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Variational Methods

In: Handbook of Uncertainty Quantification

Author

Listed:
  • Maelle Nodet

    (University Grenoble Alpes, Laboratoire Jean Kuntzmann (LJK)
    INRIA)

  • Arthur Vidard

    (University Grenoble Alpes, Laboratoire Jean Kuntzmann (LJK)
    INRIA)

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.

Suggested Citation

  • Maelle Nodet & Arthur Vidard, 2017. "Variational Methods," Springer Books, in: Roger Ghanem & David Higdon & Houman Owhadi (ed.), Handbook of Uncertainty Quantification, chapter 32, pages 1123-1142, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12385-1_32
    DOI: 10.1007/978-3-319-12385-1_32
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