An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models

Response surface methodologies can reveal important features of complex computer code models. Here, we suggest experimental designs and interpolation methods for extracting nonlinear response surfaces whose roughness varies substantially over the input domain. A sequential design algorithm for cuboid domains is initiated by selecting an extended corner/centre point design for the entire domain, then updated by decomposing this domain into disjoint cuboids and taking the corners and centre of these cuboids as new design points. A roughness criterion is used to control the domain decomposition so that the design becomes space-filling and the coverage is particularly good in the parts of the input domain where the response surface is strongly nonlinear. Finally, the model output at untried inputs is predicted by carefully selecting a local neighbourhood of each new point in the input space and fitting a full quadratic polynomial to the data points in that neighbourhood. Test runs showed that our sequential design algorithm automatically adapts to the nonlinear features of the model output. Moreover, our technique is particularly useful for extracting nonlinear response surfaces from computer code models with two to seven input variables. A simple modification of the outlined algorithm enables adequate handling of non-cuboid input domains.