Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network Part II: Computational Efficiency and Scalability*

We have introduced a new framework, the hydrodynamic interaction graph neural network (HIGNN), for fast simulation of particulate suspensions. The HIGNN, once constructed, permits fast predictions of the particles' velocities and is transferable across suspensions of different numbers/concentrations of particles subject to any external forcing. The prediction cost by the HIGNN scales at O(N²) because the two-body hydrodynamic interaction (HI) not only dominates the short-range lubrication effect but also decays very slowly (O(r^-1)) in long range. As a result, we cannot presume a cutoff distance but must include all the particles when computing their velocities. The edge connections are hence built between any two vertices in the graph as an input of GNN. In this talk, we focus on how to reduce the scaling of cost down to quasi linear, i.e., O(N logN), to further accelerate the HIGNN’s computational efficiency, by leveraging the hierarchical matrix techniques.