Bayesian Target‐Vector Optimization for Efficient Parameter Reconstruction. Issue 10 (24th August 2022) - Plock, Matthias; Andrle, Kas; Burger, Sven; Schneider, Philipp‐Immanuel
Abstract: Parameter reconstructions are indispensable in metrology. Here, the objective is to explain K experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined by least‐square methods, that is, by minimizing the sum of the squared residuals between the K model predictions and the K experimental observations, χ 2 . The model functions often involve computationally demanding numerical simulations. Bayesian optimization methods are specifically suited for minimizing expensive model functions. However, in contrast to least‐square methods such as the Levenberg–Marquardt algorithm, they only take the value of χ 2 into account, and neglect the K individual model outputs. A Bayesian target‐vector optimization scheme with improved performance over previous developments, that considers all K contributions of the model function and that is specifically suited for parameter reconstruction problems which are often based on hundreds of observations is presented. Its performance is compared to established methods for an optical metrology reconstruction problem and two synthetic least‐squares problems. The proposed method outperforms established optimization methods. It also enables to determine accurate uncertainty estimates with very few observations of the actual model function by using Markov chain Monte Carlo sampling on a trained surrogate model. Abstract : A Bayesian target‐vector optimization scheme is presented that combines the resource efficiency of Bayesian optimization methods for scalar model functions with the reconstruction performance of established least‐square methods. It is applied to parameter reconstruction problems and shown to regularly outperform established optimization schemes. The method further enables efficient Markov chain Monte Carlo sampling of expensive models for accurate uncertainty quantification of reconstructed parameters.