A Graph Neural Network Simulation of Dispersed Systems

We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119, 8459-8468 (2020) on graph network simulators, and efficiently learns the intricate dynamics of the interacting particles. Nodes and edges of the GNN correspond, respectively, to the particles with their individual properties/data (e.g., radius, position, velocity) and the pairwise interactions between the particles (e.g., electrostatics, hydrodynamics). A key contribution of our work is to account for the finite dimensions of the particles and their impact on the system dynamics. We test our GNN against a representative case study of a multidisperse mixture of two-dimensional spheres sedimenting under gravity in a liquid and interacting with each other by a Lennard-Jones potential. The present GNN framework offers a fast and accurate method for the theoretical study of complex physical systems such as field-induced behavior of colloidal suspensions and ionic liquids. Our implementation of the GNN is available on GitHub at github.com/rfjd/GNS-DispersedSystems.