Abstract
Perturbation methods based on derivatives can be applied to uncertainties in two particular contexts. First, surrogate models based on Taylor expansion can be built after methods for evaluation of first and second derivatives have been developed. Second, PC-based probabilistic functionals can be minimized after a gradient is computed. Both contexts use derivations which are intrusive. This chapter, after a definition of these approaches, concentrates on Taylor surrogate models or Moment methods.
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Acknowledgements
For the chapters “Introduction to Intrusive Perturbation Methods”, “Algorithmic Differentiation for Second Derivatives”, “Introduction to Intrusive Perturbation Methods and Their Range of Applicability” and “Use of Automatic Differentiation Tools at the Example of TAPENADE”, the author used a lot of material from the publication [1] and the reports delivered in NODESIM project.
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Dervieux, A. (2019). Introduction to Intrusive Perturbation Methods. In: Hirsch, C., Wunsch, D., Szumbarski, J., Łaniewski-Wołłk, Ł., Pons-Prats, J. (eds) Uncertainty Management for Robust Industrial Design in Aeronautics . Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-77767-2_20
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