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ABSTRACT
Mathematical models are frequently used to explore physical systems, but can be computationally expensive to evaluate. In such settings, an emulator is used as a surrogate. In this work, we propose a basis-function approach for computer model emulation. To combine field observations with a collection of runs from the numerical model, we use the proposed emulator within the Kennedy-O’Hagan framework of model calibration. A novel feature of the approach is the use of an over-specified set of basis functions where number of bases used and their inclusion probabilities are treated as unknown quantities. The new approach is found to have smaller predictive uncertainty and computational efficiency than the standard Gaussian process approach to emulation and calibration. Along with several simulation examples focusing on different model characteristics, we also use the method to analyze a dataset on laboratory experiments related to astrophysics.
Supplementary Materials
Additional details: All appendices mentioned in this article (.pdf file)
R-code and dataset: The CRASH-UQ datasets used in Section 5 and R codes to fit gPC-based model (one uses only the computer model output and another uses the computer output and experimental outcomes simultaneously) (.zip file)
Acknowledgments
This work was funded by the Predictive Sciences Academic Alliances Program in DOE/NNSA-ASC via grant DEFC52-08NA28616. Research of Dr. Bani K. Mallick is supported by U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165.
