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We investigate the utility of deep learning for modeling the clustering ofparticles that are aerodynamically coupled to turbulent fluids. Using aLagrangian particle module within the Athena++ hydrodynamics code, we simulatethe dynamics of particles in the Epstein drag regime within a periodic domainof isotropic forced hydrodynamic turbulence. This setup is an idealized modelrelevant to the collisional growth of micron to mm-sized dust particles inearly stage planet formation. The simulation data are used to train a U-Netdeep learning model to predict gridded three-dimensional representations of theparticle density and velocity fields, given as input the corresponding fluidfields. The trained model qualitatively captures the filamentary structure ofclustered particles in a highly non-linear regime. We assess model fidelity bycalculating metrics of the density field (the radial distribution function) andof the velocity field (the relative velocity and the relative radial velocitybetween particles). Although trained only on the spatial fields, the modelpredicts these statistical quantities with errors that are typically <10%. Ourresults suggest that, given appropriately expanded training data, deep learningcould complement direct numerical simulations in predicting particle clusteringwithin turbulent flows.

Particle clustering in turbulence: Prediction of spatial and statistical properties with deep learning