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These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the…
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…
We present a proof-of-principle implementation of the first fully covariant filtering scheme applied to relativistic fluid turbulence. The filtering is performed with respect to special observers, identified dynamically as moving with the…
We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe.…
We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the…
Supersonic combustion plays a vital role in various applications, including scramjets, dual-mode ramjets, and pulse detonation engines. However, the flame characteristics can vary significantly, depending on the application. To model…
Modeling turbulent flows by a random Fourier decomposition is a classical procedure in order to use simplified models of turbulence in heat transport and other applications. We carefully investigate the Fourier time series of…
We propose a novel model to obtain the subgrid-scale velocity in the context of large-eddy simulation (LES) of particle-laden turbulent flows, to recover accurate particle statistics. In the new wavelet enrichment model, the subgrid-scale…
A data-driven turbulence model for coarse-grained numerical simulations of two-dimensional Rayleigh-B\'enard convection is proposed. The model starts from high-fidelity data and is based on adjusting the Fourier coefficients of the…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
In the present study, soot formation in the turbulent lifted diffusion flame, consisting of ethylene-air is numerically investigated using three different soot modeling approaches and is comprehensively reported. For turbulence-chemistry…
Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN…
In this paper, a hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by…
A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulation (DNS) create opportunities to leverage data-driven…
Data from direct numerical simulations of turbulent flows are commonly used to train neural network-based models as subgrid closures for large-eddy simulations; however, models with low a priori accuracy have been observed to fortuitously…