Name
Abstract | ||
|---|---|---|
The Bayesian approach, a useful tool for quantifying uncertainties, has been extensively employed to solve the inverse problems of partial differential equations (PDEs). One of the main difficulties in employing the Bayesian approach to such problems is how to extract information from the posterior probability measure. Compared with conventional sampling-type methods, the variational Bayes method (VBM) has been intensively examined in the field of machine learning attributed to its ability in extracting approximately the posterior information with lower computational cost. In this paper, we generalize the conventional finite-dimensional VBM to the infinite-dimensional space to rigorously solve the inverse problems of PDEs. We further establish a general infinite-dimensional mean-field approximate theory and apply it to the linear inverse problems under the Gaussian and Laplace noise assumptions at the abstract level. The results of some numerical experiments substantiate the effectiveness of the proposed approach. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/19M130409X | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
inverse problems, variational Bayes method, mean-field approximation, machine learning, inverse source problem | Journal | 43 |
Issue | ISSN | Citations |
1 | 1064-8275 | 0 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Junxiong Jia | 1 | 6 | 2.73 |
| Qian Zhao | 2 | 0 | 0.34 |
| Zongben Xu | 3 | 3203 | 198.88 |
| Deyu Meng | 4 | 2025 | 105.31 |
| Yee Leung | 5 | 2081 | 96.44 |