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

An accurate prediction of turbulence has been very costly since it requires an infinitesimally small time step for advancing the governing equations to resolve the fast-evolving small-scale motions. With the recent development of various machine learning (ML) algorithms, the finite-time prediction of turbulence became one of promising options to relieve the computational burden. Yet, a reliable prediction of the small-scale motions is challenging. In this study, PredictionNet, a data-driven ML framework based on generative adversarial networks (GANs), was developed for fast prediction of turbulence with high accuracy down to the smallest scale using a relatively small number of parameters. In particular, we conducted learning of two-dimensional (2-D) decaying turbulence at finite lead times using direct numerical simulation data. The developed prediction model accurately predicted turbulent fields at a finite lead time of up to half the Eulerian integral time scale over which the large-scale motions remain fairly correlated. 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 and scale-interaction capability of the latent variable. Furthermore, by utilising 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.