Algorithmic differentiation applied to the optimal calibration of a shallow water model

Abstract : The information on sensitivity provided by derivatives is indispensable in many fields of science. In numerical analysis, computing the accurate value of the derivatives of a function can be a challenge. The classical Finite Differences (FD) method is a simple solution to implement when estimating the value of a derivative. However, it remains highly sensitive numerically and costly in calculation time. Conversely, the Algorithmic Differentiation Method (AD) is a powerful tool for calculating the derivatives of a function described by a computer program. Whatever the complexity of the algorithms implemented in the expression of a function, AD calculates its derivative accurately and reduces development efforts. This article presents the contribution of AD in comparison to FD in the problem of calibrating an industrial class 1D shallow water model. Model calibration is performed by a deterministic mathematical optimiser requiring accurate calculation of the sensitivity of the water surface profile in relation to the friction on a river bed. Two comparative real test cases are presented. They permit validating the better performance expected from AD as a tool used to obtain optimal calibration.
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https://hal.inria.fr/hal-01244264
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Submitted on : Tuesday, December 15, 2015 - 3:36:19 PM
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Félix Demangeon, Cédric Goeury, Fabrice Zaoui, Nicole Goutal, Valérie Pascual, et al.. Algorithmic differentiation applied to the optimal calibration of a shallow water model. La Houille Blanche - Revue internationale de l'eau, EDP Sciences, 2015. ⟨hal-01244264⟩

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