An improved computational method for sensitivity analysis: Green's function method with 'AIM'

Sensitivity analysis of initial value models via the calculation of linear sensitivity coefficients is quite important for model evaluation and validation. Direct solution of the sensitivity equations for n-dimensional, m-parameter systems of ordinary differential equations requires the solution of m × n differential equations, which can become quite expensive for large-scale models. When m > n (the usual case for chemical kinetic systems, for example), the Green's function method (GFM), which requires solutions of n² differential equations with m × n subsequent numerical quadratures, is the most efficient computational technique for determining linear sensitivity coefficients. Even so, associated computing costs can still become quite large. In the current work, an algorithm, known as the analytical integrated Magnus (AIM) modification of the GFM, is presented which dramatically reduces the computational effort required to determine linear sensitivity coefficients. The technique employs the piecewise Magnus method for more efficient calculation of Green's function kernels, and treats the sensitivity integrals analytically. An application of this technique to a chemical kinetics system is presented in which the computational effort is reduced by an order of magnitude in comparison to the unmodified GFM.