Abstract Subsurface flow modeling presents multiple obstacles for Bayesian uncertainty quantification. Markov chain Monte Carlo (MCMC), while theoretically sound, is computationally expensive for PDE-based inverse problems. These challenges include the ill-posedness of the data-to-parameter mapping, high-dimensional parameterizations, expensive and ill-conditioned forward models, and slow MCMC mixing in large parameter spaces. Building on gradient-free MCMC methods and domain decomposition, this talk introduces a global–local multiscale sampling framework. The proposed approach reduces the effective dimensionality by partitioning the computational domain and decoupling localized sampling tasks while maintaining consistency with the global posterior. Numerical experiments demonstrate the effectiveness of the method on a Darcy flow inverse problem.
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