6 papers
Enhancing Exploration in Global Optimization by Noise Injection in the Probability Measures Space
Gaëtan Serré, Pierre Germain, Samuel Gruffaz +1
McKean-Vlasov (MKV) systems provide a unifying framework for recent state-of-the-art particlebased methods for global optimization. While individual particles follow stochastic tra…
Uncovering bistability phenomena in two-layer Couette flow experiments using nonlocal evolution equations
Xingyu Wang, Pierre Germain, Demetrios T. Papageorgiou
This paper investigates the stability of interfacial long waves in two-layer plane Couette flow using a nonlinear, nonlocal asymptotic model derived from the Navier-Stokes equation…
Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
Pierre Germain, Norbert J. Mauser, Jakob Möller
We construct local (in time) strong solutions in {, } and global weak solutions with finite energy for both the Pauli-Darwin and the Pauli-Poisswell syste…
On the vanishing of eigenfunctions of the Laplacian on tori
Pierre Germain, Iván Moyano, Hui Zhu
Consider an eigenfunction of the Laplacian on a torus. How small can its -norm be on small balls? We provide partial answers to this question by exploiting the distribution of…
Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus
Nicolas Burq, Pierre Germain, Massimo Sorella +1
We investigate trace and observability inequalities for Laplace eigenfunctions on the d-dimensional torus, with respect to arbitrary Borel measures . Specifically, we character…
Stochastic moments dynamics: a flexible finite-dimensional random perturbation of Wasserstein gradient descent
Pierre Germain, Pierre Monmarché
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of differe…