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Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of…

Global spectral analysis (GSA) is used as a tool to test the accuracy of numerical methods with the help of canonical problems of convection and convection-diffusion equation which admit exact solutions. Similarly, events in turbulent flows…

Image degradation due to atmospheric turbulence is common while capturing images at long ranges. To mitigate the degradation due to turbulence which includes deformation and blur, we propose a generative single frame restoration algorithm…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as…

Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of…

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…

Variational data assimilation and machine-learning based super-resolution are two alternative approaches to state estimation in turbulent flows. The former is an optimisation problem featuring a time series of coarse observations, the…

A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

We address the problem of restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. A novel algorithm is proposed in this paper to reduce geometric distortion as well as…

Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical acoustics as well as structural…

Atmospheric Turbulence (AT) correction is a challenging restoration task as it consists of two distortions: geometric distortion and spatially variant blur. Diffusion models have shown impressive accomplishments in photo-realistic image…

Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…

In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…

Turbulence is a key element of the dynamics of astrophysical fluids, including those of interstellar medium, clusters of galaxies and circumstellar regions. Turbulent motions induce Doppler shifts of observable emission and absorption lines…

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

Seismic wave generation creates labeled waveform datasets for source parameter inversion, subsurface analysis, and, notably, training artificial intelligence seismology models. Traditionally, seismic wave generation has been time-consuming,…

Photography is the cornerstone of modern astronomical and space research. However, most astronomical images captured by ground-based telescopes suffer from atmospheric turbulence, resulting in degraded imaging quality. While multi-frame…

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the…