Physics-informed neural networks for synthesizing preferential concentration of particles in turbulent flows

Cluster and void formation are key processes in the dynamics of particle-laden turbulence. Here we consider direct numerical simulation (DNS) of inertial point particles in homogeneous isotropic turbulence at high Reynolds numbers as the database. We propose different data driven and physics-informed machine learning techniques for synthesizing preferential concentration fields. For training, we are using the enstrophy fields computed by DNS and compare the accuracy using the enstrophy either in the physical space or a sparse wavelet space representation of vorticity. We propose to use and compare autoencoder, U-net, and generative adversarial network (GAN) approaches. We assess the statistical properties of the generated fields, and we find that the best results, showing clusters and voids, are obtained with GANs. This yields interesting perspectives for reducing the computational cost of expensive DNS computations by avoiding the tracking of billions of particles. We also explore the inverse problem of synthesizing the enstrophy fields using the particle density distribution, at different Stokes numbers, as the input. Our study thus provides perspectives to use neural networks to predict the enstrophy field using particle data in experimental PIV measurements.