Publications associées à Left-inverses of fractional Laplacian and sparse stochastic processes

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

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

Anomalous dissipation and other non-smooth phenomena in fluids

Massimo Sorella

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

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

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Aleksi Antoine Bossart, Haoye Qin, Zhechen Zhang

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Nature Research2024

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

Measurement of the K+ → π+γγ decay

Alessandro Mapelli, Radoslav Marchevski, Alina Kleimenova

A sample of 3984 candidates of the K+ -> pi(+)gamma gamma decay, with an estimated background of 291 +/- 14 events, was collected by the NA62 experiment at CERN during 2017-2018. In order to describe the observed di-photon mass spectrum, the next-to-leadin ...

Elsevier2024

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

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

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

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

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

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

Cochains are all you need

Kelly Spry Maggs

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

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

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

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at √sNN=5.02 TeV

Rakesh Chawla, Andrea Rizzi, Matthias Finger, Federica Legger, Matteo Galli, Sun Hee Kim, Jian Zhao, João Miguel das Neves Duarte, Tagir Aushev, Hua Zhang, Alexis Kalogeropoulos, Yixing Chen, Tian Cheng, Ioannis Papadopoulos, Gabriele Grosso, Valérie Scheurer, Meng Xiao, Qian Wang, Michele Bianco, Varun Sharma, Joao Varela, Sourav Sen, Ashish Sharma, Seungkyu Ha, David Vannerom, Csaba Hajdu, Sanjeev Kumar, Sebastiana Gianì, Kun Shi, Abhisek Datta, Siyuan Wang, Anton Petrov, Jian Wang, Yi Zhang, Muhammad Ansar Iqbal, Yong Yang, Xin Sun, Muhammad Ahmad, Donghyun Kim, Matthias Wolf, Anna Mascellani, Paolo Ronchese, , , , , , , , , , , , , , , , , , , , , , , ,

On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros

Serguei Sekatski

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...

MDPI2024

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Katie Sabrina Catherine Rosie Marsden

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

EPFL2024

Mountaintop Gamma Ray Observations of Three Terrestrial Gamma‐Ray Flashes at the Säntis Tower, Switzerland With Coincident Radio Waveforms

Farhad Rachidi-Haeri, Marcos Rubinstein, Amirhossein Mostajabi, Antonio Sunjerga

We report on the mountain top observation of three terrestrial gamma-ray flashes (TGFs) that occurred during the summer storm season of 2021. To our knowledge, these are the first TGFs observed in a mountaintop environment and the first published European ...

2024

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Robert Dalang, Carsten Hao Ye Chong

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

INT STATISTICAL INST2023

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Elsevier2024