Publications by Fabio Nobile | EPFL Graph Search

Convergence analysis of Padé approximations for Helmholtz frequency response problems

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

MATHICSE Technical Report : A continuation-multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design

Fabio Nobile, Pénélope Leyland, Michele Pisaroni

The majority of problems in aircraft production and operation require decisions made in the presence of uncertainty. For this reason aerodynamic designs obtained with traditional deterministic optimization techniques seeking only optimality in a specific s ...

MATHICSE2018

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

Fabio Nobile

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximation ...

2018

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

Elsevier2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...

MATHICSE2017

MULTILEVEL ENSEMBLE KALMAN FILTERING FOR SPATIO-TEMPORAL PROCESSES

Fabio Nobile, Hakon Andreas Hoel

This work concerns state-space models, in which the state-space is an infinite-dimensional spatial field, and the evolution is in continuous time, hence requiring approximation in space and time. The multilevel Monte Carlo (MLMC) sampling strategy is lever ...

2017

MATHICSE Technical Report : Multilevel Monte Carlo approximation of functions

Fabio Nobile, Sebastian Krumscheid

Many applications across sciences and technologies require a careful quantification of non-deterministic effects to a system output, for example when evaluating the system's reliability or when gearing it towards more robust operation conditions. At the he ...

MATHICSE2017

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Convergence analysis of Padé approximations for Helmholtz frequency response problems

MATHICSE Technical Report : A continuation-multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

MULTILEVEL ENSEMBLE KALMAN FILTERING FOR SPATIO-TEMPORAL PROCESSES

MATHICSE Technical Report : Multilevel Monte Carlo approximation of functions

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

MATHICSE Technical Report : Multilevel Monte Carlo approximation of functions

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MULTILEVEL ENSEMBLE KALMAN FILTERING FOR SPATIO-TEMPORAL PROCESSES

MATHICSE Technical Report : A continuation-multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design

Convergence analysis of Padé approximations for Helmholtz frequency response problems

A posteriori error estimation for the steady Navier-Stokes equations in random domains