Inverse diffraction grating problems as optimization tasks: from naïve to Bayes approach

The authors consider the inverse conical diffraction problem as an optimization problem. We apply several techniques: the genetic algorithm, the stochastic gradient descent method, the Bayesian approach, and the neural network approach. The boundary integral equation method is utilized to solve the direct problem. Using a range of numerical experiments, we demonstrate that the mixed Bayesian with stochastic gradient descent optimization technique allows one to obtain the solution to the inverse diffraction grating problem in the most convenient and fast way possible. The authors provide a detailed configuration description necessary for a successful optimization process.