A Bayesian Scheme for Reconstructing Obstacles in Acoustic Waveguides

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

3 Scopus Citations
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Detail(s)

Original languageEnglish
Article number53
Journal / PublicationJournal of Scientific Computing
Volume97
Issue number3
Online published20 Oct 2023
Publication statusPublished - Dec 2023

Abstract

In this paper, we investigate inverse obstacle scattering problems in acoustic waveguides with low-frequency data. A Bayesian inference scheme, combining a multi-fidelity strategy and surrogate model with guided modes and a deep neural network is proposed to reconstruct the shapes of unknown scattering objects. First, the inverse problem is reformulated as a statistical inference problem using Bayes’ formula, which provides statistical characteristics of the posterior distribution and quantification of the uncertainties. The well-posedness of the posterior distribution is proved by using the ƒ-divergence. Subsequently, a Markov Chain Monte Carlo algorithm is used to explore the posterior density. We propose a new multi-fidelity surrogate model to accelerate the sampling procedure while maintaining high accuracy. Our numerical simulations demonstrate that this method not only produces high-quality reconstructions but also substantially reduces computational costs. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Research Area(s)

  • Acoustic waveguide, Bayesian inference, ƒ-Divergence, Machine learning

Citation Format(s)

A Bayesian Scheme for Reconstructing Obstacles in Acoustic Waveguides. / Gao, Yu; Liu, Hongyu; Wang, Xianchao et al.
In: Journal of Scientific Computing, Vol. 97, No. 3, 53, 12.2023.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review