  Predicting the dynamic behaviors of particles in suspension subject to
hydrodynamic interaction (HI) and external drive can be critical for many
applications. By harvesting advanced deep learning techniques, the present work
introduces a new framework, hydrodynamic interaction graph neural network
(HIGNN), for inferring and predicting the particles' dynamics in Stokes
suspensions. It overcomes the limitations of traditional approaches in
computational efficiency, accuracy, and/or transferability. In particular, by
uniting the data structure represented by a graph and the neural networks with
learnable parameters, the HIGNN constructs surrogate modeling for the mobility
tensor of particles which is the key to predicting the dynamics of particles
subject to HI and external forces. To account for the many-body nature of HI,
we generalize the state-of-the-art GNN by introducing higher-order connectivity
into the graph and the corresponding convolutional operation. For training the
HIGNN, we only need the data for a small number of particles in the domain of
interest, and hence the training cost can be maintained low. Once constructed,
the HIGNN permits fast predictions of the particles' velocities and is
transferable to suspensions of different numbers/concentrations of particles in
the same domain and to any external forcing. It has the ability to accurately
capture both the long-range HI and short-range lubrication effects. We
demonstrate the accuracy, efficiency, and transferability of the proposed HIGNN
framework in a variety of systems. The requirement on computing resource is
minimum: most simulations only require a desktop with one GPU; the simulations
for a large suspension of 100,000 particles call for up to 6 GPUs.
