Efficient Computation of Sensitivities for Ordinary Differential Equation Boundary Value Problems

For models described by ordinary differential equation boundary value problems (ODE BVPs), we derive adjoint equations for sensitivity analysis, giving explicit forms for the boundary conditions of the adjoint boundary value problem. The solutions of the adjoint equations are used to efficiently compute gradients of both integral-form and pointwise constraints. Existence and stability results are given for the adjoint system and its numerical solution. The use of the method is demonstrated for a simple example, where it is seen that the method is particularly advantageous for problems with more than a few parameters.