Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing

• URL: http://arxiv.org/abs/2510.03046v1
• Date: Fri, 03 Oct 2025 14:28:10 GMT
• Title: Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing
• Authors: Soohaeng Yoo Willow, Tae Hyeon Park, Gi Beom Sim, Sung Wook Moon, Seung Kyu Min, D. ChangMo Yang, Hyun Woo Kim, Juho Lee, Chang Woo Myung,
• Abstract summary: Current equis struggle with uncertainty, limiting their reliability for active learning, calibration, and out-of-distribution detection.<n>We address these challenges by developing Bayesian E(3)variants with iterative restratification of many-body message passing.<n>Our approach introduces the joint energy-force negative log-likelihood (NLL$_textJEF$) loss function, which explicitly establishes uncertainty in both energies and interatomic forces.<n>We demonstrate that NLL$_textJEF$ facilitates efficient active learning by quantifying energy and force.
• Score: 11.101638985590002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Machine learning potentials (MLPs) have become essential for large-scale atomistic simulations, enabling ab initio-level accuracy with computational efficiency. However, current MLPs struggle with uncertainty quantification, limiting their reliability for active learning, calibration, and out-of-distribution (OOD) detection. We address these challenges by developing Bayesian E(3) equivariant MLPs with iterative restratification of many-body message passing. Our approach introduces the joint energy-force negative log-likelihood (NLL$_\text{JEF}$) loss function, which explicitly models uncertainty in both energies and interatomic forces, yielding superior accuracy compared to conventional NLL losses. We systematically benchmark multiple Bayesian approaches, including deep ensembles with mean-variance estimation, stochastic weight averaging Gaussian, improved variational online Newton, and laplace approximation by evaluating their performance on uncertainty prediction, OOD detection, calibration, and active learning tasks. We further demonstrate that NLL$_\text{JEF}$ facilitates efficient active learning by quantifying energy and force uncertainties. Using Bayesian active learning by disagreement (BALD), our framework outperforms random sampling and energy-uncertainty-based sampling. Our results demonstrate that Bayesian MLPs achieve competitive accuracy with state-of-the-art models while enabling uncertainty-guided active learning, OOD detection, and energy/forces calibration. This work establishes Bayesian equivariant neural networks as a powerful framework for developing uncertainty-aware MLPs for atomistic simulations at scale.

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