Computationally Trackable and Transferable Validation of MLIPs for Moiré Materials through Topologically-Exhaustive 1D Moiré Paths

Due to their inherent structural complexity, moiré materials exhibit emergent structural and optoelectronic properties governed by long-range physics that are often intractable from first-principles methods. While machine-learned (ML) interatomic potentials (MLIPs) have successfully been employed to predict the structural properties of complex materials, it is hard to rigorously validate them on moiré materials given the large difference in the length scales of the ML descriptors and emergent moiré domains. This work introduces an approach utilizing one-dimensional (1D) periodic moiré systems as a computationally feasible surrogate model to validate the accuracy of MLIPs for moiré materials. By constructing 1D systems with continuous stacking disregistry and arbitrary, topologically inequivalent paths, our method efficiently samples the distinct paths through the entire configuration space, enabling accurate modeling of critical large-scale moiré physics.

We also develop an approach based on the Wasserstein (Earth Mover's Distance) metric to quantify the global dissimilarity between two moiré structures by evaluating the optimal transformation required to align their stacking configuration distributions. Importantly, we rigorously show that a particular MLIP's ability to describe 1D moiré materials strongly correlates with its ability to describe 2D moiré materials.

These results show that our proposed 1D surrogate approach is a practical tool for assessing the quality of MLIPs for moiré materials, which is critical for the accurate prediction of other moiré physics phenomena, such as electronic confinement effects, thermal dynamics, and electron correlations, seamlessly bridging theory and experiment.