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International Journal for Uncertainty Quantification
IF: 3.259 5-Year IF: 2.547 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019029059
pages 205-220

AN ADAPTIVE MULTIFIDELITY PC-BASED ENSEMBLE KALMAN INVERSION FOR INVERSE PROBLEMS

Liang Yan
Department of Mathematics, Southeast University, Nanjing, 210096, China
Tao Zhou
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

ABSTRACT

The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by highdimensional nonlinear PDEs, as EKI requires a relatively large ensemble size to guarantee its performance. In this paper, we propose an adaptive multifidelity polynomial chaos (PC) based EKI technique to address this challenge. Our new strategy combines a large number of low-order PC surrogate model evaluations and a small number of high-fidelity forward model evaluations, yielding a multifidelity approach. Specifically, we present a new approach that adaptively constructs and refines a local multifidelity PC surrogate during the EKI simulation. Since the forward model evaluations are only required for updating the low-order local multifidelity PC model, whose number can be much smaller than the total ensemble size of the classic EKI, the entire computational costs are thus significantly reduced. The new algorithm was tested through the two-dimensional time fractional inverse diffusion problems and demonstrated great effectiveness in comparison with PC-based EKI and classic EKI.

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