  The value of uncertainty quantification on predictions for trained neural
networks (NNs) on quantum chemical reference data is quantitatively explored.
For this, the architecture of the PhysNet NN was suitably modified and the
resulting model was evaluated with different metrics to quantify calibration,
quality of predictions, and whether prediction error and the predicted
uncertainty can be correlated. The results from training on the QM9 database
and evaluating data from the test set within and outside the distribution
indicate that error and uncertainty are not linearly related. The results
clarify that noise and redundancy complicate property prediction for molecules
even in cases for which changes - e.g. double bond migration in two otherwise
identical molecules - are small. The model was then applied to a real database
of tautomerization reactions. Analysis of the distance between members in
feature space combined with other parameters shows that redundant information
in the training dataset can lead to large variances and small errors whereas
the presence of similar but unspecific information returns large errors but
small variances. This was, e.g., observed for nitro-containing aliphatic chains
for which predictions were difficult although the training set contained
several examples for nitro groups bound to aromatic molecules. This underlines
the importance of the composition of the training data and provides chemical
insight into how this affects the prediction capabilities of a ML model.
Finally, the approach put forward can be used for information-based improvement
of chemical databases for target applications through active learning
optimization.
