Revealing nanostructures in high-entropy alloys via machine-learning accelerated scalable Monte Carlo simulation

First-principles Monte Carlo (MC) simulations at finite temperatures are computationally prohibitive for large systems due to the high cost of quantum calculations and poor parallelizability of sequential Markov chains in MC algorithms. We introduce scalable Monte Carlo at eXtreme (SMC-X), a generalized checkerboard algorithm designed to accelerate MC simulation with arbitrary short-range interactions, including machine learning potentials, on modern accelerator hardware. The GPU implementation, SMC-GPU, harnesses massive parallelism to enable billion-atom simulations when combined with machine-learning surrogates of density functional theory (DFT). We apply SMC-GPU to explore nanostructure evolution in two high-entropy alloys, FeCoNiAlTi and MoNbTaW, revealing diverse morphologies including nanoparticles, 3D-connected NPs, and disorder-stabilized phases. We quantify their size, composition, and morphology, and simulate an atom-probe tomography (APT) specimen for direct comparison with experiments. Our results highlight the potential of large-scale, data-driven MC simulations in exploring nanostructure evolution in complex materials, opening new avenues for computationally guided alloy design.