Publications associées à Low-Rank Tensor Methods for High-Dimensional Problems

Publications associées (31)

The Power of Decision Trees for Composition and Search Problems

The unifying theme of this thesis are decision trees. Given a boolean function

f

and an input

x

, a decision tree computes the value

f(x)

by repeatedly querying bits of

x

. Our work is two-fold. On one hand, we investigate direct sums and other relat ...

EPFL2025

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Paride Passelli

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

EPFL2024

The time-domain Cartesian multipole expansion of electromagnetic fields

Emanuela Radici, Farhad Rachidi-Haeri, Marcos Rubinstein, Nicolas Mora Parra, Elias Per Joachim Le Boudec

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

Nature Publishing Group2024

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Mario Paolone, André Hodder, Simone Rametti, Lucien André Félicien Pierrejean

Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closed-form or numerical so ...

2024

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Elsevier Science Sa2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Siam Publications2024

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Guillaume Michel Le Bars, Stefano Alberti, Jean-Philippe Hogge, Joaquim Loizu Cisquella, Jérémy Genoud, Francesco Romano

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

2024

Reliable data-driven decision-making through optimal transport

Bahar Taskesen

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

EPFL2024

Stochastic Simulations and Machine Learning Modeling to Predict Bedload Transport and Bed Topography

Mehrdad Kiani Oshtorjani

In computational hydraulics models, predicting bed topography and bedload transport with sufficient accuracy remains a significant challenge. An accurate assessment of a river's sediment transport rate necessitates a prior understanding of its bed topograp ...

EPFL2024

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

Jean-Philippe Thiran, Erick Jorge Canales Rodriguez, Muhamed Barakovic, Marco Pizzolato

Purpose: This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approac ...

Wiley2024

A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects

Marco Picasso, Alexandre Caboussat, Alexandre Masserey, Julien Hess

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...

Academic Press Inc Elsevier Science2024

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Maude Girardin, Marco Picasso, Alexandre Caboussat

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Elsevier Science Sa2024

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Fernando José Henriquez Barraza

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

Springer Birkhauser2024

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Johanna Kristin Maria Becker

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

EPFL2024

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Marco Picasso, Paride Passelli

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

Walter De Gruyter Gmbh2024

Randomized low-rank approximation and its applications

Ulf David Persson

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Analytical Model of Single-Sided Linear Induction Motors for High-Speed Applications

Mario Paolone, André Hodder, Simone Rametti, Lucien André Félicien Pierrejean

This article describes a field-based analytical model of single-sided linear induction motors (SLIMs) that explicitly considers the following effects altogether: finite motor length, magnetomotive force mmf space harmonics, slot effect, edge effect, and ta ...

IEEE2024