# Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials

arXiv: https://arxiv.org/abs/2410.20398 · HTML: https://mlsanity.com/paper/2410.20398/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 58 references that are in the map.
- First posted on arXiv 27 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)
- [Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks](https://mlsanity.com/paper/2101.11588/) (2021)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials](https://mlsanity.com/paper/2210.04225/) (2022)
- [Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials](https://mlsanity.com/paper/2109.07421/) (2021)
- [On the Relationship between Data Efficiency and Error for Uncertainty Sampling](https://mlsanity.com/paper/1806.06123/) (2018)
- [Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning](https://mlsanity.com/paper/2003.12081/) (2020)
- [Graph Neural Network Interatomic Potential Ensembles with Calibrated Aleatoric and Epistemic Uncertainty on Energy and Forces](https://mlsanity.com/paper/2305.16325/) (2023)

## Built on by (most cited first, 1 of 1)

- [LFaB: Low fidelity as Bias for Active Learning in the chemical configuration space](https://mlsanity.com/paper/2508.15577/) (2025)

## Abstract (arXiv)

Uncertainty estimations for machine learning interatomic potentials (MLIPs) are crucial for quantifying model error and identifying informative training samples in active learning strategies. In this study, we evaluate uncertainty estimations of Gaussian process regression (GPR)-based MLIPs, including the predictive GPR standard deviation and ensemble-based uncertainties. We do this in terms of calibration and in terms of impact on model performance in an active learning scheme. We consider GPR models with Coulomb and Smooth Overlap of Atomic Positions (SOAP) representations as inputs to predict potential energy surfaces and excitation energies of molecules. Regarding calibration, we find that ensemble-based uncertainty estimations show already poor global calibration (e.g., averaged over the whole test set). In contrast, the GPR standard deviation shows good global calibration, but when grouping predictions by their uncertainty, we observe a systematical bias for predictions with high uncertainty. Although an increasing uncertainty correlates with an increasing bias, the bias is not captured quantitatively by the uncertainty. Therefore, the GPR standard deviation can be useful to identify predictions with a high bias and error but, without further knowledge, should not be interpreted as a quantitative measure for a potential error range. Selecting the samples with the highest GPR standard deviation from a fixed configuration space leads to a model that overemphasizes the borders of the configuration space represented in the fixed dataset. This may result in worse performance in more densely sampled areas but better generalization for extrapolation tasks.