Application of Denoising Diffusion Probabilistic Models to Turbulence Prediction

Over the past few years, denoising diffusion probabilistic models (DDPMs), an advancement of the diffusion probabilistic model (DPM), have garnered attention for their comparable ability to state-of-the-art models like generative adversarial networks (GANs). DDPMs have achieved both flexibility and tractability; however, there is still ample room for improvement, as they have not been explored as extensively as GANs in terms of model architecture and hyperparameters. Particularly, applications of DDPMs to turbulence data, more generally to fluid dynamics data, are scarce, necessitating extensive analysis and research to assess the model's feasibility and performance concerning flow physics and turbulence statistics. In this presentation, we introduce an application of the simplest unconditional DDPM to turbulence generation using 2D isotropic turbulence, which provides a relatively simple and analyzable context. Additionally, we extend our investigation to turbulence prediction by utilizing the flow field from the previous time point as a condition for the backbone DDPM. Through a thorough analysis and comparison of the results by the conditional DDPM with a high-performance prediction model based on GANs, we assess the model's potential and identify whether it requires further improvements. This study can contribute to understanding DDPMs' capabilities in handling turbulence data and offer insights into their potential applications in fluid dynamics research.