Global optimization of complex optical structures using Bayesian optimization based on Gaussian processes

Abstract

Numerical simulation of complex optical structures enables their optimization with respect to specific objectives. Often, optimization is done by multiple successive parameter scans, which are time consuming and computationally expensive. We employ here Bayesian optimization with Gaussian processes in order to automatize and speed up the optimization process. As a toy example, we demonstrate optimization of the shape of a free-form reflective meta surface such that it diffracts light into a specific diffraction order. For this example, we compare the performance of six different Bayesian optimization approaches with various acquisition functions and various kernels of the Gaussian process.

Using Gaussian process regression for efficient parameter reconstruction

“…Based on the previous observation of the objective the algorithm identifies parameter values where it is expected to find a smaller function value. 11,21 Gaussian processes. Gaussian processes (GP) are frequently used as the stochastic model in Bayesian optimization.…”

Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

“…The Bayesian optimization method uses the statistical information provided by the posterior GP to determine promising parameter sets and to sequentially converge to the optimum value of f ob . There are different strategies for how to use the information provided by the GP [20]. One commonly used strategy, which is also used in this work, consists in finding the point of maximum expected improvement [17].…”

“…There are two main steps during which Bayesian optimization suffers from scalability issues: the inversion of the covariance matrix and the evaluation of the acquisition function [20] at different points. In a previous work [19], we proposed a technique to mitigate the problem of the time for evaluating the acquisition function.…”

Role of Geometric Shape in Chiral Optics

“…Bayesian Optimization (BO) is a procedure based on a stochastic model given by Gaussian processes (GPs) [21]. The optimization starts at a random point in the parameter space and predicts the objective function in the full space based on the previously obtained values.…”