Publications associées à Orlicz regularity of the gradient of solutions to quasilinear elliptic equations in the plane

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

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Boris Buffoni

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Matthieu Claude Martin, Sebastian Krumscheid

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Annalisa Buffa, Rafael Vazquez Hernandez

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these result ...

Springer2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Jean-Pascal Théodor Pfister, Johanni Michael Brea

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020

Preferential retention of algal carbon in benthic invertebrates: Stable isotope and fatty acid evidence from an outdoor flume experiment

Tom Ian Battin

According to the River Continuum Concept, headwater streams are richer in allochthonous (e.g. terrestrial leaves) than autochthonous (e.g. algae) sources of organic matter for consumers. However, compared to algae, leaf litter is of lower food quality, par ...

WILEY2020

On the equation A del u plus (del u)(t) A = G

Bernard Dacorogna, David Valentin Strütt

Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates

Luigi Forcella

We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...

2021

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

A cellulolytic fungal biofilm enhances the consolidated bioconversion of cellulose to short chain fatty acids by the rumen microbiome

Robert Lawrence Shahab

The ability of the multispecies biofilm membrane reactors (MBM reactors) to provide distinguished niches for aerobic and anaerobic microbes at the same time was used for the investigation of the consolidated bioprocessing of cellulose to short chain fatty ...

2019

Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

Fabio Nobile, Eleonora Musharbash

In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational ...

Elsevier2018

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Clément Hongler, Arthur Ulysse Jacot-Guillarmod, Franck Raymond Gabriel

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

Multi space reduced basis preconditioners for large-scale parametrized PDEs

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, whi ...

2018

MATHICSE Technical Report : Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Matthieu Claude Martin, Sebastian Krumscheid

We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...

MATHICSE2018

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

A mixture of thermoelastic solids with two temperatures

Maria Masid Barcon

In this work we study, from the numerical point of view, a problem involving one-dimensional thermoelastic mixtures with two different temperatures; that is, when each component of the mixture has its own temperature. The mechanical problem consists of two ...

Pergamon-Elsevier Science Ltd2017

A Dirichlet problem involving the divergence operatord

Bernard Dacorogna, Gyula Csató

We consider the problem {div u + (a; u) = f in Omega u = u(0) on partial derivative Omega. We show that if curl a (x(0)) not equal for some x(0) epsilon Omega, then the problem is solvable without restriction on f. We also discuss the regularity of the sol ...

Elsevier Science Bv2016