Fig. 3

The architecture of the (A) molecule-based and (B) atom-based uncertainty model. The network takes molecular graphs with initial atoms and bonds information as input (\({h}_{i}^{0}\)). With \(t\) iteration through D-MPNN message passing, each atom exchanges information with its neighbor atoms to generate the learned atomic fingerprints \({h}_{i}^{t}\). In (A), the learned atomic fingerprints are summed to form the learned molecular fingerprints. The molecular representation is passed into the fully-connected layer (FC Layer), and then into the mean layer (ML) and variance layer (VL), respectively, to obtain the mean \({\mu }_{m}\) and variance \({\sigma }_{m}^{2}\) of molecular property distribution \(\widehat{y}\). On the other hand, in (B), the learned atomic fingerprints are passed into the FC Layer, ML, and VL to predict the property distribution \({\widehat{y}}_{i}\) of each atom separately. The molecular property distribution \(\widehat{y}\) is obtained by aggregating \({\widehat{y}}_{i}\) of each atom in the molecule