References of "Hauseux, Paul 50009562"
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See detailUncertainty Quantification in Finite Element Models:Application to SoftTissue Biomechanics
Hauseux, Paul UL; Hale, Jack UL; Bulle, Raphaël UL et al

Scientific Conference (2018, July 23)

We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree ... [more ▼]

We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree of uncertainty. It is therefore important to study how this statistical uncertainty in parameters propagates to a safety-critical quantity of interest in the output of a model. Efficient Monte Carlo methods based on variance reduction techniques (Sensitivity Derivatives Monte Carlo methods [Hauseux et al. 2017] and MultiLevel Monte Carlo [Giles 2015] methods) are employed to propagate this uncertainty for both random variables and random fields. Inverse and forward problems are strongly connected. In a bayesian setting [Matthies et al. 2017], developing methods that reduce the number of evaluations of the forward model to an absolute minimum to achieve convergence is crucial for tractable computations. Numerical results in the context of soft tissue biomechanics are presented and discussed. [less ▲]

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See detailUsing higher-order adjoints to accelerate the solution of UQ problems with random fields
Hale, Jack UL; Hauseux, Paul UL; Bordas, Stéphane UL

Poster (2018, January 08)

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 ... [more ▼]

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. [less ▲]

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See detailQuantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters
Hauseux, Paul UL; Hale, Jack UL; Cotin, Stéphane et al

in Applied Mathematical Modelling (2018), 62

We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than ... [more ▼]

We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden-Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material. [less ▲]

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See detailCalculating the Malliavin derivative of some stochastic mechanics problems
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

in PLoS ONE (2017), 12(12), 0189994

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 ... [more ▼]

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. [less ▲]

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See detailAccelerating Monte Carlo estimation with derivatives of high-level finite element models
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics & Engineering (2017), 318

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 ... [more ▼]

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. [less ▲]

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See detailUncertainty Quantification - Sensitivity Analysis / Biomechanics
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Presentation (2017, February)

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See detailImage to analysis pipeline: single and double balloons kyphoplasty
Baroli, Davide UL; Hauseux, Paul UL; Hale, Jack UL et al

Poster (2016, December 12)

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼]

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲]

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See detailUncertainty quantification for soft tissue biomechanics
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Poster (2016, December)

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See detailStochastic FE analysis of brain deformation with different hyper-elastic models
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Scientific Conference (2016, September)

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See detailFE modelling with strong discontinuities for 3D tensile and shear fractures: Application to underground excavation
Hauseux, Paul UL; Roubin, Emmanuel; Seyedi, Darius M. et al

in Computer Methods in Applied Mechanics & Engineering (2016), 309

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See detailSolving the stochastic Burgers equation with a sensitivity derivative-driven Monte Carlo method
Hauseux, Paul UL; Hale, Jack UL; Bordas, Stéphane UL

Software (n.d.)

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Detailed reference viewed: 94 (13 UL)