Accurate, transferable, and verifiable machine-learned interatomic potentials for layered materials

Twisted layered van der Waals materials often exhibit unique electronic and optical properties absent in their non-twisted counterparts. Unfortunately, predicting such properties is hindered by the difficulty in determining the atomic structure in materials displaying large moiré domains. Here, we introduce a split machine-learned interatomic potential (MLIP) and dataset curation approach that separates intralayer and interlayer interactions and significantly improves model accuracy, yielding roughly a tenfold improvement in energy and force predictions relative to conventional models. We further demonstrate that traditional MLIP validation metrics - force and energy errors - are inadequate for moiré structures and develop a holistic, physically-motivated metric based on the distribution of stacking configurations. This metric effectively compares the entirety of large-scale moiré domains between two structures instead of relying on conventional measures evaluated on smaller commensurate cells. Finally, we establish that one-dimensional, rather than two-dimensional, moiré structures can serve as efficient surrogate systems for validating MLIPs, permitting validation protocols against explicit DFT calculations. Applying our framework to HfS₂/GaS bilayers reveals that accurate structural predictions directly translate into reliable electronic properties. Our model-agnostic approach integrates with various intralayer and interlayer interaction models, enabling computationally tractable relaxation of moiré materials, from bilayer to complex multilayers, with rigorously validated accuracy.