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

We demonstrate 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 mmsized dust particles in early stage planet formation. The simulation data is 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 structure (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 be used to accelerate calculations of particle clustering and collision outcomes both in protoplanetary disks, and in related two-fluid turbulence problems that arise in other disciplines.

PGNets: Planet mass prediction using convolutional neural networks for radio continuum observations of protoplanetary disks

We developed Convolutional Neural Networks (CNNs) to rapidly and directly infer the planet mass from radio dust continuum images. Substructures induced by young planets in protoplanetary disks can be used to infer the potential young planets' properties. Hydrodynamical simulations have been used to study the relationships between the planet's properties and these disk features. However, these attempts either fine-tuned numerical simulations to fit one protoplanetary disk at a time, which was time-consuming, or azimuthally averaged simulation results to derive some linear relationships between the gap width/depth and the planet mass, which lost information on asymmetric features in disks. To cope with these disadvantages, we developed Planet Gap neural Networks (PGNets) to infer the planet mass from 2D images. We first fit the gridded data in Zhang et al. (2018) as a classification problem. Then, we quadrupled the data set by running additional simulations with near-randomly sampled parameters, and derived the planet mass and disk viscosity together as a regression problem. The classification approach can reach an accuracy of 92\%, whereas the regression approach can reach 1$\sigma$ as 0.16 dex for planet mass and 0.23 dex for disk viscosity. We can reproduce the degeneracy scaling $\alpha$ $\propto$ $M_p^3$ found in the linear fitting method, which means that the CNN method can even be used to find degeneracy relationship. The gradient-weighted class activation mapping effectively confirms that PGNets use proper disk features to constrain the planet mass. We provide programs for PGNets and the traditional fitting method from Zhang et al. (2018), and discuss each method's advantages and disadvantages.