Non-parametric-validated computer-simulation surrogates: a Pareto formulation

In the surrogate approach to simulation-based optimization, the large-scale simulation is evoked only to construct and validate a simpli ed input{output model; this simpli ed input{output model then serves as a simulation surrogate in subsequent engineering optimization studies. We present here `basicʹ and Pareto surrogate formulations through an illustrative application from uid dynamics. The critical ingredient of both formulations is a non-parametric statistical validation and error estimation procedure which, based on veri able hypotheses, precisely quanti es the e ect of surrogate-for-simulation substitution on system predictability, stability, and optimality. The Pareto formulation improves upon the basic approach by operating only in the vicinity of the e cient frontier of the output achievable set A; for problems with many inputs and few outputs, this considerably reduces the dimensionality of the problem, and correspondingly improves the surrogate error estimates.