Diagnostic within a micro-structure using microwave and analysis by convolutional neural network
Résumé
A finite set of infinitely long, regularly-distributed dielectric rods is illuminated from the outside by time-harmonic ideal electric line sources at a single microwave frequency and the fields scattered in each experiment are collected accordingly. Some of the rods are missing in unknown fashion, that is, they are associated to a lacunary (damaged) micro-structure, here within the demanding hypothesis of radii of rods and inter-rod distances that are small versus the wavelength of operation. To detect those missing rods in such a complex situation in terms of electromagnetic behavior and achievable resolution, convolutional neural networks (CNN) will be shown to provide for an efficient diagnostic in addition also to the appraisal of the permittivity maps of the micro-structure as a whole. The approach developed herein arises from machine learning within the domain of waves and fields. Provided that a well-designed network architecture, and evidently well training data sets and adequate training method, among other necessary features, good results follow if and in effect only if quite much numerical experimentation on known micro-structures so as to design and validate a network efficient enough, computationally speaking and in terms of the physical output. Super-resolution, where one does aim at sub-wavelength features of the provided maps of the dielectric distribution, indeed is successfully achieved by CNN as confirmed by extensive numerical simulations. Notice one has to train the network (here by Adam's algorithm) using a regularized misfit (loss function) between ground truth and prediction, and have comprehensive training data sets. Complications when getting to a 3-D vector scattering case are foreseen, with the need of fast and versatile fast direct solvers, and an acute evaluation of the physics behind the scene, and about information content of the data (rather sparse ones usually, and noisy), unless certainly going nowhere, work being in progress on that challenge. The 3-minute PhD video proposed here within the 3MT contest of EUSIPCO 2019 takes a low-key path based on comparisons to answers of school kids within a class room.