Nonlinear kinetic parameter identification through map inversion

A nonlinear method for parameter identification in kinetic systems is presented. Parameter identification is achieved through the use of HDMR (high-dimensional model representation), which can reduce greatly the computational cost of high-dimensional function inversion. The technique is demonstrated in simulations to extract rate constants from concentration data in a linear kinetic system, the reaction of H₂ with Br₂, and the oxidation of formaldehyde. The results of inversion for the latter case are compared with a previously published linear inversion procedure. The new algorithm shows excellent performance in identifying the full distribution of rate constants consitent with the data. The speed and accuracy of the HDMR permits full inversion of all relevant model parameters without the introduction of hidden biases from prior assumptions on the quality of the model parameters.