A Bayesian Scheme for Reconstructing Obstacles in Acoustic Waveguides

作者：Gao, Yu; Liu, Hongyu^*; Wang, Xianchao; Zhang, Kai^*

来源：JOURNAL OF SCIENTIFIC COMPUTING, 2023, 97(3): 53.

DOI：10.1007/s10915-023-02368-2

• Acoustic waveguide
• Bayesian inference
• f-Divergence
• Machine learning

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 f-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.

• 单位
  吉林大学