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We study the preconditioning of Markov Chain Monte Carlo (MCMC) methods using coarse-scale models with applications to subsurface characterization. The purpose of preconditioning is to reduce the fine-scale computational cost and increase the acceptance rate in the MCMC sampling. This goal is achieved by generating Markov chains based on two-stage(More)
In this paper, we propose a numerical method based on Wiener Chaos expansion and apply it to solve the stochastic Burgers and Navier–Stokes equations driven by Brownian motion. The main advantage of the Wiener Chaos approach is that it allows for the separation of random and deterministic effects in a rigorous and effective manner. The separation principle(More)
The main goal of this paper is to design an efficient sampling technique for dynamic data integration using the Langevin algorithms. Based on a coarse-scale model of the problem, we compute the proposals of the Langevin algorithms using the coarse-scale gradient of the target distribution. To guarantee a correct and efficient sampling, each proposal is(More)
with the computational physics of electronic structure. Graetz for very helpful discussions. Thank Joanna Dodd for help with sample preparation and XRD measurements. Thank Carol Garland for help in using the transmission electron microscope. Thank Dr. Jiao Lin and Max Kresch for their help with the Linux cluster. Thank my pure-French team of officemates who(More)
I could only run this far because you tied my shoe laces. iv Acknowledgements I want to thank my advisor Professor Thomas Hou for the opportunity to work with him. This thesis acquires more meaning within the context of the rest of his research because all his projects revolve around the same ideas and shed light to them from different angles. I admire his(More)
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