NbSe2 Charge Density Waves with Machine-Learned Interatomic Potentials This archive contains the datasets, machine-learned interatomic potentials (MLIPs), and input files used in: Rivano et al., "Exploring Charge Density Waves in two-dimensional NbSe2 with Machine Learning", npj Computational Materials (2026). ---------------------------------------- OVERVIEW ---------------------------------------- This repository provides: - Density functional theory (DFT) datasets (structures, energies, and forces) used for training and validation - Machine-learned interatomic potentials (MLIPs) based on the Allegro architecture - Example training input files, including a `allegro_training_example.yaml ` configuration file - Main input files for atomistic simulations using Quantum ESPRESSO and LAMMPS - Main outputs used to generate the main results and figures of the paper The archive is organized to enable reproducibility of key results, including charge density wave (CDW) energetics, structural properties, and temperature-dependent behavior. ---------------------------------------- REPOSITORY STRUCTURE ---------------------------------------- ├── datasets/ DFT datasets used for training and validation (see Table S1 of the Supplementary Information) ├── models/ Trained MLIPs and example training input (train.yaml) ├── inputs/ Input files for Quantum ESPRESSO (DFT) and LAMMPS (MLIP simulations) ├── results/ Processed outputs and data used to generate the main figures ├── pseudo/ Pseudopotentials used in DFT calculations ├── README.txt ---------------------------------------- DATA AND INPUT FILES ---------------------------------------- The DFT data included in this archive serve as reference data for the development and validation of the machine-learned interatomic potentials. These datasets include atomic structures, total energies, and atomic forces. The final results reported in the manuscript are obtained primarily using the trained MLIPs, with selected comparisons to DFT. Multiple models are provided, each trained for a specific task (e.g., structural energetics or vibrational properties, monolayer or bilayer systems). Corresponding datasets and training details are described in Table S1 of the Supplementary Information. An example training input file is included. Users should adapt the hyperparameters and datasets for each model as described in the main text and Supplementary Information. ---------------------------------------- INPUTS AND RESULTS ---------------------------------------- The `inputs/` folder contains: - Quantum ESPRESSO input files used to generate the reference DFT data for the main phases discussed in the paper - LAMMPS input files and structures used to perform simulations with the trained MLIPs, including: - parity checks (MLIP vs DFT) for the monolayer - critical temperature simulations for the monolayer - coexistence simulations between CDW phases for the monolayer The `results/` folder contains the main outputs obtained using the trained MLIPs, including: - Structural properties (coexistence and incommensurate supercells, monolayer) - Vibrational properties (phonons), organized by monolayer and bilayer - Processed data used to generate the figures shown in the paper ---------------------------------------- REFERENCES ---------------------------------------- Allegro: Musaelian, A., Batzner, S., Johansson, A., Sun, L., Owen, C. J., Kornbluth, M., & Kozinsky, B. "Learning local equivariant representations for large-scale atomistic dynamics." Nature Communications 14, 579 (2023). FLARE: Vandermause, J., Torrisi, S. B., Batzner, S., Xie, Y., Sun, L., Kolpak, A. M., & Kozinsky, B. "On-the-fly active learning of interpretable Bayesian force fields for atomistic rare events." npj Computational Materials 6, 20 (2020).