Stochastic Analysis of LES Atmospheric Turbulence Solutions With Generative Machine Learning Models

The Large Eddy Simulations (LES) modeling of turbulence effects is computationally expensive even when not all scales are resolved, especially in the presence of deep turbulence effects in the atmosphere. Machine learning techniques provide a novel way to propagate the effects from inner- to outer-scale in atmospheric turbulence spectrum and to accelerate its characterization on long-distance laser propagation. We simulated the turbulent flow of atmospheric air in an idealized box with a temperature difference between the lower and upper surfaces of about 27 degrees Celsius with the LES method. The volume was voxelized, and several quantities, such as the velocity, temperature, and the pressure were obtained at regularly spaced grid points. These values were binned and converted into symbols that were concatenated along the length of the box to create a ‘text’ that was used to train a long short-term memory (LSTM) neural network and propose a way to use a naive Bayes model. LSTMs are used in speech recognition, and handwriting recognition tasks and naïve Bayes is used extensively in text categorization. The trained LSTM and the naïve Bayes models were used to generate instances of turbulent-like flows. Errors are quantified, and portrait as a difference that enables our studies to track error quantities passed through stochastic generative machine learning models — considering that our LES studies have a high state of the art high-fidelity approximation solutions of the Navier-Stokes. In the present work, LES solutions are imitated and compare against generative machine learning models.