Publications related to Uncertainty Quantification for Reduced Basis Approximations: "Natural Norm" A Posteriori Error Estimators

Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

The estimation of the apparent axon diameter (AAD) via diffusion MRI is affected by the incoherent alignment of single axons around its axon bundle direction, also known as orientational dispersion. The simultaneous estimation of AAD and dispersion is chal ...

SPRINGER-VERLAG BERLIN2018

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

Jan Skaloud, Stéphane Guerrier, Philipp Clausen

The proliferation of (low-cost) sensors provokes new challenges in data fusion. This is related to the correctness of stochastic characterization that is a prerequisite for optimal estimation of parameters from redundant observations. Different (statistica ...

2017

MATHICSE Technical Report : A posteriori error estimators for hierarchical B-spline discretizations

Annalisa Buffa

In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the energy error. Th ...

MATHICSE2017

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Alfio Quarteroni, Andrea Manzoni

When relying on Newton iterations to solve nonlinear problems in the context of Reduced Basis (RB) methods, the assembling of the RB arrays during the online stage depends on the dimension of the underlying high-fidelity approximation. This is more of an i ...

Elsevier Science Sa2017

A posteriori error estimation for partial differential equations with random input data

Diane Sylvie Guignard

This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...

EPFL2016

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...

2016

Reduced Basis Approximation And A Posteriori Error Estimates For Parametrized Elliptic Eigenvalue Problems

Andrea Manzoni, Nicola Parolini

We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...

Edp Sciences S A2016

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

Alfio Quarteroni, Andrea Manzoni

When using Newton iterations to solve nonlinear parametrized PDEs in the context of Reduced Basis (RB)methods, the assembling of the RB arrays in the online stage depends in principle on the high-fidelityapproximation. This task is even more challenging wh ...

MATHICSE2016

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

Sohrab Mirshams Shahshahani

We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from

S^2\times R

to

S^2

parameterized by

\nu \epsilon (\frac{1}{2},1]

. The longitudinal function

u(t,\alpha)

which is the main object of study will be ...

2016

A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolera ...

2015

Uncertainty Quantification for Reduced Basis Approximations: "Natural Norm" A Posteriori Error Estimators

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Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

MATHICSE Technical Report : A posteriori error estimators for hierarchical B-spline discretizations

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

A posteriori error estimation for partial differential equations with random input data

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Reduced Basis Approximation And A Posteriori Error Estimates For Parametrized Elliptic Eigenvalue Problems

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

A continuation multilevel Monte Carlo algorithm

Parameter Determination of Sensor Stochastic Models under Covariate Dependency

A posteriori error estimation for partial differential equations with random input data

Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

A posteriori error estimations for elliptic partial differential equations with small uncertainties

MATHICSE Technical Report : A posteriori error estimators for hierarchical B-spline discretizations

Reduced Basis Approximation And A Posteriori Error Estimates For Parametrized Elliptic Eigenvalue Problems

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

A continuation multilevel Monte Carlo algorithm

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems