Data-efficient exploration of atomic clusters via uncertainty quantification on complex potential energy surfaces

Machine learning interatomic potentials have become an effective method for exploring complex potential energy surfaces; however, their application to atomic clusters is frequently hindered by the high cost of sampling diverse isomer spaces and the difficulty in ensuring model generalizability across complex energy landscapes. While uncertainty quantification (UQ) offers a pathway to mitigate data scarcity, its efficacy in capturing continuous potential energy surface features and guiding active learning within the complex landscape of clusters remains systematically unverified. In this study, we developed and evaluated three different UQ frameworks based on advanced UQ methods and integrated with graph neural networks: Bayesian Neural Networks, Evidence Neural Networks (ENN), and Monte Carlo Dropout (MCD). We first validated these models on the MD17 dataset to establish baseline performance, followed by a rigorous assessment on complex cluster systems (Ta2N3- and LaSi24) to probe their decision-making mechanisms in high-dimensional spaces. Our results show that ENN effectively reflects data adequacy, while MCD exhibits excellent robustness, with an MSE of <0.3 eV2 in the first 20 epochs. Furthermore, active learning driven by MCD significantly reduces the computational overhead of first-principles calculations while maintaining high predictive accuracy. This study provides a physics-informed guideline for selecting UQ strategies, facilitating the autonomous and efficient discovery of stable cluster isomers.