Inverse problems in chemical dynamics: The calculation of inverse coefficients

A general technique is described for gaining insight into inversion processes. Upon solving the equation of motion associated with a given physical model, specialized inverse coefficients are calculated to address questions on inverse modeling. The number of accessible independent inverse coefficients is shown to be directly related to the number of independent pieces of modeling data taken as available. Although the inverse coefficients do not in themselves form an inversion algorithm, they do give a quantitative measure of the importance of performing certain additional measurements for the ultimate purpose of inversion. The concepts are illustrated by some simple dynamical models. The calculations show that the normal forward sensitivities and the new inverse coefficients generally exhibit disparate behavior in accord with the differing physical quantities being addressed.