Surrogate Optimization by Kriging with First Derivatives

• Main Authors: Chun-Jen Hsueh, 薛竣壬
• Other Authors: 王偉仲
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/89hpz6

碩士 === 國立臺灣大學 === 應用數學科學研究所 === 107 === A photonic crystal is a kind of periodic structure composed of materials with different dielectric constants. It has a physical characteristic of total re- flecting photons with some frequencies. These groups of frequencies form a continuous interval called photonic band gap. To find the band gap of a pho- tonic crystal, one needs to solve numerous corresponding generalized eigen- value problems then search the extremes of the eigencurves. The process is time-consuming so we introduce the surrogate model to accelerate it. The surrogate model is a statistical model that describes the behavior of a black-box function (a function without explicit formulation). By inputting sample points and function values at there, we can choose proper basis func- tions then construct a smooth approximate function to predict function values at points we are interested in. After investigating the surrogate model, we can find the possible places in the domain that the extremes of the function may appear. In this thesis, the core technique we used in surrogate is the Kriging basis functions. To improve accuracy, we modify the model with first derivatives at sample points. We test the new model by some experiments such as find- ing the band gap of a photonic crystal. The results of comparing Kriging with first derivatives model to original Kriging model are also included.