  Cluster and void formations are key processes in the dynamics of
particle-laden turbulence. In this work, we assess the performance of various
neural network models for synthesizing preferential concentration fields of
particles in turbulence. A database of direct numerical simulations of
homogeneous isotropic two-dimensional turbulence with one-way coupled inertial
point particles, is used to train the models using vorticity as the input to
predict the particle number density fields. We compare autoencoder, U--Net,
generative adversarial network (GAN), and diffusion model approaches, and
assess the statistical properties of the generated particle number density
fields. We find that the GANs are superior in predicting clusters and voids,
and therefore result in the best performance. Additionally, we explore a
concept of ``supersampling", where neural networks can be used to predict full
particle data using only the information of few particles, which yields
promising perspectives for reducing the computational cost of expensive DNS
computations by avoiding the tracking of millions of particles. We also explore
the inverse problem of synthesizing the enstrophy fields using the particle
number density distribution as the input at different Stokes numbers. Hence,
our study also indicates the potential use of neural networks to predict
turbulent flow statistics using experimental measurements of inertial
particles.
