Allegro machine learned interatomic potential for silica up to 15000 K

This repository contains the data, scripts, and configurations used for the active learning of a machine learning interatomic potential (using the Allegro architecture) for amorphous silica, trained on DFT data at the r2SCAN level of theory.

Overview

We train an interatomic potential for silica by iteratively sampling configurations using molecular dynamics and retraining the model on an increasingly large set of structures. The reference electronic structure calculations were performed using VASP with the r2SCAN meta-GGA functional.

File Structure

20241108_silica_active_learning_r2scan_v4.ipynb: The main driver script for the active learning loop. It defines the initial systems, the VASP calculator settings, the NequIP/Allegro trainer settings, and the LAMMPS sampler settings. It manages the iterative process of training, sampling, and labeling.

compute_single_atom_energies.ipynb: A standalone script used to compute the reference energies of isolated Silicon and Oxygen atoms. These energies are necessary for normalizing the total energies during model training.

allegro_input_v4.yaml: The configuration file for the Allegro model architecture and training hyperparameters.

active_learning_analysis.ipynb: A notebook for analyzing the progress of the active learning loop, including training/validation set growth, parity plots (energy, forces, virial), and uncertainty calibration analysis.

sampler_analysis.ipynb: A notebook for analyzing the sampling phase, specifically checking LAMMPS log files for simulation temperatures, lengths, and halt conditions.

al_out_allegro_v4/: The main output directory containing the data and results for each iteration of the active learning loop. This includes:

Trained models

Sampled structures

VASP calculation outputs

Training/validation datasets

encut_sensitivity_analysis/: Contains VASP calculations and an analysis notebook (dataset_analysis.ipynb) performing convergence tests for the plane-wave energy cutoff (ENCUT). Calculations are performed at varying ENCUT values (e.g., 800, 1000, 1200, 1400, 1600 eV) to assess the impact on pressure (Pulay stress) and forces, justifying the choice of 1000 eV for the main dataset generation.

initial_system_generation/: Contains the initial structures used to start the active learning process (e.g., alpha-quartz, beta-cristobalite, coesite, and amorphous structures).

single_atom_energies/: Output directory for the single atom energy calculations.

templates/: LAMMPS input templates used for various sampling strategies (melt, quench, shear, tension).

silica_fracture_data/: data + scripts to reproduce crack velocity, fracture surface energy, crack tip temperature and eleastic properties figures of the paper about fracture simulations using the present silica potential

Methodology

Active Learning Workflow

The workflow is orchestrated by the 20241108_silica_active_learning_r2scan_v4.ipynb notebook using the hyal framework. The methodology is based on the approach described in:

Cezar, H. M., Bodenstein, T., Sveinsson, H. A., et al. "Learning atomic forces from uncertainty-calibrated adversarial attacks." npj Comput Mater 11, 200 (2025). https://doi.org/10.1038/s41524-025-01703-5

Key steps include:

Initialization: Starting with a set of crystalline silica structures.

Training: An ensemble of Allegro models is trained on the available labeled data.

Sampling: The ensemble is used to drive Molecular Dynamics (MD) simulations (using LAMMPS). The simulations employ various protocols (melt, melt-quench, mechanical deformation) to explore the configuration space.

Configurational refinement: Selected configurations are driven to moderate model disagreement (uncertainty) .

Labeling: The selected configurations are calculated using VASP (r2SCAN) to obtain ground truth energies, forces, and virials.

Loop: The new data is added to the training set, and the cycle repeats.

Electronic Structure Details (VASP)

Functional: r2SCAN (Meta-GGA)

Pre-convergence: PBE (relaxed constraints)

Plane Wave Cutoff: 1000 eV

Precision: Accurate

Machine Learning Model (Allegro)

Architecture: Allegro (E(3)-equivariant local interaction neural network)

Cutoff Radius: 5.5 Å

L_max: 1 (Full O(3) parity)

Layers: 1 tensor product layer

Features: 64 tensor features

Optimization: Adam optimizer with ReduceLROnPlateau scheduler

Requirements

The scripts rely on several Python packages and external software:

Python Libraries: hyal, hyif, hyset (internal/project-specific wrappers), ase, nequip, numpy, pandas, matplotlib, lammps_logfile.

External Software:

VASP (for DFT calculations)

LAMMPS (with Allegro/NequIP pair style support for MD sampling)

Single Atom Energies

The compute_single_atom_energies.ipynb script calculates the reference energies for isolated atoms.

Box size: 15.0 x 15.0 x 15.0 Å

Species: Si, O

Method: Same VASP settings as the main active learning loop.