149 citations · 316 across the 36 of their papers we have counts for
43 papers
The mean-field Limit of sparse networks of integrate and fire neurons
Pierre-Emmanuel Jabin, Datong Zhou
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuou…
Hölder and Sobolev regularity of optimal transportation potentials with rough measures
Pierre-Emmanuel Jabin, Antoine Mellet
We consider a Kantorovich potential associated to an optimal transportation problem between measures that are not necessarily absolutely continuous with respect to the Lebesgue mea…
Global Existence of Weak Solutions for Compresssible Navier--Stokes--Fourier Equations with the Truncated Virial Pressure Law
Didier Bresch, Pierre-Emmanuel Jabin, Fei Wang
This paper concerns the existence of global weak solutions {\it à la Leray} for compressible Navier--Stokes--Fourier systems with periodic boundary conditions and the truncated vir…
Discretizing advection equations with rough velocity fields on non-cartesian grids
Pierre-Emmanuel Jabin, Datong Zhou
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have re…
Collective motion driven by nutrient consumption
Pierre-Emmanuel Jabin, Benoît Perthame
A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written…
From interacting agents to Boltzmann-Gibbs distribution of money
Fei Cao, Pierre-Emmanuel Jabin
We investigate the unbiased model for money exchanges: agents give at random time a dollar to one another (if they have one). Surprisingly, this dynamics eventually leads to a geom…
A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
Didier Bresch, Pierre-Emmanuel Jabin, Juan Soler
This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the…
Mean-field limit of non-exchangeable systems
Pierre-Emmanuel Jabin, David Poyato, Juan Soler
This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent…
A novel multi-scale loss function for classification problems in machine learning
Leonid Berlyand, Robert Creese, Pierre-Emmanuel Jabin
We introduce two-scale loss functions for use in various gradient descent algorithms applied to classification problems via deep neural networks. This new method is generic in the…
Entropy dissipation and propagation of chaos for the uniform reshuffling model
Fei Cao, Pierre-Emmanuel Jabin, Sebastien Motsch
We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean…
Mean-field limit and quantitative estimates with singular attractive kernels
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full…
Compressible Navier-Stokes equations with heterogeneous pressure laws
Didier Bresch, Pierre Emmanuel Jabin, Fei Wang
This paper concerns the existence of global weak solutions à la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space…
Commutator Method for Averaging Lemmas
Pierre-Emmanuel Jabin, Hsin-Yi Lin, Eitan Tadmor
We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This method requir…
Stability for the Training of Deep Neural Networks and Other Classifiers
Leonid Berlyand, Pierre-Emmanuel Jabin, C. Alex Safsten
We examine the stability of loss-minimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training t…
Modulated Free Energy and Mean Field Limit
Didier Bresch, Pierre-Emmanuel Jabin, Zhenfu Wang
This is the document corresponding to the talk the first author gave at IH{É}S for the Laurent Schwartz seminar on November 19, 2019. It concerns our recent introduction of a modul…
Local regularity result for an optimal transportation problem with rough measures in the plane
P. -E. Jabin, A. Mellet, M. Molina
We investigate the properties of convex functions in the plane that satisfy a local inequality which generalizes the notion of sub-solution of Monge-Ampere equation for a Monge-Kan…
Transport Model for Feature Extraction
Wojciech Czaja, Dong Dong, Pierre-Emmanuel Jabin +1
We present a new feature extraction method for complex and large datasets, based on the concept of transport operators on graphs. The proposed approach generalizes and extends the…
A kinetic approach to active rod dynamics in confined domains
Leonid Berlyand, Pierre-Emmanuel Jabin, Mykhailo Potomkin +1
The study of active matter consisting of many self-propelled (active) swimmers in an imposed flow is important for many applications. Self-propelled swimmers may represent both liv…
Global weak solutions to the relativistic BGK equation
Juan Calvo, Pierre-Emmanuel Jabin, Juan Soler
In this paper the global existence of weak solutions to the relativistic BGK model for the relativistic Boltzmann equation is analyzed. The proof relies on the strong compactness o…
Continuum approximations to systems of correlated interacting particles
Leonid Berlyand, Robert Creese, Pierre-Emmanuel Jabin +1
We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and…
Quantitative estimate of propagation of chaos for stochastic systems with kernels
Pierre-Emmanuel Jabin, Zhenfu Wang
We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between t…
Convergence of numerical approximations to non-linear continuity equations with rough force fields
F. Ben Belgacem, P-E Jabin
We prove quantitative regularity estimates for the solutions to non-linear continuity equations and their discretized numerical approximations on Cartesian grids when advected by a…
Hydrodynamic limit of granular gases to pressureless Euler in dimension 1
Pierre-Emmanuel Jabin, Thomas Rey
We investigate the behavior of granular gases in the limit of small Knudsen number, that is very frequent collisions. We deal with the strongly inelastic case, in one dimension of…
Selection-Mutation dynamics with spatial dependence
Pierre-Emmanuel Jabin, Raymond Strother Schram
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-po…