  We investigate the utility of deep learning for modeling the clustering of
particles that are aerodynamically coupled to turbulent fluids. Using a
Lagrangian particle module within the Athena++ hydrodynamics code, we simulate
the dynamics of particles in the Epstein drag regime within a periodic domain
of isotropic forced hydrodynamic turbulence. This setup is an idealized model
relevant to the collisional growth of micron to mm-sized dust particles in
early stage planet formation. The simulation data are used to train a U-Net
deep learning model to predict gridded three-dimensional representations of the
particle density and velocity fields, given as input the corresponding fluid
fields. The trained model qualitatively captures the filamentary structure of
clustered particles in a highly non-linear regime. We assess model fidelity by
calculating metrics of the density field (the radial distribution function) and
of the velocity field (the relative velocity and the relative radial velocity
between particles). Although trained only on the spatial fields, the model
predicts these statistical quantities with errors that are typically <10%. Our
results suggest that, given appropriately expanded training data, deep learning
could complement direct numerical simulations in predicting particle clustering
within turbulent flows.
