A response-modeling alternative to surrogate models for support in computational analyses

Often, the objectives in a computational analysis involve characterization of system performance based on some function of the computed response. In general, this characterization includes (at least) an estimate or prediction for some performance measure and an estimate of the associated uncertainty. Surrogate models can be used to approximate the response in regions where simulations were not performed. For most surrogate modeling approaches, however, (1) estimates are based on smoothing of available data and (2) uncertainty in the response is specified in a point-wise (in the input space) fashion. These aspects of the surrogate model construction might limit their capabilities.One alternative is to construct a probability measure, G(r), for the computer response, r, based on available data. This “response-modeling” approach will permit probability estimation for an arbitrary event, E(r), based on the computer response. In this general setting, event probabilities can be computed: prob(E)=∫rI(E(r))dG(r) where I is the indicator function. Furthermore, one can use G(r) to calculate an induced distribution on a performance measure, pm. For prediction problems where the performance measure is a scalar, its distribution Fpm is determined by: Fpm(z)=∫rI(pm(r)⩽z)dG(r). We introduce response models for scalar computer output and then generalize the approach to more complicated responses that utilize multiple response models.