Temperature-Dependent Small-Molecule Solubility Prediction Using MoE-Enhanced Directed Message Passing Neural Networks

Solubility prediction is crucial for drug development and materials science, yet existing models struggle with generalizability across diverse solvents and temperatures. This study develops a novel solubility prediction model, DMPNN-MoE, which integrates a directed message passing neural network (DMPNN) with a mixture-of-experts (MoE) algorithm to address these limitations. Leveraging a curated data set of 56,945 experimental solubility values spanning 791 solutes, 140 solvents, and temperatures from 243.15 to 403.15 K, the model effectively captures molecular structural features and solute–solvent interactions. The DMPNN enhances feature extraction through directional message passing, while the MoE dynamically allocates experts to improve adaptability across diverse solute–solvent systems. Rigorous 10-fold cross-validation demonstrates superior performance (MAE = 0.256 ± 0.010, R2 = 0.863 ± 0.016), outperforming graph-based (DMPNN, MPNN-MoE, MPNN, GINE-MoE, GINE, GAT-MoE, and GAT) and descriptor-based (RDkit/Mol2vec-ANN/RF/SVR) benchmarks by up to 35%. The model retains high accuracy for unseen rare solvents (MAE = 0.341 on 2380 low-sample data) and generalizes to 12 unseen solutes across 1221 data points (MAE = 0.413), indicating robust generalization with some limitations. Feature importance evaluation further elucidates critical molecular features influencing solubility, such as three-membered ring structures and bond E/Z configurations. This work establishes a robust, interpretable model for temperature-dependent solubility prediction, with broad applications in pharmaceutical discovery and chemical engineering.