Publications

Mathematics

New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results

Helmholtz wave scattering by open screens in 2D can be formulated as first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introduce two new preconditioners in the form of square-roots of on-curve…

François Alouges, Martin Averseng

Numerische Mathematik - 2021

Analysis of PDEs

A Morawetz Inequality for Gravity-Capillary Water Waves at Low Bond Number

Thomas Alazard, Mihaela Ifrim, Daniel Tataru

Water Waves - 2021

Numerical Analysis

Hypocoercivity of Piecewise Deterministic Markov Process-Monte Carlo

In this paper we derive spectral gap estimates for several Piecewise Deterministic Markov Processes, namely the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler. The hypocoercivity technique we use, presented…

Christophe Andrieu, Alain Durmus, Nikolas Nüsken, Julien Roussel

The Annals of Applied Probability - 2021

Environmental Sciences

Constrained prediction time random forests using equivalent trees and genetic programming: application to fall detection model embedding

Budgeted learning is a research field of growing interest that aims at including real world resource constraints into the design of machine learning models, for instance to reduce real environment prediction time. One family of method to do so…

Atiq Mounir, Peignier Sergio, Mougeot Mathilde

33rd IEEE International Conference on Tools with Artificial Intelligence - 2021

Spectral Theory

A Spectral Approach of Multi-Scale Metamodelling Applied to Acoustic Propagation

There exists many numerical methods to simulate wave propagation through complex media with a very good precision. However, taking into account the fluctuations of the propagation medium necessitates a statistical approach implying a prohibitive…

Alexandre Goupy

Statistics

Monte Carlo Variational Auto-Encoders

Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance…

Achille Thin, Nikita Kotelevskii, Alain Durmus, Maxim Panov, Eric Moulines, Arnaud Doucet

38th International Conference on Machine Learning - 2021

Analysis of PDEs

On the dynamics of the roots of polynomials under differentiation

This article is devoted to the study of a nonlinear and nonlocal parabolic equation introduced by Stefan Steinerberger to study the roots of polynomials under differentiation; it also appeared in a work by Dimitri Shlyakhtenko and Terence Tao on…

Thomas Alazard, Omar Lazar, Quoc-Hung Nguyen

Analysis of PDEs

Cauchy theory for the water waves system in an analytic framework

In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $\varepsilon$ in a space of analytic functions which have a holomorphic…

Thomas Alazard, Nicolas Burq, Claude Zuily

Analysis of PDEs

On the Cauchy problem for the Muskat equation with non-Lipschitz initial data

Thomas Alazard, Quoc-Hung Nguyen

Communications in Partial Differential Equations - 2021

Acoustics

On the sound speed in two-fluid mixtures and the implications for CFD model validation

Study of the propagation of sound in a single non-ideal fluid originates with Stokes in 1845 and Kirchhoff in 1868. The situation is much more complex in the case of two-fluid flow, both from the physical point of view, as the configuration of the…

Saad Benjelloun, Jean-Michel Ghidaglia