As this is also a linear re-calibration, we will only get good calibrated uncertainties, if there is a strong linear correlation between RMSE and RMV. Figure shows an example of the error-calibration plot before and after re-calibration according to the validation set following Eqn. 8 for one of the models with λ = 0.1 (random seed = 19 for the training data split). After the re-calibration, the RMSE vs RMV plot is in agreement with perfect error-based calibration (all 95% confidence intervals of the RMSE bins overlap the identity line). For comparison, we also train some simple feed forward NNs with the same training-validation splits as for the evidential models, and analyse the LS uncertainties (details on model architecture in SI). The RMSE is similar to that of the evidential models (Table ). The uncertainty distribution fitted with Eqn. 6 have similar problematic behaviour as we observed for the LS-GCN 150k uncertainties for the logP regression models (e.g. ρ rank > ρ sim rank and slopes generally too high, see Section S4). Here, we focus on the uncertainties fitted with the more flexible linear relationship (Eqn. 7) with UQ evaluation metrics are summarized in Table In this case, the linear fit is decent but not great (R 2 =0.74). Note that some of the models with different train/validation splits show much better linear correlation with R 2 -values of 0.96 and 0.97 (Figure ). The slope and intercept are both pretty good (close to 1 and 0, respectively and from the error-based calibration plots (Figures and) we do generally see good local calibration. In particular, unlike most of the uncertainty estimates analyzed above, we do not see systematic over or underestimated uncertainties. This is also reflected in the Spearman's rank correlation coefficient (ρ rank = 0.22) which is in good agreement with the simulated value (ρ sim rank = 0.27 ± 0.06).