85 citations · 405 across the 34 of their papers we have counts for
38 papers
Dynamical Low-Rank Approximation for Stochastic Differential Equations
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating th…
Unbiased likelihood estimation of Wright-Fisher diffusion processes
Celia García-Pareja, Fabio Nobile
In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright-Fisher diffusions. Our approach provides an unbiased estimator of the l…
A multigrid solver for PDE-constrained optimization with uncertain inputs
Gabriele Ciaramella, Fabio Nobile, Tommaso Vanzan
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimizatio…
A combination technique for optimal control problems constrained by random PDEs
Fabio Nobile, Tommaso Vanzan
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of Op…
Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method
Sundar Ganesh, Fabio Nobile
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-ba…
Quantifying uncertain system outputs via the multi-level Monte Carlo method -- distribution and robustness measures
Quentin Ayoul-Guilmard, Sundar Ganesh, Sebastian Krumscheid +1
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at…
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…
Density estimation in RKHS with application to Korobov spaces in high dimensions
Yoshihito Kazashi, Fabio Nobile
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel func…
Uncertainty Quantification by MLMC and Local Time-stepping For Wave Propagation
Marcus J. Grote, Simon Michel, Fabio Nobile
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values…
Analysis of a class of Multi-Level Markov Chain Monte Carlo algorithms based on Independent Metropolis-Hastings
Juan Pablo Madrigal-Cianci, Fabio Nobile, Raul Tempone
In this work, we present, analyze, and implement a class of Multi-Level Markov chain Monte Carlo (ML-MCMC) algorithms based on independent Metropolis-Hastings proposals for Bayesia…
Integration of activation maps of epicardial veins in computational cardiac electrophysiology
Simone Stella, Christian Vergara, Massimiliano Maines +7
In this work we address the issue of validating the monodomain equation used in combination with the Bueno-Orovio ionic model for the prediction of the activation times in cardiac…
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 combi…
Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification
Vesa Kaarnioja, Yoshihito Kazashi, Frances Y. Kuo +2
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…
Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations
Yoshihito Kazashi, Fabio Nobile, Eva Vidličková
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 approx…
Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem
Francesca Bonizzoni, Fabio Nobile
We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of…
Generalized Parallel Tempering on Bayesian Inverse Problems
Jonas Latz, Juan P. Madrigal-Cianci, Fabio Nobile +1
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found…
Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
Yoshihito Kazashi, Fabio Nobile
An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at ea…
A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters
Matthieu Martin, Fabio Nobile, Panagiotis Tsilifis
In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Prob…
Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines
Panagiotis Tsilifis, Iason Papaioannou, Daniel Straub +1
The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenge…
Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations
Simone Brugiapaglia, Stefano Micheletti, Fabio Nobile +1
We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed Sol…
Stable high-order randomized cubature formulae in arbitrary dimension
Giovanni Migliorati, Fabio Nobile
We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure defined on a domain $Γ\subseteq \math…
PDE-constrained optimal control problems with uncertain parameters using SAGA
Matthieu C. Martin, Fabio Nobile
We consider an optimal control problem (OCP) for a partial differential equation (PDE) with random coefficients. The optimal control function is a deterministic, distributed forcin…
Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure
Francesca Bonizzoni, Fabio Nobile, Ilaria Perugia +1
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator…
Least-Squares Padé approximation of parametric and stochastic Helmholtz maps
Francesca Bonizzoni, Fabio Nobile, Ilaria Perugia +1
The present work deals with the rational model order reduction method based on the single-point Least-Square (LS) Padé approximation technique introduced in [3]. Algorithmical aspe…