Machine-Learning Interatomic Potentials for Charge-Density-Wave Phases in mono- and bilayers NbSe₂

Niobium diselenide (NbSe₂) exhibits intertwined superconducting and charge-density-wave (CDW) phases that persist to the monolayer limit. Modeling these collective distortions and their vibrational signatures poses a major challenge for first-principles methods, especially in large or incommensurate cells. We develop machine-learning interatomic potentials (MLIPs) based on the E(3)-equivariant Allegro architecture, trained to capture subtle CDW energetics, structural reconstructions, and lattice dynamics in mono- and bilayer NbSe₂. [1] The models accurately reproduce CDW stability and its sensitivity to stacking and layer number, while targeted extensions address the more demanding prediction of phonon spectra and their temperature dependence through the stochastic self-consistent harmonic approximation (SSCHA). Beyond achieving quantitative fidelity, our study identifies key dataset and hyperparameter choices that govern MLIP transferability. These models provide an efficient foundation for exploring CDW phenomena across dimensionalities and underpin a follow-up study on twisted bilayers, where moiré superlattices introduce a new degree of freedom to engineer CDW order.

[1] Norma Rivano et al. Exploring Charge Density Waves in NbSe₂ with Machine Learning arXiv.2504.13675 (2025)