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The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
We reanalyse the time evolution of the $K^0-\bar{K^0}$ system in the language of certain spectral function whose Fourier transforms give the time dependent survival and transition amplitudes. The reanalysis turned out to be necessary in…
In this work, we provide a mathematical formulation for error propagation in flow trajectory prediction using data-driven turbulence closure modeling. Under the assumption that the predicted state of a large eddy simulation prediction must…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ…
The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
Connecting short time microscopic dynamics with long time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is very difficult to determine various hydrodynamic coefficients like the…
A rigorous asymptotic analysis of the Boltzmann equation for small Knudsen numbers leads, in the general case, to more complicated sets of differential equations than widely used to describe the behavior of gas in terms of classical fluid…
This study focuses on the numerical simulation of high Reynolds number separated flows and proposes a data-driven approach to improve the predictive capability of the SA turbulence model. First, data assimilation was performed on two…
We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…
This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…
In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…
The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream…
Given the growth in the variety and precision of astronomical datasets of interest for cosmology, the best cosmological constraints are invariably obtained by combining data from different experiments. At the likelihood level, one…
A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, the true reduced dynamics of the system is…
We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly…
Large Eddy Simulation (LES) with dynamic Smagorinsky model has been applied to numerically investigate the complicated flow structures that evolve in the near wake of a cylindrical after body aligned with a uniform Mach 2.46 flow. Mean flow…