Work

Solving inverse acoustic obstacle scattering problem from phaseless far-field measurement using deep neural network surrogates*

Year: 2025

Type: article

Abstract: In this work, we investigate the use of deep neural networks (DNNs) as surrogates for solving the inverse acoustic scattering problem of recovering a sound-soft obstacle from phaseless far-field measurements. We approximate the forward maps from the obstacle to the far-field data using DNNs, and for star-shaped domains in two and three dimensions, we establish the expression rates for fully connected feedforward neural networks with the rectified linear unit activation for approximating the forward maps. The analysis is based on the weak formulation of the direct problem, and can handle variable coefficients. Numerically we validate the accuracy of the DNN surrogates of the forward maps, and demonstrate the use of DNN surrogates in the Bayesian treatment of the inverse obstacle scattering problem. Numerical experiments indicate that the surrogates are effective in both two- and three-dimensional cases, and can significantly speed up the exploration of the posterior distribution of the shape parameters using Markov chain Monte Carlo.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ae0362

Authors: Yuxin Fan, Jiho Hong, Bangti Jin

Institution: Chinese University of Hong Kong

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: Research Grants Council, University Grants Committee