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Friday, 15 January 2021 12:00

How to choose the right optimization method?

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  • Abstract 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.

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  • Abstract 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.

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  • Abstract 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.

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  • Abstract This blog post is based on the publication P.-I. Schneider, et al. Numerical optimization of the extraction efficiency of a quantum-dot based single-photon emitter into a single-mode fiber. Opt. Express 26, 8479 (2018). The publication introduces a finite-element method for the accurate and efficient simulation of strongly localized light sources, such as quantum dots, embedded in dielectric micro-optical structures. The method is applied in order to optimize the photon extraction efficiency of a single-photon emitter and to study the robustness of the extraction efficiency with respect to fabrication errors and defects.
Sunday, 15 November 2020 12:00

Bayesian Optimization (Part 2)

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  • Abstract 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.
Sunday, 01 November 2020 12:00

Bayesian Optimization (Part 1)

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  • Abstract 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.

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  • Abstract JCMsuite employs the finite element method (FEM) in order to simulate the electrodynamic, mechanic and thermodynamic behavior of nano-optical systems. In this blog we want to motivate and describe the usage FEM for determining the electrodynamic system properties. We will compare the method to other common approaches like the rigorous coupled-wave analysis (RCWA) and the finite difference time domain (FDTD). Finally, we will present some benchmarks to show that FEM can be orders of magnitude faster and more precise than alternative methods.
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