Computationally Efficient Parameter Estimation of a Simulation Model for Multiple Observation Vectors

Abstract

This thesis introduces the problem of estimating the parameters of a simulation model for given multiple observation vectors when the simulation model is computationally expensive. Specifically, the simulation model is designed to describe the behavior of a physical system, and a vector of parameters can be inferred by comparing the observations from the system with the simulation results. In this case, estimating vectors of parameters for multiple observation vectors requires huge computations that may prevent timely decisions in practice. Therefore, this thesis aims to solve the target problem with low computational costs while maintaining the high quality of the parameter values. For the target problem, the optimization and Bayesian approaches are considered. As optimization approaches, two frameworks have been proposed by defining the problem using the least squares method and introducing heuristic search algorithms. The first framework, called the distribution-guided heuristic search, incorporates the prior distribution information of the parameter vector into heuristic search algorithms, and the second framework, called the surrogate- assisted parameter estimation, appropriately uses both the surrogate and simulation models within heuristic search algorithms. As a Bayesian inference approach, another proposed framework, called the parallel parameter estimation with surrogate-assisted proposals, introduces both the surrogate and simulation models within the Metropolis-Hastings algorithm and shares candidate vectors and their simulation results to identify multiple posterior distributions of parameters for the vectors of observations. The proposed frameworks were applied to numerical examples and a case study problem, the optical critical dimension measurements in semiconductor manufacturing. The empirical results show that the proposed frameworks may significantly reduce computational costs while maintaining the high quality of the parameter values. These frameworks are also applicable to a wide range of application problems, including but not limited to non-destructive testing in manufacturing industries, detection of the source of groundwater contamination, determination of epicenters from seismic waves, and volatility assessment of financial derivatives.