Publications by Fabio Nobile | EPFL Graph Search

Probabilistic Load Forecasting of distribution power systems based on empirical copulas

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

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Fabio Nobile, Thomas Simon Spencer Trigo Trindade

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

Springer Nature Switzerland2025

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, 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 the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2024

Petrov-Galerkin Dynamical Low Rank Approximation: SUPG stabilisation of advection-dominated problems

Fabio Nobile, Thomas Simon Spencer Trigo Trindade

We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamles ...

Elsevier BV2024

Personalized computational electro-mechanics simulations to optimize cardiac resynchronization therapy

Fabio Nobile

In this study, we present a computational framework designed to evaluate virtual scenarios of cardiac resynchronization therapy (CRT) and compare their effectiveness based on relevant clinical biomarkers. Our approach involves electro-mechanical numerical ...

2024

A multigrid method for PDE-constrained optimization with uncertain inputs

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 optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024

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 optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

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 likelihood function and is based on exact simulation techniques that are of s ...

Springer Cham2024

Density estimation in RKHS with application to Korobov spaces in high dimensions

Fabio Nobile, Yoshihito Kazashi

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

2023

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Jürg Alexander Schiffmann, Fabio Nobile, Dimitri Maurice Goutaudier

Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requi ...

2023

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Fabio Nobile, Juan Pablo Madrigal Cianci

In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo(ML-MCMC) algorithms based on independent Metropolis--Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving ...

2023

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Jürg Alexander Schiffmann, Fabio Nobile, Dimitri Maurice Goutaudier

Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requi ...

Amer Soc Mechanical Engineers2023

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

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

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-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2023

A new method to interpolate POD reduced bases-Application to the parametric model order reduction of a gas bearings supported rotor

Jürg Alexander Schiffmann, Fabio Nobile, Dimitri Maurice Goutaudier

The proper orthogonal decomposition (POD) is successfully employed in a variety of projection-based methods for parametric model order reduction (pMOR) of large dynamical systems. It extracts the most energetic modes describing the dynamics of a system fro ...

Wiley2023

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

Fabio Nobile, Sebastian Krumscheid, Sundar Subramaniam Ganesh

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-risk, of output quantities of complex random differential models by the MLM ...

2023

Some first results on the consistency of spatial regression with partial differential equation regularization

Fabio Nobile, Eleonora Arnone

We study the consistency of the estimator in spatial regression with partial differential equa-tion (PDE) regularization. This new smoothing technique allows to accurately estimate spatial fields over complex two-dimensional domains, starting from noisy ob ...

2022

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

Fabio Nobile, Davide Pradovera

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate mo ...

2022

Computational electrophysiology of the coronary sinus branches based on electro-anatomical mapping for the prediction of the latest activated region

Fabio Nobile, Alfio Quarteroni

This work dealt with the assessment of a computational tool to estimate the electrical activation in the left ventricle focusing on the latest electrically activated segment (LEAS) in patients with left bundle branch block and possible myocardial fibrosis. ...

2022