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Full-Text Articles in Physical Sciences and Mathematics
Multilevel Hierarchical Decomposition Of Finite Element White Noise With Application To Multilevel Markov Chain Monte Carlo, Hillary R. Fairbanks, Umberto E. Villa, Panayot S. Vassilevski
Multilevel Hierarchical Decomposition Of Finite Element White Noise With Application To Multilevel Markov Chain Monte Carlo, Hillary R. Fairbanks, Umberto E. Villa, Panayot S. Vassilevski
Mathematics and Statistics Faculty Publications and Presentations
In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable …
Estimating Posterior Quantity Of Interest Expectations In A Multilevel Scalable Framework, Hillary R. Fairbanks, Sarah Osborn, Panayot S. Vassilevski
Estimating Posterior Quantity Of Interest Expectations In A Multilevel Scalable Framework, Hillary R. Fairbanks, Sarah Osborn, Panayot S. Vassilevski
Mathematics and Statistics Faculty Publications and Presentations
Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large‐scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element‐agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state‐of‐the‐art scalable AMG. To showcase the applicability …