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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1007/BF03346400

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1572-9265

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Numerical methods for computing sensitivities for

Authors: Jonathan Calver Wayne Enright
Publish Date: 2016/09/21
Volume: 74, Issue: 4, Pages: 1101-1117
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Abstract

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

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