A Sequential Design Method for the Inversion of an Unknown System

Abstract

A design method presented in a previous paper for the sequential generation of observation sites used for the inversion of a prediction model is extended to cope with practical issues such as delayed observations and design of batches of imposed size. The final objective of the construction is to be able to associate with any target T in the output space a value xT of the input factors such that the response of the system at xT will be “close” to T (from an industrial point of view, xT corresponds to manufactory conditions that yield a product whose feature of interest is described by T). The problem is thus much different from the more standard one where one wishes to build a precise model over the whole input space: here the model only has to be precise over a set of values xT that permit to reach any target T, that is, the observation sites should not be spread over the entire admissible input space, but should rather concentrate in areas that cover the reachable output space when mapped by the system. Examples in low dimensions are presented that illustrate the behavior of the method and allow a comparison to be made with a standard sequential method for designing exploratory experiments.