Publications

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

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

Analysis of PDEs

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

Thomas Alazard, Quoc-Hung Nguyen

Annals of PDE - 2021

Acoustics

On the dispersion relation for compressible Navier-Stokes Equations

In this paper we revisit the classical sound dispersion and attenuation theory due to Stokes [5], 1845, and Kirchhoff [3], 1868, for the propagation of sound in non-ideal fluids. In particular we reformulate the analysis due to Fletcher[2], 1974,…

Saad Benjelloun, Jean-Michel Ghidaglia

Analysis of PDEs

Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem

We exhibit a new decomposition of the nonlinearity for the Muskat equation and use it to commute Fourier multipliers with the equation. This allows to study solutions with critical regularity. As a corollary, we obtain the first well-posedness…

Thomas Alazard, Quoc-Hung Nguyen

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

Mathematics

KFC: A clusterwise supervised learning procedure based on the aggregation of distances

Sothea Has, Aurélie Fischer, Mathilde Mougeot

Journal of Statistical Computation and Simulation - 2021