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Turbulence is a complex phenomenon that has a chaotic nature with multiple spatio-temporal scales, making predictions of turbulent flows a challenging topic. Nowadays, an abundance of high-fidelity databases can be generated by experimental…

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…

Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling…

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned,…

Turbulence-degraded image frames are distorted by both turbulent deformations and space-time-varying blurs. To suppress these effects, we propose a multi-frame reconstruction scheme to recover a latent image from the observed image…

Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…

A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial…

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This…

Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machine learning. Classical interpolation methods fail to recover…

The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…

It remains a challenge to simultaneously remove geometric distortion and space-time-varying blur in frames captured through a turbulent atmospheric medium. To solve, or at least reduce these effects, we propose a new scheme to recover a…

Fluid flow around a random distribution of stationary spherical particles is a problem of substantial importance in the study of dispersed multiphase flows. In this paper we present a machine learning methodology using Generative…

Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…

Speech super-resolution (SR) is the task that restores high-resolution speech from low-resolution input. Existing models employ simulated data and constrained experimental settings, which limit generalization to real-world SR. Predictive…

Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

Convolutional neural networks were recently employed to fully reconstruct fluid simulation data from a set of reduced parameters. However, since (de-)convolutions traditionally trained with supervised L1-loss functions do not discriminate…

Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular…