Sensitivity Analysis Using Parallel Ode Solvers and Automatic Diierentiation in C: Senspvode and Adic

PVODE is a high-performance ordinary diierential equation solver for the types of initial value problems (IVPs) that arise in large-scale computational simulations. Often, one wants to compute sensitivities with respect to certain parameters in the IVP. We discuss the use of automatic diierentiation (AD) to compute these sensitivities in the context of PVODE. Results on a simple test problem indicate that the use of AD-generated derivative code can reduce the time to solution over nite diierence approximations. 1 Background In complicated, large-scale computational simulations, the governing equations can often be spatially discretized and then numerically solved as a system of ordinary diierential equation (ODE) or diierential-algebraic equation (DAE) initial-value problems. PVODE BH99] and IDA HT99] are powerful, parallel codes for solving these types of ODEs and DAEs, respectively. The codes are written in C and use MPI to achieve parallelism and portability. Typically, the equations contain parameter values (e.g., chemical reaction rates) that are not precisely known. In analyzing the simulations, the scientist would like to know which parameters are most innuential in aaecting the behavior of the simulation. Such sensitivity information is useful because it identiies which parameters will require precise measurements if the simulation results are to be made more accurate. This article summarizes preliminary work in which automatic diierenti-ation (AD) is being used with PVODE to create a solver that computes