Fig. 3

Ensemble models of MLP and GNN architecture-based deep neural networks using the SEF descriptors to increase the prediction accuracy of molecular properties. a Comparison of model performance of MLP-based deep neural network with cumulative addition of different Shannon entropies to the descriptor set. Predictions of partition coefficient (logP) values of binding molecules to the p53-binding protein Mdm2 were analyzed in the triangular radar plot. A combination of MW, and Shannon entropies based on SMILES Shannon and fractional Shannon (SMILES) showed the best comparative performance (blue dash). b The 3-dimensional (3D) GNN (GCN-based) model performed better than the 2-dimensional (2D) GNN (GCN-based) model under the same training and testing conditions. When SMILES Shannon was used as an additional node feature, the performance of 3D GNN improved further. c The hybrid model of MLP and 3D GNN architectures performed better than the individual MLP or 3D GNN-based model with the same set of Shannon entropy-based node features. The relevant connection was (− 2, − 4) from MLP layers. d Schematic of the MLP-GNN hybrid network architecture which used the (− m, − n) connections from MLP layers to the dense and final model, respectively. The scaling factors of all metrics were listed in Additional file 1: Table S10 and all prediction metrics were averaged over at least 5 independent runs