Prediction and control of two-dimensional decaying turbulence using generative adversarial networks

Abstract

With the recent rapid developments in machine learning (ML), several attempts have been made to apply ML methods to various fluid dynamics problems. However, the feasibility of ML for predicting turbulence dynamics has not yet been explored in detail. In this study, PredictionNet, a data-driven ML framework based on generative adversarial networks (GANs), was developed to predict two-dimensional (2D) decaying turbulence. The developed prediction model accurately predicted turbulent fields at a finite lead time of up to half the Eulerian integral time scale. In addition to the high accuracy in pointwise metrics, various turbulence statistics, such as the probability density function, spatial correlation function, and enstrophy spectrum, were accurately captured by the employed GAN. Scale decomposition was used to interpret the predictability depending on the spatial scale, and the role of latent variables in the discriminator network was investigated. The good performance of the GAN in predicting small-scale turbulence is attributed to the scale-selection capability of the latent variable. Results also revealed that the recursive applications of the prediction model yielded better predictions than single predictions for large lead times. Furthermore, by utilizing PredictionNet as a surrogate model, a control model named ControlNet was developed to identify disturbance fields that drive the time evolution of the flow field in the direction that optimises the specified objective function. Therefore, an illustrative example in which the evolution of 2D turbulence can be predicted within a finite time horizon and controlled using a GAN-based deep neural network is presented.