Variational Bayesian inversion for the reaction coefficient in space-time nonlocal diffusion equations

In the paper, a variational Bayesian method is used to identify the reaction coefficient for space-time nonlocal diffusion equations using nonlocal averaged flux data. To show the posterior measure to be well-defined, we rigorously prove that the forward operator is continuous with respect to the un...

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Bibliographic Details
Published in:Advances in computational mathematics 2021-06, Vol.47 (3), Article 31
Main Authors: Song, Xiaoyan, Zheng, Guang-Hui, Jiang, Lijian
Format: Article
Language:English
Subjects:
Bayesian analysis
Coefficients
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Inverse problems
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Relativity
Spacetime
Visualization
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Summary:In the paper, a variational Bayesian method is used to identify the reaction coefficient for space-time nonlocal diffusion equations using nonlocal averaged flux data. To show the posterior measure to be well-defined, we rigorously prove that the forward operator is continuous with respect to the unknown reaction field. Then, gradient-based prior information is proposed to explore oscillation features in the reaction coefficient. Moreover, the Bayesian inverse problem is shown to be well-posed in Hellinger distance. To accurately characterize the posterior density using uncorrelated samples, an efficient variational Bayesian method is used to estimate the reaction coefficient in the nonlocal models. A few numerical results are presented to illustrate the efficacy of the proposed approach and confirm some theoretic discoveries.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-021-09850-1