Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 28 for “"Stochastic Partial Differential Equations"”.
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Approximation of random/stochastic partial differential equations
… of this thesis lies in approximations of partial differential equations (PDEs) with randomness or stochasticity. We focus on three rather different problems: a study of random fields on spherical shells, and its applications to PDE problems; quasi-Monte Carlo (QMC) methods for a class of …
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Preconditioning techniques for stochastic partial differential equations
… preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. …
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Optimal control of stochastic partial differential equations in Banach spaces
… optimal control problems in Banach spaces for stochastic partial differential equations. We investigate two different approaches. In the first part we study Hamilton-Jacobi-Bellman equations (HJB) in Banach spaces associated with optimal feedback control of a class of non-autonomous semilinear …
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Deep Learning-based Numerical Methods for Stochastic Partial Differential Equations and Applications
… we are concerned with approximating solutions of stochastic partial differential equations (SPDEs) and their applications. Inspired by Huré, Pham, and Warin [15], we propose and study the deep learning-based methods for both the forward and backward SPDEs. In particular, the forward SPDEs may …
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Mathematical and computational modelling of stochastic partial differential equations applied to advanced methods
Mathematical modelling and simulations were carried to study diblock copolymer system confined in circular annular pores, cylindrical pores and spherical pores using Cell Dynamics simulation (CDS) method employed in physically motivated discretization. The lamella, cylindrical and spherical forming …
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Large Deviations and Higher Order Fluctuation Expansions for Conservative Stochastic PDEs
… order fluctuation expansions for conservative stochastic partial differential equations arising from fluctuating hydrodynamics. In particular, the thesis is divided into two parts. We studied large deviations for the Landau-Lifshitz-Navier-Stokes equations and higher-order fluctuation …
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Numerical approximations of coupled forward-backward SPDEs with applications
… approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic …
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Fractional Diffusion in Gaussian Noisy Environment
Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and …
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Closure Modeling for Accelerated Multiscale Evolution of a 1-Dimensional Turbulence Model
… challenge in the context of the one-dimensional stochastic Burgers' equation, a widely used toy model for turbulence. We employ an encoder-decoder recurrent neural network to perform super-resolution reconstruction of the velocity field from lower-dimensional energy spectrum data, enabling …
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SPDEs with Infinite-Variance Lévy Noise
… of the existence and uniqueness of solutions for stochastic partial differential equations (SPDEs) driven by Lévy noise. The main contributions of this work are contained in the recent publications [32] and [5]. Article [32] focuses on a stochastic wave equation with multiplicative Lévy noise. We …
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The Convex Integration Paradigm in Stochastic Fluid Dynamics
… role of convex integration in the analysis of stochastic partial differential equations in the realm of fluid dynamics, with particular emphasis on the incompressible Navier--Stokes equations and shear-thinning fluid flows. <br /><br /> The method of convex integration, discussed in Part I, is …
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The use of stochastic collocation for sampling from expensive distributions with applications in finance
… this, Grzelak et al. (2015) introduced the stochastic collocation Monte Carlo sampler. This sampling method is based on a generalisation of the stochastic collocation method of Mathelin and Hussaini (Mathelin andHussaini, 2003) which was introduced in the context of solving stochastic …
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SPDE-derived random fields in structural optimisation and elastodynamics
… established connection between random fields and stochastic partial differential equations (SPDEs). For a random field with Matérn covariance, the precision matrix (the inverse of the covariance matrix) corresponds to the finite element stiffness matrix of a potentially fractional PDE involving a …
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Some application of Malliavin calculus to SPDE and convergence of densities
Some applications of Malliavin calculus to stochastic partial differential equations (SPDEs) and to normal approximation theory are studied in this dissertation. In Chapter 3, a Feynman-Kac formula is established for a stochastic heat equation driven by Gaussian noise which is, with respect to …
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Necessary and Sufficient Conditions for the Transfer of Kinetic Energy at Asymptotically Large Reynolds Numbers
… turbulent flows are typically modeled using stochastic partial differential equations to model the apparent randomness of the turbulent flow. Moreover, from a physics perspective, this method accounts for external noise on the system, such as the vibrations of the table holding the cup of …
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Stochastic Terrain and Soil Modeling for Off-Road Mobility Studies
… approach for solving linear second-order stochastic partial differential equations. We currently use this approach to model non-stationary terrain profiles in two dimensions (i.e., surface maps). Certain assumptions are made for the values of the model coefficients to obtain the terrain …
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Density Fluctuations and Phase Behaviour in Non-Equilibrium Systems
… where coarse-grained density fields evolve via stochastic partial differential equations that encode the spatiotemporal evolution of the system. These field theories can be constructed in two directions: either bottom-up, by coarse-graining the microscopic rules of particle motion, or top-down, …
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Mild solutions of SPDE's driven by Poisson noise in infinite dimensions and their dependence on initial conditions
We investigate stochastic partial differential equations in an infinite dimensional Hilbert space H of the following form: dX(t)=[AX(t)+F(X(t))]dt+B(X(t),y)q(dt,dy), X(0)=g, where q(dt,dy) is a compensated Poisson random measure associated to a stationary Poisson point process on a [sigma]-finite …
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