Speaker
Description
The inverse scattering problem formulated for the Schrödinger operators arises in various fields, including quantum mechanics, radars, viscoelasticity, Biot problems, remote sensing, geophysical, and medical imaging. The goal of imaging is to find medium properties in the domain using near-field measured data. The model based nonlinear optimization which is the method of choice for the solution of the inverse problems can be unreliable and particularly expensive for such problems. Data driven nonlinear transforms can be an opening, however it was recently shown that the ReLU networks are intractable for reliable solution of the inverse problems in continuum using conventional digital computers. In the present work, following the success of data-driven reduced-order models (ROMs) developed in recent years, we propose a robust direct method for solving inverse scattering problems for the Schrödinger equation. Our approach is based on a Lippmann-Schwinger algorithm with a crucial component composed of adaptive data-driven ROMs in the frequency domain and efficient learning the internal solutions. In the talk we will discuss the details of the algorithms as well as some bottlenecks.