Predicting rigidity and connectivity percolation in disordered particulate networks using graph neural networks

Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimized for two large-scale classification problems: the rigidity of a molecular network, and the connectivity percolation status, which is nontrivial to determine for systems with periodic boundaries. Models trained on lattice systems were found to achieve accuracies >95% for rigidity classification, with slightly lower scores for connectivity percolation due to the inherent class imbalance in the data. Dynamically generated off-lattice networks achieved consistently lower accuracies overall due to the correlated nature of the network geometry that was absent in the lattices. An open source tool is provided allowing usage of the highest-scoring trained models, and directions for future improved tools to surmount the challenges limiting accuracy in certain situations are discussed.