Continuation-in-Frequency and Data-Driven Methods for Nonlinear Inverse Acoustic Scattering

In the first part of this talk, we present a fast and robust algorithm for solving nonlinear inverse acoustic scattering problems from full-aperture far-field data. Using a continuation-in-frequency approach inspired by Chen’s recursive linearization, the method reconstructs unknown domain parameters with high resolution solving a sequence of well-conditioned linear least-squares problems. Each iteration employs fast analysis-based solvers for the forward problem integral formulation. Numerical experiments in two dimensions, involving both penetrable and impenetrable obstacles, demonstrate the framework’s accuracy, stability, and efficiency. The approach naturally extends to three-dimensional inverse scattering and applies to related problems such as the fractional Helmholtz and biharmonic wave equation.
In the second part, we present ongoing research combining direct methods and machine learning to address cases without low-frequency data, using these techniques to obtain high-quality initial guesses for the framework introduced earlier. We will show numerical results for the impenetrable 2D obstacle problem, highlighting the potential of these hybrid strategies for advancing inverse scattering analysis.