In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely used modeling approach involves predicting both a mean and variance for each energy value. However, this model is not differentiable under the usual white noise assumption, so energy uncertainty does not naturally translate to force uncertainty. In this work we propose a machine learning potential energy model in which energy and force aleatoric uncertainty are linked through a spatially correlated noise process. We demonstrate our approach on an equivariant messages passing neural network potential trained on energies and forces on two out-of-equilibrium molecular datasets. Furthermore, we also show how to obtain epistemic uncertainties in this setting based on a Bayesian interpretation of deep ensemble models.

翻译：在原子系统的机器学习能量势中，力通常通过能量函数对原子位置的负导数获得。为量化预测能量中的偶然不确定性，一种广泛使用的建模方法涉及对每个能量值同时预测均值和方差。然而，该模型在通常的白噪声假设下不可微，因此能量不确定性无法自然转化为力不确定性。本文提出一种机器学习势能模型，其中能量和力的偶然不确定性通过空间相关噪声过程相互关联。我们基于等变消息传递神经网络势，在两个非平衡分子数据集上验证了该方法，该势函数同时针对能量和力进行训练。此外，我们还展示了如何基于深度集成模型的贝叶斯解释，在此设置下获得认知不确定性。