Coherent energy and force uncertainty in deep learning force fields
Peter Bjørn Jørgensen Jonas Busk Ole Winther Mikkel N. Schmidt
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.