Reference : Accelerating Monte Carlo estimation with derivatives of high-level finite element models
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/28618
Accelerating Monte Carlo estimation with derivatives of high-level finite element models
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 >]
1-May-2017
Computer Methods in Applied Mechanics & Engineering
Elsevier Science
318
917-936
Yes (verified by ORBilu)
International
0045-7825
Lausanne
Switzerland
[en] In this paper we demonstrate the ability of a derivative-driven Monte Carlo estimator to accelerate the propagation of uncertainty through two high-level non-linear finite element models. The use of derivative information amounts to a correction to the standard Monte Carlo estimation procedure that reduces the variance under certain conditions. We express the finite element models in variational form using the high-level Unified Form Language (UFL). We derive the tangent linear model automatically from this high-level description and use it to efficiently calculate the required derivative information. To study the effectiveness of the derivative-driven method we consider two stochastic PDEs; a one- dimensional Burgers equation with stochastic viscosity and a three-dimensional geometrically non-linear Mooney-Rivlin hyperelastic equation with stochastic density and volumetric material parameter. Our results show that for these problems the first-order derivative-driven Monte Carlo method is around one order of magnitude faster than the standard Monte Carlo method and at the cost of only one extra tangent linear solution per estimation problem. We find similar trends when comparing with a modern non-intrusive multi-level polynomial chaos expansion method. We parallelise the task of the repeated forward model evaluations across a cluster using the ipyparallel and mpi4py software tools. A complete working example showing the solution of the stochastic viscous Burgers equation is included as supplementary material.
FWO ; Fonds National de la Recherche - FnR
Researchers
http://hdl.handle.net/10993/28618
10.1016/j.cma.2017.01.041
http://dx.doi.org/10.6084/m9.figshare.3561306.v2
FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
FnR ; FNR6693582 > Jack Samuel Hale > ACCeSS > Advanced Computational Methods for the Simulation of Cutting in Surgery > 01/01/2014 > 31/12/2015 > 2013

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