Speaker
Description
Characterizing subsurface formations poses significant challenges due to the high-dimensional stochastic space inherent in inverse problems. To make this task computationally tractable, we employ the Karhunen–Loève Expansion (KLE) for dimensionality reduction. Given the heterogeneity of rock properties such as permeability and porosity, a domain-decomposed sampling strategy proves advantageous. Within a Bayesian Markov Chain Monte Carlo (MCMC) framework, we formulate an inverse problem governed by an elliptic partial differential equation modeling porous media flow. To address this, we introduce a novel multiscale sampling algorithm in which the prior distribution is represented through local KLEs across non-overlapping subdomains. We view multiscale sampling as a two-level dimensional reduction method: in Level 1, we reduce the dimension from the fine computational grid using a global KLE; in Level 2, the global stochastic dimension is further reduced to local stochastic dimensions. Our research focuses on identifying optimal coupling conditions among subdomains so that the local stochastic dimension dominates the convergence of the global problem as much as possible. Numerical experiments based on multiple MCMC simulations demonstrate that the proposed algorithm significantly improves the convergence rate of a preconditioned MCMC method.
| References | A. Ali, A. Al-Mamun, F. Pereira, A. Rahunanthan, Multiscale sampling for the inverse modeling of partial differential equations, Journal of Computational Physics, Volume 497, 2024, 112609, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2023.112609. |
|---|---|
| Country | USA |
| Acceptance of the Terms & Conditions | Click here to agree |
