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Variational Methods

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Handbook of Uncertainty Quantification

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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.

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Authors and Affiliations

  1. Laboratoire Jean Kuntzmann (LJK), University Grenoble Alpes, 51 rue des Mathématiques, Cedex 9, F-38000, Grenoble, France

    Maelle Nodet & Arthur Vidard

  2. INRIA, 51 rue des Mathematiques, Cedex 9, F-38000, Rocquencourt, France

    Maelle Nodet & Arthur Vidard

Authors
  1. Maelle Nodet
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  2. Arthur Vidard
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Correspondence to Maelle Nodet .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, Virginia, USA

    David Higdon

  3. Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, USA

    Houman Owhadi

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Nodet, M., Vidard, A. (2017). Variational Methods. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-12385-1_32

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