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Turbulent flows, characterized by their chaotic and stochastic nature, have historically presented formidable challenges to predictive computational modeling. Traditional eddy-resolved numerical simulations often require vast computational resources, making them impractical or infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. In this study, we introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence under various conditions. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, as well as scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We evaluate and showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: (1) the synthesis of Large Eddy Simulations (LES) simulated instantaneous flow sequences from unsteady Reynolds-Averaged Navier–Stokes (URANS) inputs; (2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; (3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation. 

Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations. 

Abstract This paper proposes a deep-learning based generalized empirical flow model (EFM) that can provide a fast and accurate prediction of the glottal flow during normal phonation. The approach is based on the assumption that the vibration of the vocal folds can be represented by a universal kinematics equation (UKE), which is used to generate a glottal shape library. For each shape in the library, the ground truth values of the flow rate and pressure distribution are obtained from the high-fidelity Navier-Stokes (N-S) solution. A fully-connected deep neural network (DNN) is then trained to build the empirical mapping between the shapes and the flow rate and pressure distributions. The obtained DNN based EFM is coupled with a finite-element method (FEM) based solid dynamics solver for flow-structure-interaction (FSI) simulation of phonation. The EFM is evaluated by comparing to the N-S solutions in both static glottal shapes and FSI simulations. The results demonstrate a good prediction performance in accuracy and efficiency.