Topics in Computer Experiments

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

This project will study problems that occur in the design of computer and physical experiments and the analysis of their output. Physical experiments are the gold standard for measuring input-output relationships but these measurements that contain noise and possibly unrecognized sources of bias. Computer codes that model input-output relationships are used increasingly in place of, or in conjunction with, physical experiments because of they can provide decreased lead times in the engineering design of manufactured goods as well as for the assessment of designs in varying field-use conditions and varying conditions of fabrication. In general a deeper understanding of product and process performance can be made by using a combination of computer and physical experiments. However, computer codes provide a biased measurement of input-output relationships because of the inevitably inadequate physics or biology used in their development. This proposal will address the following problems that arise from the challenges sketched above. 1. To increase the computational efficiency of screening methodology for identifying the most important inputs to a computer code. 2. To develop methodology for estimating the upper (or lower) percentile of a computer code output with respect to the distributionof the field inputs. 3. To estimate the set of Pareto optimal input values for multivariate computer output and the corresponding Pareto Frontier of output vectors corresponding to the Pareto optimal inputs. 4. To develop statistical methodology for simultaneous determination of calibration parameters and tuning inputs for computer models, including those with mixed quantitative and qualitative inputs. Experimental modeling using computer codes is increasingly prevalent in engineering, in biomechanics, in the physical sciences, in the life sciences, in economics, and other areas of natural science such as the assessment of climate change and cosmology. Over the past twenty years, the use of computer codes as experimental tools has become increasingly sophisticated due to the fact that the number of inputs to such codes has steadily increased as well as the level of detail embodied by the codes. Researchers can now vary both ``engineering'' inputs as well as inputs that describe the operating conditions in the model. In addition, more detailed mathematical models of the input-output relationship as well as more accurate numerical solution of these models often produce codes that require 5-24 hours for a single run. In addition, multiple codes are often used to describe different aspects of the phenomenon being studied. This project will study problems that occur in the design of experiments involving such computer codes including screening the important inputs to such codes to determine important inputs, the efficient use of code output for optimization and other problems, and the calibration of corresponding physical experiments to further improve their prediction accuracy.