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Concept

Divergence theorem

Related publications (27)

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

On Speed and Advantage : Results in Information Velocity and Monitoring Problems

Reka Inovan

Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

EPFL2024

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Sage Publications Ltd2023

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

Jiannong Fang

To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equ ...

2023

QFT without infinities and hierarchy problem

Mikhail Chapochnikov, Sander Johannes Nicolaas Mooij

The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a "heavy" sector into the physical observables of the "light" (or low energy) sector - the phenome ...

ELSEVIER2023

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

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Michael Christoph Gastpar, Amedeo Roberto Esposito, Adrien Vandenbroucque

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results i ...

2022

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

Is there an analog of Nesterov acceleration for gradient-based MCMC?

Nicolas Henri Bernard Flammarion

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm perfor ...

2021

Robust Generalization via f−Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

Given two probability measures P and Q and an event E, we provide bounds on P(E) in terms of Q(E) and f-divergences. In particular, the bounds are instantiated when the measures considered are a joint distribution and the corresponding product of marginals ...

IEEE2020

Functional penalised basis pursuit on spheres

Matthieu Martin Jean-André Simeoni

In this work, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain using functional ...

2020

Tokamak Edge Plasma Turbulence Interaction with Magnetic X-Point in 3D Global Simulations

Davide Galassi

Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduc ...

2019

Sparse Spline Approximation on the Hypersphere by Generalised Total Variation Basis Pursuit

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field –namely a scalar quantity defined over a continuum of directions– from generalised samples of the latter. Typically, a convex optimisation problem is formulated in terms ...

2019

Scrape-off-layer current loops and floating potential in limited tokamak plasmas

Paolo Ricci, Joaquim Loizu Cisquella, Paola Paruta, Federico David Halpern

We investigate the question of how plasma currents circulate and close in the scrape-off-layer (SOL) of convection-limited tokamak plasmas. A simplified two-fluid model describes how currents must evacuate charge at the sheaths due to cross-field currents ...

Cambridge University Press2017

Divergence-Free Wavelet Frames

Michaël Unser, John Paul Ward, Emrah Bostan

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

IEEE Institute of Electrical and Electronics Engineers2015

Electrical Neuroimaging with Irrotational Sources

This paper discusses theoretical aspects of the modeling of the sources of the EEG (i.e., the bioelectromagnetic inverse problem or source localization problem). Using theHelmholtz decomposition (HD) of the current density vector (CDV) of the primary curre ...

Hindawi Publishing Corporation2015

The inviscid, compressible and rotational, 2D isotropic Burgers and pressureless Euler-Coriolis fluids: Solvable models with illustrations

The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics (Wu et al., 2006, pp. 3, 6) is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler Coriolis fluids respec ...

Elsevier Science Bv2014

Analytic Sensing For Multi-Layer Spherical Models With Application To EEG Source Imaging

Dimitri Nestor Alice Van De Ville, Thierry Blu, Djano Kandaswamy

Source imaging maps back boundary measurements to underlying generators within the domain; e. g., retrieving the parameters of the generating dipoles from electrical potential measurements on the scalp such as in electroencephalography (EEG). Fitting such ...

Amer Inst Mathematical Sciences2013

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013