Inexpensive machine learning potentials are increasingly being used to speed up structural optimization and molecular dynamics simulations of materials by iteratively predicting and applying interatomic forces. In these settings, it is crucial to detect when predictions are unreliable to avoid wrong or misleading results. Here, we present a complete framework for training and recalibrating graph neural network ensemble models to produce accurate predictions of energy and forces with calibrated uncertainty estimates. The proposed method considers both epistemic and aleatoric uncertainty and the total uncertainties are recalibrated post hoc using a nonlinear scaling function to achieve good calibration on previously unseen data, without loss of predictive accuracy. The method is demonstrated and evaluated on two challenging, publicly available datasets, ANI-1x (Smith et al.) and Transition1x (Schreiner et al.), both containing diverse conformations far from equilibrium. A detailed analysis of the predictive performance and uncertainty calibration is provided. In all experiments, the proposed method achieved low prediction error and good uncertainty calibration, with predicted uncertainty correlating with expected error, on energy and forces. To the best of our knowledge, the method presented in this paper is the first to consider a complete framework for obtaining calibrated epistemic and aleatoric uncertainty predictions on both energy and forces in ML potentials.

翻译：廉价的机器学习势函数通过迭代预测并施加原子间力，正越来越多地被用于加速材料的结构优化和分子动力学模拟。在此类应用中，检测预测结果不可靠的时刻至关重要，以避免产生错误或误导性结论。本文提出了一套完整的框架，用于训练和重新校准图神经网络系综模型，使其能够生成带有校准不确定性估计的准确能量和力预测。所提出的方法同时考虑了认知不确定性和偶然不确定性，并利用非线性缩放函数对总不确定性进行事后重新校准，从而在保持预测精度的同时，实现对未见数据的良好校准。该方法在两个具有挑战性的公开数据集 ANI-1x（Smith 等人）和 Transition1x（Schreiner 等人）上得到了验证与评估，这两个数据集均包含远离平衡态的多样化构型。我们对预测性能和不确定性校准进行了详细分析。在所有实验中，所提出的方法在能量和力预测方面均达到了低预测误差和良好的不确定性校准，且预测的不确定性与预期误差相关。据我们所知，本文提出的方法是首个针对机器学习势函数中能量和力的校准认知不确定性和偶然不确定性预测而构建的完整框架。