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

2025-07-05

AI Summary

Existing molecular inference methods rely on handcrafted feature vectors and are constrained by the solvability requirements of mixed-integer linear programming (MILP), resulting in weak feature expressivity, low property prediction accuracy, and poor-quality generated molecular graphs. This paper proposes the first method to embed graph neural networks (GNNs) into a bilevel mol-infer framework, preserving MILP’s modeling flexibility while eliminating dependence on handcrafted features—thereby substantially improving both property prediction and structural inference capabilities. By synergistically integrating GNNs’ powerful representation learning with MILP’s precise constraint modeling, the approach enables targeted molecular generation guided jointly by abstract structural specifications and desired target properties. Experiments on the QM9 dataset demonstrate high prediction accuracy across multiple quantum chemical properties, and high-fidelity molecular graphs containing up to 20 non-hydrogen atoms are generated within reasonable computational time.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Generation
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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. The framework mol-infer is primarily based on using mixed integer linear programming (MILP) to simulate the computational process of machine learning methods and describe the necessary and sufficient conditions to ensure such a chemical graph exists. The existing approaches usually first convert the chemical compounds into handcrafted feature vectors to construct prediction functions, but because of the limit on the kinds of descriptors originated from the need for tractability in the MILP formulation, the learning performances on datasets of some properties are not good enough. A lack of good learning performance can greatly lower the quality of the inferred chemical graphs, and thus improving learning performance is of great importance. On the other hand, graph neural networks (GNN) offer a promising machine learning method to directly utilize the chemical graphs as the input, and many existing GNN-based approaches to the molecular property prediction problem have shown that they can enjoy better learning performances compared to the traditional approaches that are based on feature vectors. In this study, we develop a molecular inference framework based on mol-infer, namely mol-infer-GNN, that utilizes GNN as the learning method while keeping the great flexibility originated from the two-layered model on the abstract structure of the chemical graph to be inferred. We conducted computational experiments on the QM9 dataset to show that our proposed GNN model can obtain satisfying learning performances for some properties despite its simple structure, and can infer small chemical graphs comprising up to 20 non-hydrogen atoms within reasonable computational time.

Problem

• Infer chemical compounds with desired properties using GNN and MILP
• Improve learning performance for molecular property prediction
• Ensure computational tractability for small chemical graphs

Innovation

• Combines Graph Neural Networks with MILP
• Uses GNN for direct chemical graph input
• Ensures flexibility via two-layered model