Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model

Recently, a novel two-phase framework named mol-infer for inference of chemical compounds with prescribed abstract structures and desired property values has been proposed. Framework mol-infer uses mixed integer linear programming (MILP) to simulate the computational process of machine learning methods and to describe the necessary and sufficient conditions to ensure such a chemical graph exists. However, because of the limit on the kinds of descriptors originated from the need for tractability in the MILP formulation, the learning performances on some datasets are not good enough. On the other hand, graph neural network (GNN) is a promising machine learning method. In this study, we develop a molecular inference framework mol-infer-GNN, that utilizes GNN as the learning method while keeping the flexibility on the abstract structure of the chemical graph to be inferred. Experimental results on the QM9 dataset show that our proposed GNN model can obtain improved performance than existing mol-infer for some properties, and can infer chemical graphs with up to 20 non-hydrogen atoms within a reasonable computational time.