Variational methods

Maelle Nodet 1, * Arthur Vidard 1
* Corresponding author
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : This contribution presents derivative-based methods for local sensitivity analysis, called Variational Sensitivity Analysis (VSA). If one defines an output called the response function, its sensitivity to inputs variations around a nominal value can be studied using derivative (gradient) information. The main issue of VSA is then to provide an efficient way of computing gradients. This contribution first presents the theoretical grounds of VSA: framework and problem statement, tangent and adjoint methods. Then it covers pratical means to compute derivatives, from naive to more sophisticated approaches, discussing their various 2 merits. Finally, applications of VSA are reviewed and some examples are presented, covering various applications fields: oceanography, glaciology, meteorology.
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Maelle Nodet, Arthur Vidard. Variational methods. Handbook of Uncertainty Quantification, Springer International Publishing, pp.1-20, 2016, 978-3-319-11259-6. ⟨10.1007/978-3-319-11259-6_32-1⟩. ⟨hal-01251720⟩

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