het-GPR4Materials

Heteroscedastic Gaussian process Regression (GPR) for Atomistic Materials Modeling with Uncertainty Quantification

This repository provides a Gaussian process regression framework for predicting density functional theory (DFT) quantities—such as energies and forces—with:

• Predictive uncertainty quantification
• Support for input-dependent noise
• Accurate energy and force predictions using SOAP descriptors
• Modular design using PyTorch and Metatensor

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Motivation

Traditional atomistic machine learning models assume:

• Homoscedastic noise: constant uncertainty across configurations
• No uncertainty estimates: models give predictions but not confidence

This project addresses these gaps by introducing:

• Per-structure and per-atom noise levels (heteroscedasticity)
• Predictive variances using the GPR kernel posterior
• An error-informed approach that enables more efficient and flexible use of multi-fidelity data
• Built-in uncertainty quantification, which supports more efficient active learning workflows

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Features

• Gaussian process regression using the Subset of Regressors (SoR) method
• Efficient SOAP vectorization with gradients using featomic
• Energy and force fitting with automatic handling of gradients
• Modular training and evaluation with YAML-configurable hyperparameters

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Installation

git clone https://github.com/yourusername/het-GPR4Materials.git
cd het-GPR4Materials
pip install -r requirements.txt

File structure

.
├── gpr.py               # Core GPR model and kernel solver
├── gpr_example.ipynb    # End-to-end training + evaluation notebook
├── options.yaml         # Model, training, and dataset configuration
├── data/                # Train and test data
├── report/              # Report and slides
└── README.md