Gaussian Process Metamodeling: Emulating Code Input/Output for Faster Evaluation

This chapter provides an overview of computer simulation metamodeling based on Gaussian stochastic process, the main idea behind it and practical aspects of it. The chapter also seeks to demonstrate the application of such an approach to metamodeling of a reflood facility model in TRACE. The Gaussian process metamodeling This

Inn Gaussian Process Fundamentals gives an overview of the fundamental ideas behind and some important properties of Gaussian stochastic process. This will be done especially through its relation to the more familiar multivariate Gaussian random variable. In Metamodeling based on Gaussian Process metamodeling approach based on Gaussian stochastic process, known as the Kriging model is presented. The practical aspects of constructing a Gaussian process metamodel, namely the design of experiment, model fitting, and its validation strategy are presented in Constructing GP Metamodel. In GP Metamodeling of a Simple Problem those aspects are illustrated by constructing a metamodel of a simple problem. Before moving on to the application to a model in TRACE, some ideas on how to deal with high-dimensional output is presented in Dimension Reduction. Finally metamodeling of a reflood facility model in TRACE is presented in GP Metamodel of TRACE FEBA Model and Chapter Summary summarizes the Chapter.

Gaussian Process:

• Gaussian Process Fundamentals
  • Multivariate Random Variable
  • Multivariate Gaussian (Normal) Random Variable
  • Gaussian Stochastic Process
  • Covariance Kernel Functions
  • Mean Function
• Metamodeling based on Gaussian Process
• Constructing GP Metamodel
• GP Metamodeling of a Simple Problem
• Dimension Reduction
• GP Metamodel of TRACE FEBA Model
• Chapter Summary