  Graph neural networks (GNNs) have been shown to be astonishingly capable
models for molecular property prediction, particularly as surrogates for
expensive density functional theory calculations of relaxed energy for novel
material discovery. However, one limitation of GNNs in this context is the lack
of useful uncertainty prediction methods, as this is critical to the material
discovery pipeline. In this work, we show that uncertainty quantification for
relaxed energy calculations is more complex than uncertainty quantification for
other kinds of molecular property prediction, due to the effect that structure
optimizations have on the error distribution. We propose that distribution-free
techniques are more useful tools for assessing calibration, recalibrating, and
developing uncertainty prediction methods for GNNs performing relaxed energy
calculations. We also develop a relaxed energy task for evaluating uncertainty
methods for equivariant GNNs, based on distribution-free recalibration and
using the Open Catalyst Project dataset. We benchmark a set of popular
uncertainty prediction methods on this task, and show that latent distance
methods, with our novel improvements, are the most well-calibrated and
economical approach for relaxed energy calculations. Finally, we demonstrate
that our latent space distance method produces results which align with our
expectations on a clustering example, and on specific equation of state and
adsorbate coverage examples from outside the training dataset.
