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Fabio Nobile

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Related publications (97)

Page 2 of 5

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Davide Pradovera, Francesca Bonizzoni

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

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

Daniel Kressner, Fabio Nobile, 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 hybrid collocation-perturbation approach for PDEs with random domains

Fabio Nobile

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

2021

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

Modeling spatially dependent functional data via regression with differential regularization

Fabio Nobile

We propose a method for modelling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of phenomenon under study ...

2019

Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification

Fabio Nobile, Yoshihito Kazashi

This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice-a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New Y ...

Springer2022

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

An active strain electromechanical model for cardiac tissue

Alfio Quarteroni, Fabio Nobile, Ricardo Esteban Ruiz Baier

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...

Wiley2012

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 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

Multilevel Monte Carlo Approximation of Functions

Fabio Nobile, Sebastian Krumscheid

Many applications across sciences and technologies require a careful quantification of nondeterministic 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 ...

2018

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2023

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

Fabio Nobile

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

2018

Probabilistic Load Forecasting of distribution power systems based on empirical copulas

Mario Paolone, Fabio Nobile, Pål Forr Austnes, Celia Garcia Pareja

Accurate and reliable electricity load forecasts are becoming increasingly important as the share of intermittent resources in the system increases. Distribution System Operators (DSOs) are called to accurately forecast their production and consumption to ...

Elsevier BV2025

A Continuation Multi Level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible inviscid aerodynamics

Fabio Nobile, Pénélope Leyland, Michele Pisaroni

In this work we apply the Continuation Multi-Level Monte Carlo (C-MLMC) algorithm proposed in Collier et al. (2014) to efficiently propagate operating and geometric uncertainties in inviscid compressible aerodynamics numerical simulations. The key idea of ...

Elsevier2017

Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations

Fabio Nobile, Eva Vidlicková, Yoshihito Kazashi

We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete variational formulation ...

Springer2021

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

Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

Fabio Nobile, Davide Pradovera

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the param ...

2021

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014