Publications associées à Équation aux dérivées partielles hyperbolique

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

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

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

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Charles Stuart

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

2024

Soliton gas: Theory, numerics, and experiments

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted (rarefied) soliton gas, solitons with ...

Amer Physical Soc2024

Hyperbolic representations of PU(1,n)

Gonzalo Emiliano Ruiz Stolowicz

The work is about the study of group representations in the group of isometries of a separable complex hyperbolic space. The main part is the classification of the representations of the group of isometries of a finite dimensional complex hyperbolic spa ...

EPFL2023

T-5 configurations and hyperbolic systems

Carl Johan Peter Johansson, Riccardo Tione

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

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

Essays in macro-finance and deep learning

Goutham Gopalakrishna

This thesis studies the origins and consequences of financial crises, and computational techniques to solve continuous-time economic models that explain such crises. The first chapter shows that financial recessions are typically characterised by a large ...

EPFL2023

On the symmetries in the dynamics of wide two-layer neural networks

Lénaïc Chizat

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Yannis Dirk Voet

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Continuous-variable neural network quantum states and the quantum rotor model

Giuseppe Carleo

We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunc ...

SPRINGERNATURE2023

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

Alfio Quarteroni, Luca Dede'

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our mod ...

Wiley2023

Conservation of Forces and Total Work at the Interface Using the Internodes Method

Simone Deparis

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

2022

Fast global spectral methods for three-dimensional partial differential equations

Daniel Kressner, Christoph Max Strössner

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

OXFORD UNIV PRESS2022

Adaptive analysis-aware defeaturing

Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...

EPFL2022

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Raphaël Jean Berthier

Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...

OXFORD UNIV PRESS2022

Adaptive analysis-aware defeaturing

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...

2022

Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete

Ali Falsafi

The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...

EPFL2022