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Bayesian statistical inference on the material parameters of a hyperelastic body
Hale, Jack; Farrel, Patrick E.; Bordas, Stéphane
2016In Proceedings of the ACME-UK 2016 24th Conference on Computational Mechanics
 

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Keywords :
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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
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
External co-authors :
yes
Language :
English
Title :
Bayesian statistical inference on the material parameters of a hyperelastic body
Publication date :
31 March 2016
Event name :
ACME-UK 2016 24th Conference on Computational Mechanics
Event organizer :
UKACM
Event place :
Cardiff, United Kingdom
Event date :
31-03-2016 to 1-04-2016
Main work title :
Proceedings of the ACME-UK 2016 24th Conference on Computational Mechanics
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
Funders :
EPSRC - Engineering and Physical Sciences Research Council [GB]
CE - Commission Européenne [BE]
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