEA systems (a-d) using EPI and ETI BRR models. Waterfall plots illustrating the evolution of the $\rm{R^2}$ values for both training (left) and testing (right) datasets. Each bar represents the marginal increase or decrease in $\rm{R^2}$ values relative to the preceding model iteration, with the baseline established at the 1 EPI-BRR model. Bars are color-coded by feature type.
• Figure 5: The Shapely value analysis of four HEA systems (a-d). The EPI descriptors are indexed by their nested shells and elements, while the ETI descriptors are defined by the angular orientation within element-specific triplets. The aggregated EPI and ETI of a specific element within a given coordination shell were calculated by integrating the SHAP values corresponding to its constituent EPI and ETI descriptors, respectively.