Discussion of “Experimental Design and Modeling for Forward-Inverse Maps” by R. Barton & M. Morris, appearing in Technometrics

Abstract

Inverse design—essentially the problem of finding system parameter values that achieve a given performance metric—is an enormously important problem across a wide range of engineering fields. Typical methods for inverse design employ a forward model for example, a complex computer simulation mapping design parameters to performance metrics, and embed it in an optimization loop. If the forward model is a black box, for which direct evaluation of gradients is intractable, then one must resort to derivative-free or so-called “zeroth order” optimization approaches (e.g., Močkus Citation1975; Jones, Schonlau, and Welch Citation1998; Conn, Scheinberg, and Vicente Citation2009; Larson, Menickelly, and Wild Citation2019). Most of these approaches iteratively construct a metamodel for the forward map during optimization. Barton and Morris (henceforth “the authors” or “BM”) propose instead to build an inverse metamodel, that is, a computationally inexpensive approximation of the performance metric-to-parameter map. The promise of such an inverse metamodel is that it makes inverse design much faster and more direct, bypassing the need for explicit optimization.