Emulation of Numerical Models With Over-Specified Basis Functions

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.