Learn More
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)
Many physical and engineering problems involving uncertainty enjoy certain low-dimensional structures, e.g., in the sense of Karhunen-Loeve expansions (KLEs), which in turn indicate the existence of reduced-order models and better formulations for efficient numerical simulations. In this thesis, we target a class of time-dependent stochastic partial(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)
We derive the two-scale limit of a linear or nonlinear saturation equation with a flow-based coordinate transformation. This transformation consists of the pressure and the streamfunction. In this framework the saturation equation is decoupled to a family of one-dimensional nonconservative transport equations along streamlines. This simplifies the(More)
  • 1