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

Coherent energy and force uncertainty in deep learning force fields