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Calculating the Malliavin derivative of some stochastic mechanics problems.
- Source :
-
PLoS ONE . 12/20/2017, Vol. 12 Issue 12, p1-18. 18p. - Publication Year :
- 2017
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19326203
- Volume :
- 12
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- PLoS ONE
- Publication Type :
- Academic Journal
- Accession number :
- 126874075
- Full Text :
- https://doi.org/10.1371/journal.pone.0189994