Modeling Mesh Density in Computer Experiments

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Rui Tuo*+ and C. F. Jeff Wu and Dan Yu
• Companies: Georgia Institute of Technology and Georgia Institute of Technology and Chinese Academy of Sciences
• Keywords: kriging ; multi-resolution data ; nonstationary guassian process models ; tuning parameters

Abstract

In a computer experiment a set of partial differential equations is solved numerically to simulate the result of a corresponding physical experiment. The accuracy of a numerical algorithm such as the finite element method is determined by the mesh density. As the mesh density increases, the numerical accuracy is improved, while the computational cost goes up. The quantitative relationship between error and mesh density is available in the theory of finite element. New nonstationary Gaussian process models are proposed to establish a framework consistent with the results in numerical analysis. These models can be analyzed by Bayesian methods. The proposed method is also applicable to multi-resolution experiments. The methodology is illustrated by two examples.