Turbulence Enrichment using Generative Adversarial Networks

Generative Adversarial Networks (GANs) have been widely used for generating photo-realistic images. A variant of GANs called SRGAN has also been used successfully for image super-resolution. However, when such generative models are used for physical data, the governing equations may not be obeyed by the generated data. In this work, we develop a method for generative modeling of turbulence. We incorporate a physics informed learning methodology by a modification to the loss function that tries to minimize the residuals of the governing equations for the generated data. The proposed method is demonstrated on isotropic turbulence data at Taylor Re ~ 17 obtained using a pseudospectral method on a 64^3 grid. 1260 statistically decorrelated snapshots are collected of which 920 are used to train two models: a supervised residual network and a GAN, both of which are then shown to outperform bicubic interpolation. Using the physics informed learning is also shown to significantly improve the model’s ability to respect the physical governing equations. The results of the GAN enrichment are compared to ground truth data through pointwise errors as well as statistical quantities like 3D energy spectra, longitudinal and lateral correlation functions and third order structure functions.