Displaying items by tag: optimization and parameter retrieval methods
This blog post gives some insights in common optimization methods used in computational photonics: L-BFGS-B, the downhill-simplex method, differential evolution, and Bayesian optimization. It tries to give some hints on which method is the best for which optimization problem depending on the number of parameters, the evaluation time of the objective function, and the availability of derivative information.
This blog post is based on the publication P.-I. Schneider, et al. Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction.ACS Photonics 6, 2726 (2019). Several global optimization methods for three typical nano-optical optimization problems are benchmarked: particle swarm optimization, differential evolution, and Bayesian optimization as well as multistart versions of downhill simplex optimization and the limited-memory Broydenu2013Fletcheru2013Goldfarbu2013Shanno (L-BFGS) algorithm. In the shown examples, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.
This blog post is based on the publication P.-I. Schneider, et al. Using Gaussian process regression for efficient parameter reconstruction.Proc. SPIE 10959, 1095911 (2019). Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. The performance of Bayesian optimization as implemented in JCMsuite`s optimization toolbox is compared to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. The paper examines how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.
This is the second blog of a series that introduces the concept oy Bayesian optimization (BO). In the first part, we have introduced Gaussian processes as a means to predict the behaviour of the objective function for unkown parameter values. In this second part the BO algorithm is introduced, which uses these predictions to find promising parameter values to sample the expensive objective function. Finally, the performance of BO is compared to other optimization methods showing a great perfomance gain.
This is the first blog of a series that introduces the concept oy Bayesian optimization (BO). BO uses a stochastic model of the objective function in order to find promising parameter values. The most commonly applied model is a Guassian process. The first part of the series explains Gaussian processes and Gaussian process regression.