COMPUTATION OF THE GRADIENT AND SENSITIVITY COEFFICIENTS IN SUM OF SQUARES MINIMIZATION PROBLEMS WITH DIFFERENTIAL-EQUATION MODELS

In parameter estimation problems where the system model consists of di fferential equations, methods for minimizing a sum of squares of resid uals objective function require derivatives of the residuals with resp ect to the parameters being estimated (sensitivity coefficients) or th e gradient of the objective function (depending on the numerical optim ization method). This paper considers two methods for generating such derivatives: (1) the adjoint equation - gradient formula; and (2) comp limentary sensitivity coefficient differential equations. Particular a ttention is given to the consistency between the method used to solve the model equations and the proper formulation of the additional equat ions required by the two methods. Two example problems illustrate comp utational experience using a modified quasi-Newton method with the adj oint method used to generate gradients and applying a modified Gauss-N ewton approach with the sensitivity coefficient equations to calculate both the Gauss-Newton matrix and the objective function gradient. Res ults indicate the superiority of the sensitivity coefficient approach. When comparing the computational effort required by the two methods a nd the results from the simple examples, it appears that the use of co mplimentary sensitivity coefficient equations is much more efficient t han using only the gradient of the sum of squares function. (C) 1997 E lsevier Science Ltd.