Publications related to First-order partial differential equation

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

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

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

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

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

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

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

Analytic modelling of passive microfluidic mixers

Jean-Michel Sallese, Christophe Lallement

This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...

AMER INST MATHEMATICAL SCIENCES-AIMS2022

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

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Tommaso Vanzan

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

2022

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to ...

2020

Two-Dimensional RBF-ENO Method on Unstructured Grids

Jan Sickmann Hesthaven, Fabian Mönkeberg

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well stud ...

SPRINGER/PLENUM PUBLISHERS2020

Dynamics of optical forces and torques in plasmonic systems: a surface integral equation

Olivier Martin, Karim Achouri, Andrei Kiselev

A novel approach is introduced to determine the time evolution of optical forces and torques on arbitrary shape nanostructures by combining Maxwell's stress tensor with the surface integral equation method (SIE). Conventional time averaging of Maxwell’s st ...

SPIEDigitalLibrary2020

High-order essentially nonoscillatory methods based on radial basis functions

Fabian Mönkeberg

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely employed to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well s ...

EPFL2020

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Julien Gilles Edgar Gateau

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after e ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2020

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Fabio Nobile, Simone Brugiapaglia

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

2021

Machine learning for fast and reliable solution of time-dependent differential equations

Alfio Quarteroni, Francesco Regazzoni

We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential Equations (ODEs) or time-dependent Partial Differential Equations (PDEs). Unlike ...

2019

Electrical conductivity of hot Abelian plasma with scalar charge carriers

Oleksandr Sobol

We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant alpha using the Boltzmann kinetic equation. The leading contribution to the collision integral is due to the ...

American Physical Society2019

Méthodes numériques liées à la distribution d'alumine dans une cuve d'électrolyse d'aluminium

Thomas Frédéric Hilke

Metallic aluminium plays a key role in our modern economy. Primary metallic aluminium is produced by the transformation of aluminium oxide using the Hall-Héroult industrial process. This process, which requires enormous quantities of energy, consists in pe ...

EPFL2019

Eigenmode Analysis in Plasmonics: Application to Second Harmonic Generation and Electron Energy Loss Spectroscopy

Gabriel David Bernasconi

Eigenmodes are central to the study of resonant phenomena in all areas of physics. However, their use in nano-optics seems to have been hindered and delayed for various reasons. First, due to their small size, the response of nanostructures to a far-field ...

EPFL2019