NSF/Sandia: Discrepancy Sensitivity for Efficiently Choosing Computer Experiments in Design and Uncertainty Quantification

University Of Southern California, Los Angeles CA

Investigators

Abstract

This project will explore and develop a new method, based on the mathematical definitions of discrepancy and discrepancy sensitivity (DS), of quantifying sample point contribution to sample uniformity in the entire input/output domain, and the resulting strategies for the design of computer experiments (DoCE). Essentially, DS quantifies the change in sample point uniformity due to the addition of new simulation sample points. The project will aim to derive "DS fields" to efficiently locate a new sample point, develop DS strategies to best choose the next N simulation points, and investigate a number of open questions integral to effective use of DS for DoCE. The expected results are innovative algorithms for efficiently choosing sample points for response surface exploration, propagation of uncertainty through complex systems, and design optimization. Whether for model validation, design optimization or reliability analysis, it is difficult to efficiently choose sample points for computer experiments in the presence of uncertainty. Even with recent computational advances, simulation of complex uncertain systems taxes today's most capable computers. Thus, methods are required to select which simulations will provide the most useful information given a limited computational budget. Such problems are widespread in science and engineering, where physical testing is often impractical for financial, safety, policy or other pragmatic reasons, and include high-priority applications in accident investigation, protein modeling, projectile penetration, cosmological models, and complex system reliability. Some approaches exist for choosing sample points, but lack quantitative measures of "information" added by new sample points, particularly in the output space.