In engineering design, approximations to engineering simulation or analysis models can provide quick, approximate predictions of system or part performance as a function of system/part design parameters. There are often preliminary requirements for performance, which can be mapped to specific values of design parameters via an inverse model. Typically, only forward models exist explicitly, but an inverse approximation can be fitted. The quality of an approximation depends on the set of runs (the experiment design) used to fit the approximation. This paper examines experiment design construction strategies for simultaneously fitting forward and inverse approximation models, using the commonly applied measure of D-optimality.