Bayesian neural networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials
4 affiliations
- 1Institut de Química Teòrica i Computacional (IQTCUB) Universitat de Barcelona
- 2Leitat Technological Center
- 3Debye Institute for Nanomaterials Science Utrecht University
- 4ICREA (Institució Catalana de Recerca i Estudis Avançats)
Abstract
Neural-network-based machine learning interatomic potentials have emerged as powerful tools for predicting atomic energies and forces, enabling accurate and efficient simulations in atomistic modeling. A key limitation of traditional deep learning approaches, however, is their inability to provide reliable estimates of predictive uncertainty. Such uncertainty quantification is critical for assessing model reliability, especially in materials science, where often the model is applied on out-of-distribution data. Different strategies have been proposed to address this challenge, with deep ensembles (DE) and Bayesian neural networks (BNNs) being among the most widely used. In this work, we introduce an implementation of BNNs with variational inference in the ænet-PyTorch framework. To evaluate their applicability to machine learning interatomic potentials (MLIPs), we systematically compare the performance of variational BNNs (VBNNs) and DE on a dataset of 7815 TiO 2 structures, and further assess the generalizability of our conclusions on the chemically more diverse QM7 dataset of 7165 small organic molecules. The models are trained on both a full dataset and a smaller subset to assess how variations in data representation influence predictive accuracy and uncertainty estimation. Our findings reveal that, despite its more empirical and less theory-grounded nature and in addition to its lower inference cost and implementation simplicity, DE outperform VBNNs on most accuracy and uncertainty-quantification metrics across data regimes, the main exceptions being the calibration error and the energy accuracy on the chemically diverse QM7 dataset, where the BNNs are competitive or better. This analysis provides insights into the strengths and limitations of each approach, offering practical guidance for the development and evaluation of uncertainty-aware MLIPs.
Related
- Towards Out-of-Distribution Uncertainty Quantification for Machine-Learned Interatomic Potentials via Pre-Training
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- Dyna-Mat: End-to-end benchmarking of foundation machine learning interatomic potentials in finite-temperature ensembles
- AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials
- Development and Bayesian Uncertainty Quantification of Transferable Coarse-Grained Models for Carbohydrates
BibTeX
@article{farris2026bayesian,
title = {{Bayesian neural networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials}},
author = {Riccardo Farris and Emanuele Telari and Nongnuch Artrith and Konstantin M. Neyman and Albert Bruix},
journal = {Machine Learning Science and Technology},
year = {2026},
month = aug,
doi = {10.1088/2632-2153/ae9de8},
url = {https://doi.org/10.1088/2632-2153/ae9de8},
note = {CC BY},
}
RIS
TY - JOUR
TI - Bayesian neural networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials
AU - Riccardo Farris
AU - Emanuele Telari
AU - Nongnuch Artrith
AU - Konstantin M. Neyman
AU - Albert Bruix
PY - 2026
DA - 2026/08/24
JO - Machine Learning Science and Technology
DO - 10.1088/2632-2153/ae9de8
UR - https://doi.org/10.1088/2632-2153/ae9de8
AB - Neural-network-based machine learning interatomic potentials have emerged as powerful tools for predicting atomic energies and forces, enabling accurate and efficient simulations in atomistic modeling. A key limitation of traditional deep learning approaches, however, is their inability to provide reliable estimates of predictive uncertainty. Such uncertainty quantification is critical for assessing model reliability, especially in materials science, where often the model is applied on out-of-distribution data. Different strategies have been proposed to address this challenge, with deep ensembles (DE) and Bayesian neural networks (BNNs) being among the most widely used. In this work, we introduce an implementation of BNNs with variational inference in the ænet-PyTorch framework. To evaluate their applicability to machine learning interatomic potentials (MLIPs), we systematically compare the performance of variational BNNs (VBNNs) and DE on a dataset of 7815 TiO 2 structures, and further assess the generalizability of our conclusions on the chemically more diverse QM7 dataset of 7165 small organic molecules. The models are trained on both a full dataset and a smaller subset to assess how variations in data representation influence predictive accuracy and uncertainty estimation. Our findings reveal that, despite its more empirical and less theory-grounded nature and in addition to its lower inference cost and implementation simplicity, DE outperform VBNNs on most accuracy and uncertainty-quantification metrics across data regimes, the main exceptions being the calibration error and the energy accuracy on the chemically diverse QM7 dataset, where the BNNs are competitive or better. This analysis provides insights into the strengths and limitations of each approach, offering practical guidance for the development and evaluation of uncertainty-aware MLIPs.
SN - 2632-2153
ER -