Experimental Design and Modeling for Forward-Inverse Maps

In customer-driven design of systems or products, one has performance targets in mind and would like to determine values for product or system parameters that meet such targets. Engineering computer simulation models predict performance given design parameter values; meeting a target is done iteratively through an optimization search procedure, typically by optimizing a regression, neural network or other type of approximation metamodel of the computer model. We pose the thesis that, since forward metamodel construction is a key part of this strategy, constructing an inverse metamodel directly is advantageous. The inverse metamodel obviates the need for optimization in many settings. One can design experiments that allow simultaneous fitting of forward and inverse metamodels. We discuss the potential for this strategy, the connection with the calibration problem, and some of the issues that must be resolved to make the approach practical.