Fine-Tuned Machine-Learned Interatomic Potentials for Structural and Vibrational Properties of Twisted 2D Materials

Twisted van der Waals bilayers form moir\'e superlattices whose structural and vibrational properties are highly sensitive to variations in local stacking registry and the degree of atomic reconstruction, yet accurate atomistic modeling of these systems at the DFT level remains computationally prohibitive at small twist angles. We investigate machine-learned interatomic potentials for moir\'e systems, using twisted bilayer graphene, \textit{h}-BN, and MoS$_2$ as representative materials spanning a broad spectrum of mechanical compliance and atomic reconstruction behavior. We show that fine-tuning universal atomistic foundation models is essential to achieve DFT accuracy for layered materials, as broadly trained foundation models prove insufficient for resolving the subtle interlayer energetics that govern atomic reconstruction. Through local strain tensor analysis and the phonon band unfolding technique, our fine-tuned MACE model reveals a consistent reconstruction-induced strain landscape in all three materials, with extended low-energy stacking domains separated by narrow soliton lines where deformation concentrates. The system progressively optimizes the local stacking registry within each domain, giving rise to a spatially structured deformation field whose amplitude scales with the mechanical compliance of the material and can be further tuned by external perturbation. The obtained results of both atomic reconstructed structures and moir\'e phonon spectra present a good agreement with the reported experiments, thereby demonstrating the accuracy and efficiency of our methodology in modeling of these large scale nanomaterials.