Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

TL;DR

This paper introduces a Bayesian target-vector optimization method that efficiently reconstructs parameters in metrology by considering all model outputs, outperforming traditional methods especially with limited observations.

Contribution

The paper presents a novel Bayesian target-vector optimization approach that improves parameter reconstruction by incorporating all model outputs, suitable for computationally expensive simulations.

Findings

Outperforms established optimization methods in optical metrology reconstruction.

Enables accurate uncertainty estimation with few observations.

Effective for problems with hundreds of observations.

Abstract

Parameter reconstructions are indispensable in metrology. Here, the objective is to 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, i.e., by minimizing the sum of the squared residuals between the $K$ model predictions and the $K$ experimental observations, $\chi^2$. 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 $\chi^2$ into account, and neglect the $K$ individual model outputs. We present 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. 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.