  Graph Neural Networks (GNNs) are promising surrogates for quantum mechanical
calculations as they establish unprecedented low errors on collections of
molecular dynamics (MD) trajectories. Thanks to their fast inference times they
promise to accelerate computational chemistry applications. Unfortunately,
despite low in-distribution (ID) errors, such GNNs might be horribly wrong for
out-of-distribution (OOD) samples. Uncertainty estimation (UE) may aid in such
situations by communicating the model's certainty about its prediction. Here,
we take a closer look at the problem and identify six key desiderata for UE in
molecular force fields, three 'physics-informed' and three
'application-focused' ones. To overview the field, we survey existing methods
from the field of UE and analyze how they fit to the set desiderata. By our
analysis, we conclude that none of the previous works satisfies all criteria.
To fill this gap, we propose Localized Neural Kernel (LNK) a Gaussian Process
(GP)-based extension to existing GNNs satisfying the desiderata. In our
extensive experimental evaluation, we test four different UE with three
different backbones and two datasets. In out-of-equilibrium detection, we find
LNK yielding up to 2.5 and 2.1 times lower errors in terms of AUC-ROC score
than dropout or evidential regression-based methods while maintaining high
predictive performance.
