Implicit sampling methods and their applications

University Of Kansas Center For Research Inc, Lawrence KS

Investigators

Abstract

Data assimilation incorporates the observations, which can be real-time data, into a computational model of a real system. The output of this process is the adjusted states of the system based on both computational model and the observations. These adjusted states are better than those that could be obtained using just the data or model alone. Data assimilation is required in many fields such as statistical signal processing, oceanography, meteorology, hydrology, geosciences, econometrics, and finance. Due to the large-scale and nonlinear properties of the models in those applications, commonly used methods rely on unrealistic assumptions. The PI and her collaborators develop an efficient data assimilation method without those unrealistic assumptions. As one example, successful application of this method to reservoir history matching will greatly benefit the reservoir management. This project involves undergraduate and graduate students. The PI has outreach for successful participation of underrepresented group in STEM-related disciplines. Data-driven computations, such as data assimilation, need to identify the state of a system and/or unknown parameters in the system from an uncertain model supplemented by a stream of noisy and incomplete data. The Bayesian framework is a standard approach for such problems and it involves characterizing the posterior distribution of the state and/or parameters in terms of given prior distribution and data. Commonly used methods, like ensemble Kalman filter-type and variational methods, rely on assumptions of Gaussianity or near Gaussianity. By contrast, the implicit sampling methods obtain high qualify samples of the posterior density by using importance sampling with good proposal density and can be applied to more general non-Gaussian situations. These samples are independent and focus on the high probability regions. The first step in the implicit sampling methods usually requires solving an optimization problem, which is the most time-consuming part of the methods. The proposed research is to develop and analyze preconditioners using domain decomposition methods, a widely-used paradigm for parallel computation, combined with efficient nonlinear solvers to accelerate this procedure and make it suitable for high performance computation. The PI and her collaborators apply these newly developed implicit sampling methods to data assimilation and uncertainty quantification in subsurface flow applications including reservoir history matching.