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 moir'e domains. Here, we introduce a split machine-learned interatomic potential and dataset curation approach that separates intralayer and interlayer interactions and significantly improves model accuracy -- with a tenfold increase in energy and force prediction accuracy relative to conventional models. We further demonstrate that traditional MLIP validation metrics -- force and energy errors -- are inadequate for moir'e structures and develop a more holistic, physically-motivated metric based on the distribution of stacking configurations. This metric effectively compares the entirety of large-scale moir'e domains between two structures instead of relying on conventional measures evaluated on smaller commensurate cells. Finally, we establish that one-dimensional instead of two-dimensional moir'e structures can serve as efficient surrogate systems for validating MLIPs, allowing for a practical model validation protocol 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 seamlessly with various intralayer and interlayer interaction models, enabling computationally tractable relaxation of moir'e materials, from bilayer to complex multilayers, with rigorously validated accuracy.