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Fabio Nobile

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Publications associées (97)

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

2016

A Multi Level Monte Carlo Algorithm for the Treatment of Geometrical and Operational Uncertainties in Internal and External Aerodynamics

Pénélope Leyland, Fabio Nobile, Michele Pisaroni

In this work we present an efficient Multi Level Monte Carlo (MLMC) algorithm capable of propagating operational uncertainties, due to atmospheric variability of external aerodynamics flows and geometrical uncertainties due to manufacturing tolerances and ...

AIAA2016

Multi-index Stochastic Collocation for random PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the ...

2016

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

Marco Picasso, Fabio Nobile, 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

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

Springer2016

Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...

Springer2016

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Fabio Nobile, Daniel Kressner, Francesca Bonizzoni

We study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the coefficient. The resulting recursive deterministic pr ...

Elsevier2016

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

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

Numerical Methods For Uncertainty Quantification

Fabio Nobile

Begell House Inc2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Christine Tobler, Daniel Kressner, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

A Multi Level Monte Carlo Method with Control Variate for elliptic PDEs with log-normal coefficients

Fabio Nobile, Francesco Tesei

We consider the numerical approximation of the stochastic Darcy problem with log-normal permeability field and propose a novel Multi Level Monte Carlo (MLMC) approach with a control variate variance reduction technique on each level. We model the log-perme ...

2015

Analysis and Computation of Hyperbolic PDEs with Random Data

Fabio Nobile

Hyperbolic partial differential equations (PDEs) are mathematical models of wave phenomena, with applications in a wide range of scientific and engineering fields such as electromagnetic radiation, geosciences, fluid and solid mechanics, aeroacoustics, and ...

2015

An effective algorithm for the generation of patient-specific Purkinje networks in computational electrocardiology

Fabio Nobile, Christian Vergara, Elena Faggiano

The Purkinje network is responsible for the fast and coordinated distribution of the electrical impulse in the ventricle that triggers its contraction. Therefore, it is necessary to model its presence to obtain an accurate patient-specific model of the ven ...

Elsevier2015

Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we compare different families of nested quadrature points, i.e. the classic Clenshaw-Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests th ...

Springer2015

Analysis and computation of the elastic wave equation with random coefficients

Fabio Nobile

We analyze the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given ...

2015

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

Fabio Nobile, Eleonora Musharbash

In this work we discuss the dynamically orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

2015

Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Fabio Nobile, Giovanni Migliorati

We analyze the stability and accuracy of discrete least squares on multivariate polynomial spaces to approximate a given function depending on a multivariate random variable uniformly distributed on a hypercube. The polynomial approximation is calculated s ...

2015

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