Computer Experiments (Tena Katsaounis, organizer/David Higdon, chair)


Michael Trosset (Department of Mathematics, College of William and Mary)
Sean Kugele (Departments of Computer Science and Mathematics, Virginia Tech)
Layne Watson (Departments of Computer Science and Mathematics, Virginia Tech)
Sequential Computer Experiments for Robust Design Optimization with Reliability Constraints

Saturday 10:30-10:50, San Rafael

Abstract:

The DACE methodology described by Welch and Sacks (1991) was proposed for solving a decision-theoretic formulation of the problem of robust design optimization. This formulation requires integrating functions that can only be evaluated by performing computationally expensive computer simulations; DACE was motivated by the observation that the computational expense of these operations precludes traditional numerical optimization strategies. We combine a decision-theoretic formulation of robust design with a reliability constraint, viz., that the probability of failure not exceed a specified tolerance. We illustrate the mathematical structure of such problems with a simple example and report on our efforts to develop effective algorithms for solving such problems.


Connie Borror (Arizona State University)
Design Construction for Computer Experiments Involving Categorical Factors

Saturday 10:50-11:10, San Rafael

Abstract:

For problems involving several categorical factors, higher-order interactions (three factor or more) are not necessarily negligible and must be detected. That is, the sparsity of effects principle may not apply. As a result, experiments quickly become prohibitively large and uneconomical in order to detect significant factors and interactions. Computer experiments have become a valuable tool for screening purposes and eventual modeling in these and other situations. In this presentation, designs involving mixed level categorical variables where higher-order interactions are possibly important and need to be detected are discussed. Design construction techniques will be discussed with attention given to applications in areas such as software engineering.


Brian Williams (Los Alamos National Laboratory)
Uncertainty Quantification for Combining Experimental Data and Computer Simulations

Saturday 11:10-11:30, San Rafael

Abstract:

This work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out inference. This typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator. We consider applications in characterizing equation of state and material properties for which the field data and the simulator output are multivariate. For example, the data may be the velocity profile of a metal plate subjected to a plane shock wave at high strain rates. We use the basic framework of Kennedy and O'Hagan (2001). However, the size and multivariate nature of the data lead to computational challenges for implementing the framework. We consider adaptive basis methods (e.g. principal components, kernel smoothing) to achieve significant dimension reduction in the statistical formulation. We illustrate the proposed methodology with experimental data and simulations from a flyer plate experiment that was conducted to learn about material behavior in high strain rate environments.


David Higdon (Los Alamos National Laboratory)
Katrin Heitmann (ISR-1, Los Alamos National Laboratory)
Charles Nakhleh (X-2, Los Alamos National Laboratory)
Salman Habib (T-8, Los Alamos National Laboratory)
Estimating Cosmological Parameters using Physical Observations and Simulations

Saturday 11:30-11:50, San Rafael

Abstract:

This collaborative effort is focused on using recent observations of the universe to determine uncertain cosmological parameters that govern the behavior and evolution of the universe. The data used to constrain these cosmological parameters comes from a variety of sources. At the largest scales, the best measurements come from maps of the (cosmic) microwave sky made by satellite observations such as the ongoing WMAP mission and the future Planck probe (scheduled for launch in 2007). At smaller scales, information from large-scale structure surveys such as the Sloan Digital Sky Survey is an essential component. Finally, the most reliable information at the smallest scale presently comes from analysis of the Lyman-alpha forest from many thousands of quasar spectra. Uncertainties and errors associated with these observations include finite-volume sampling limitations, observational errors, and a host of systematic modeling errors including insufficient understanding of the basic physical processes and inadequately error-controlled coupling of simulations to observations.

Comparing these data to model output is most typically done using the mass density power spectrum. For a given setting of cosmological parameters, a model-based spectrum can be computed and compared to the observed data. Previous work has focused on the linear part of the spectrum. However, recent advances in fast, N-body solver codes (Heitmann, Ricker, Warren and Habib, 2005) make it possible to utilize observations corresponding to the non-linear regions of the power spectrum, making it possible to incorporate more data sources into the analysis. In order to utilize information from the computationally demanding simulations, we rely on a statistical framework adapted from Kennedy and O'Hagan (2001).