Learning Inter-Graph Interactions Between Heterogeneous Substructures of Chemical Systems

Accurate prediction of the physicochemical properties of molecular mixtures using graph neural networks remains a significant challenge, as it requires simultaneous embedding of intramolecular interactions while accounting for mixture composition (i.e., concentrations and ratios). Existing approaches are ill-equipped to emulate realistic mixture environments, where densely coupled interactions propagate across hierarchical levels - from atoms and functional groups to entire molecules - and where cross-level information exchange is continuously modulated by composition. To bridge the gap between isolated molecules and realistic chemical environments, we present ChemFlow, a novel hierarchical framework that integrates atomic, functional group, and molecular-level features, facilitating information flow across these levels to predict the behavior of complex chemical mixtures. ChemFlow employs an atomic-level feature fusion module, Chem-embed, to generate context-aware atomic representations influenced by the mixture state and atomic characteristics. Next, bidirectional group-to-molecule and molecule-to-group attention mechanisms enable ChemFlow to capture functional group interactions both within and across molecules in the mixture. By dynamically adjusting representations based on concentration and composition, ChemFlow excels at predicting concentration-dependent properties and significantly outperforms state-of-the-art models in both concentration-sensitive and concentration-independent systems. Extensive experiments demonstrate ChemFlow's superior accuracy and efficiency in modeling complex chemical mixtures.

Molecular message-passing neural networks commonly propagate chemically diverse interactions through a single graph, which may mix interaction-specific signals and require deep propagation to capture long-range effects. We introduce the Multi-level, Multi-color Graph Neural Network (MMGNN), a hierarchical framework that decomposes a molecular graph into overlapping atom-type-pair-specific subgraphs while preserving atom-level resolution. MMGNN-2D constructs chemical-colored subgraphs from covalent connectivity, whereas MMGNN-3D constructs geometric-colored subgraphs from spatial proximity and augments their edges with distance, angular, and torsional descriptors. Both variants apply a shared communicative message-passing backbone to each subgraph and combine the resulting representations through atom-wise aggregation and molecular readout. We evaluated MMGNN on five classification and three regression benchmarks from MoleculeNet using common scaffold splits and five independent runs. MMGNN-2D achieved the highest macro-average AUC-ROC of 0.838 across the classification datasets and the lowest RMSE on ESOL (0.803). MMGNN-3D obtained the highest mean AUC-ROC on BBBP (0.956) and the lowest RMSE on FreeSolv (1.793), indicating complementary strengths of topological and geometric representations. Structural and leave-one-out analyses further illustrate how the subgraph decomposition affects learned representations and atom-type-pair sensitivities. These results support overlapping interaction-specific graph decomposition as a competitive strategy for molecular property prediction.

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.