| Abstract: |
| This talk presents a robust unsupervised deep learning approach for reconstructing the location and shape of impenetrable sound-soft obstacles in two dimensions from scattered field data. The method formulates the inverse acoustic scattering problem as a PDE-constrained shape optimization, where the obstacle boundary is parameterized by a neural network, and the forward problem is solved efficiently using the Discrete Source Method. Reconstruction accuracy is enhanced through a multi-frequency continuation strategy, in which low-frequency reconstructions are progressively refined using higher-frequency data. Moreover, targeting phaseless far-field data, we propose an imaging algorithm for obstacle localization, which is coupled with deep learning approach to thereby reconstruct the obstacle`s shape with high precision. The approach leverages automatic differentiation to compute gradients, avoiding the need for adjoint solvers, and integrates multi-angle measurements for improved stability. Numerical experiments demonstrate accurate recovery of complex geometries, including sharp corners and multiple obstacles, even under sparse sampling and severe noise. |
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