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

arXiv: https://arxiv.org/abs/2507.03920 · HTML: https://mlsanity.com/paper/2507.03920/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 5 Jul 2025.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective](https://mlsanity.com/paper/1906.11081/) (2019)
- [FP-GNN: a versatile deep learning architecture for enhanced molecular property prediction](https://mlsanity.com/paper/2205.03834/) (2022)
- [A Universal Framework for Accurate and Efficient Geometric Deep Learning of Molecular Systems](https://mlsanity.com/paper/2311.11228/) (2023)
- [A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming](https://mlsanity.com/paper/2009.09646/) (2020)
- [Mixed-Integer Optimisation of Graph Neural Networks for Computer-Aided Molecular Design](https://mlsanity.com/paper/2312.01228/) (2023)
- [Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search](https://mlsanity.com/paper/2108.10266/) (2021)
- [Augmenting optimization-based molecular design with graph neural networks](https://mlsanity.com/paper/2312.03613/) (2023)
- [An Inverse QSAR Method Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2107.02381/) (2021)
- [Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes](https://mlsanity.com/paper/2305.00801/) (2023)

## Built on by (most cited first, 1 of 1)

- [Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming](https://mlsanity.com/paper/2605.29329/) (2026)

## Abstract (arXiv)

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.