Cheap Second Order Directional Derivatives of Stiff ODE Embedded Functionals

A second order adjoint method is described for calculating directional derivatives of stiff ODE embedded functionals. The derivation of the general directional second order adjoint equations for point- and integral-form functionals is presented. A numerical procedure for calculating these directional derivatives that is relatively insensitive to the number of parameters is described and showcased. By combining automatic differentiation (AD) to obtain the adjoint and sensitivity equations with the staggered corrector method to solve the sensitivity systems, we achieve computational costs noticeably lower than directional finite differences based on a first order adjoint code.

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