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Error estimation approaches for progressive response surfaces -more results

Romero, Vicente J.; Slepoy, R.; Swiler, Laura P.; Giunta, A.A.; Krishnamurthy, T.

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. "Progressive" response surfaces are built up incrementally as global information is added from new sample points added to the previous points in the parameter space. As the response surfaces are globally upgraded, indicators of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured or unstructured fashion. Whatever the approach, it is usually desirable to sample the entire parameter space uniformly (at least in early stages of sampling). At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly (progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in previous stages of sampling ("adaptive" response surfaces). Here we consider progressive response surfaces where a balanced representation of global response over the parameter space is desired. We use Kriging and Moving-Least-Squares methods to fit Halton quasi-Monte-Carlo data samples and interpolate over the parameter space. On 2-D test problems we use the response surfaces to compute various response measures and assess the accuracy/applicability of heuristic error estimates based on convergence behavior of the computed response quantities. Where applicable we apply Richardson Extrapolation for estimates of error, and assess the accuracy of these estimates. We seek to develop a robust methodology for constructing progressive response surface approximations with reliable error estimates.