Bayesian Neural Networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials

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 and Bayesian neural networks being among the most widely used. In this work, we introduce an implementation of Bayesian neural networks with variational inference in the aenet-PyTorch framework. To evaluate their applicability to machine learning interatomic potentials, we systematically compare the performance of variational BNNs and deep ensembles on a dataset of 7,815 TiO$_{2}$ structures. The models are trained on both the full dataset and a subset to assess how variations in data representation influence predictive accuracy and uncertainty estimation. This analysis provides insights into the strengths and limitations of each approach, offering practical guidance for the development of uncertainty-aware machine learning interatomic potentials.