monte carlo; variance reduction; uncertainty quantification; taylor series; FEniCS; PETSc; DOLFIN
Abstract :
[en] A powerful Monte Carlo variance reduction technique introduced in Cao and Zhang 2004 uses
local derivatives to accelerate Monte Carlo estimation. This work aims to: develop a new derivative-driven estimator that works for SPDEs with uncertain data modelled as Gaussian random fields with Matérn covariance functions (infinite/high-dimensional problems) (Lindgren, Rue, and Lindström, 2011), use second-order derivative (Hessian) information for improved variance reduction over our approach in (Hauseux, Hale, and Bordas, 2017), demonstrate a software framework using FEniCS (Logg and Wells, 2010), dolfin-adjoint (Farrell et al., 2013) and PETSc (Balay et al., 2016) for automatic acceleration of MC estimation for a wide variety of PDEs on HPC architectures.
Disciplines :
Mathematics
Author, co-author :
HALE, Jack ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
HAUSEUX, Paul ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
BORDAS, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
no
Language :
English
Title :
Using higher-order adjoints to accelerate the solution of UQ problems with random fields
Publication date :
08 January 2018
Number of pages :
A0
Event name :
Key UQ methodologies and motivating applications
Event organizer :
Isaac Newton Institute for Mathematical Sciences
Event place :
Cambridge, United Kingdom
Event date :
8-1-2018 to 12-1-2018
Audience :
International
Focus Area :
Computational Sciences
European Projects :
FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
FnR Project :
FNR6693582 - Advanced Computational Methods For The Simulation Of Cutting In Surgery, 2013 (01/01/2014-31/12/2015) - Jack Samuel Hale