Variational Methods

Maelle Nodet () and Arthur Vidard ()
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Maelle Nodet: University Grenoble Alpes, Laboratoire Jean Kuntzmann (LJK)
Arthur Vidard: University Grenoble Alpes, Laboratoire Jean Kuntzmann (LJK)

Chapter 32 in Handbook of Uncertainty Quantification, 2017, pp 1123-1142 from Springer

Abstract: 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 input 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 and tangent and adjoint methods. Then it covers practical means to compute derivatives, from naive to more sophisticated approaches, discussing their various merits. Finally, applications of VSA are reviewed, and some examples are presented, covering various applications fields: oceanography, glaciology, and meteorology.

Keywords: Variational sensitivity analysis; Variational methods; Tangent model; Adjoint model; Gradient; Automatic differentiation; Derivative; Local sensitivity analysis; Stability analysis; Geophysical applications; Meteorology; Glaciology; Oceanography (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-12385-1_32

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