Reference : Calculating the Malliavin derivative of some stochastic mechanics problems
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
http://hdl.handle.net/10993/33796
Calculating the Malliavin derivative of some stochastic mechanics problems
English
Hauseux, Paul mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Hale, Jack mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
20-Dec-2017
PLoS ONE
Public Library of Science
12
12
e0189994
Yes (verified by ORBilu)
International
1932-6203
San Franscisco
CA
[en] The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper.
University of Luxembourg - UL
Researchers ; Professionals
http://hdl.handle.net/10993/33796
10.1371/journal.pone.0189994
http://dx.doi.org/10.6084/m9.figshare.5432722
© 2017 Hauseux et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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