Solving Inverse Problems with Deep Learning

Many electromagnetic design problems can be cast as an inverse problem. That is, one may specify a desired scattering state and seek to find the ideal configuration of an antenna, waveguide, power amplifier, and related constituent materials and geometry needed to achieve the goal. However, inverse problems are a long standing and challenging problem in physics and engineering and many electromagnetic design problems suffer from ill-posedness. Recently deep learning has been used to tackle ill-posed inverse design, and many novel results have been demonstrated. We overview and benchmark several deep inverse methods and use two metrics to characterize their performance - inference speed and accuracy of solutions. Deep inverse methods are benchmarked against three electromagnetics problems and a discussion of Hadamard's well posed criteria is used as a point of discussion for the future of this exciting field.