A neural operator framework for solving inverse scattering problems

TL;DR

This paper introduces a neural operator approach combining DeepONet and neural tangent kernel analysis to improve inverse scattering problem solutions, validated through 2D experiments and a Python toolbox.

Contribution

It develops a novel neural operator framework that integrates regularization with the Linear Sampling Method for enhanced inverse scattering reconstructions.

Findings

Effective reconstruction of scatterers in 2D experiments

Neural tangent kernel analysis guides neural network architecture

Provides a reproducible Python toolbox

Abstract

We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within the Linear Sampling Method to validate the initial reconstruction. The neural operator is implemented as a DeepONet with a fixed radial-basis-function trunk, while the noise level required for rescaling is estimated using a dedicated neural network. A neural tangent kernel analysis guides the architectural design, reducing the network tuning to a single discretization parameter, adjustable according to the wavelength. Two-dimensional numerical experiments demonstrate the method's effectiveness, with a Python toolbox provided for reproducibility.