Reference : Bayesian statistical inference on the material parameters of a hyperelastic body

	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/24855

Title :	Bayesian statistical inference on the material parameters of a hyperelastic body
Language :	English
Author, co-author :	Hale, Jack [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Farrel, Patrick E. []
	Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Publication date :	31-Mar-2016
Main document title :	Proceedings of the ACME-UK 2016 24th Conference on Computational Mechanics
Peer reviewed :	No
Audience :	National
Event name :	ACME-UK 2016 24th Conference on Computational Mechanics
Event date :	31-03-2016 to 1-04-2016
Event organizer :	UKACM
Event place (city) :	Cardiff
Event country :	United Kingdom
Keywords :	[en] Bayesian inference ; dolfin-adjoint ; posterior ; FEniCS ; hyperelasticity
Abstract :	[en] We present a statistical method for recovering the material parameters of a heterogeneous hyperelastic body. Under the Bayesian methodology for statistical inverse problems, the posterior distribution encodes the probability of the material parameters given the available displacement observations and can be calculated by combining prior knowledge with a finite element model of the likelihood. In this study we concentrate on a case study where the observations of the body are limited to the displacements on the surface of the domain. In this type of problem the Bayesian framework (in comparison with a classical PDE-constrained optimisation framework) can give not only a point estimate of the parameters but also quantify uncertainty on the parameter space induced by the limited observations and noisy measuring devices. There are significant computational and mathematical challenges when solving a Bayesian inference problem in the case that the parameter is a field (i.e. exists infinite-dimensional Banach space) and evaluating the likelihood involves the solution of a large-scale system of non-linear PDEs. To overcome these problems we use dolfin-adjoint to automatically derive adjoint and higher-order adjoint systems for efficient evaluation of gradients and Hessians, develop scalable maximum aposteriori estimates, and use efficient low-rank update methods to approximate posterior covariance matrices.
Funders :	EPSRC
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/10993/24855
Framework Programme / European Project :	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 :	FnR ; FNR6693582 > Jack Samuel Hale > > Advanced Computational Methods for the Simulation of Cutting in Surgery > 01/01/2014 > 31/12/2015 > 2013

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