Publications related to Divergence

Anomalous dissipation and other non-smooth phenomena in fluids

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, Anqing Duan

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

QFT without infinities and hierarchy problem

Sander Johannes Nicolaas Mooij, Mikhail Chapochnikov

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

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

Directionality-Aware Design of Embroidery Patterns

Zhenyuan Liu

Embroidery is a long-standing and high-quality approach to making logos and images on textiles. Nowadays, it can also be performed via automated machines that weave threads with high spatial accuracy. A characteristic feature of the appearance of the threa ...

2023

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

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

From Generalisation Error to Transportation-cost Inequalities and Back

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback- Leibler Divergences/Mutu ...

2022

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

Nicolas Henri Bernard Flammarion, Xiang Cheng

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

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

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

On the density of the supremum of the solution to the linear stochastic heat equation

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

SPRINGER2020

Robust Generalization via $\alpha$-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

The aim of this work is to provide bounds connecting two probability measures of the same event using Rényi

\alpha

-Divergences and Sibson’s

\alpha

-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon’s Mutual ...

ETHZ2020

Conformal 3-Point Functions and the Lorentzian OPE in Momentum Space

Marc Gillioz

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that t ...

SPRINGER2020

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with t ...

Institute of Electrical and Electronics Engineers2019

Entropy as a tool for crystal discovery

Pablo Miguel Piaggi

The computational prediction of crystal structures has emerged as an useful alternative to expensive and often cumbersome experiments. We propose an approach to the prediction of crystal structures and polymorphism based on reproducing the crystallization ...

EPFL2019

A structural test for the conformal invariance of the critical 3d Ising model

João Miguel Augusto Penedones Fernandes, Pierre Mathieu Yvernay

How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current a non-conserved vector operator of dimension exactly (d - 1), whose divergence exp ...

Springer Nature2019

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

Davide Galassi, Eric Serre

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

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