A novel method for inference of chemical compounds with prescribed topological substructures based on integer programming

Recently, extensive studies have been done on design of chemical graphs using artificial neural networks (ANNs). However, most existing studies do not guarantee optimal or exact solutions. On the other hand, a novel framework has been proposed for design of chemical graphs using both ANNs and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector $f(G)$ of a chemical graph $G$ is introduced and a prediction function $\psi_{\mathcal{N}}$ on a chemical property $\pi$ is constructed with an ANN $\mathcal{N}$. In the second phase, given a target value $y^*$ of the chemical property $\pi$, a feature vector $x^*$ is inferred by solving an MILP formulated from the trained ANN $\mathcal{N}$ so that $\psi_{\mathcal{N}}(x^*)$ is equal to $y^*$ and then a set of chemical structures $G^*$ such that $f(G^*)= x^*$ is enumerated by a graph enumeration algorithm. Although exact solutions are guaranteed by this framework, types of chemical graphs are restricted to such classes as trees, monocyclic graphs and graphs with a specified polymer topology with cycle index up to 2. To overcome this limitation, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph.