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Numerical methods for computing sensitivities for ODEs and DDEs. (English) Zbl 1362.65070
Summary: We investigate the performance of the adjoint approach and the variational approach for computing the sensitivities of the least squares objective function commonly used when fitting models to observations. We note that the discrete nature of the objective function makes the cost of the adjoint approach for computing the sensitivities dependent on the number of observations. In the case of ordinary differential equations (ODEs), this dependence is due to having to interrupt the computation at each observation point during numerical solution of the adjoint equations. Each observation introduces a jump discontinuity in the solution of the adjoint differential equations. These discontinuities are propagated in the case of delay differential equations (DDEs), making the performance of the adjoint approach even more sensitive to the number of observations for DDEs. We quantify this cost and suggest ways to make the adjoint approach scale better with the number of observations. In numerical experiments, we compare the adjoint approach with the variational approach for computing the sensitivities.

65L05 Numerical methods for initial value problems
65L03 Numerical methods for functional-differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
Full Text: DOI
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