Numerical Linear Algebra with Applications
Bayesian networks, Optimization, Multilevel Monte Carlo
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 of this approach, numerical tests are performed on two 3D examples—a unit cube and an egg‐shaped domain with an irregular boundary—where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.
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Fairbanks, H. R., Osborn, S., & Vassilevski, P. S. (2020). Estimating posterior quantity of interest expectations in a multilevel scalable framework. Numerical Linear Algebra with Applications. https://doi.org/10.1002/nla.2352