Publications (11)
A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts
Guillaume Carlier, Maxime Laborde
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive a…
Simulation of multiphase porous media flows with minimizing movement and finite volume schemes
Clément Cancès, Thomas O. Gallouët, Maxime Laborde +1
The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Cancès, T. O. Gallouët, and L. Monsaingeon, {…
On systems of continuity equations with nonlinear diffusion and nonlocal drifts
Guillaume Carlier, Maxime Laborde
This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein grad…
Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent
Maxime Laborde, Adam M. Oberman
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when…
On some non linear evolution systems which are perturbations of Wasserstein gradient flows
Maxime Laborde
This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction. These systems can be viewed as regular per…
A differential approach to the multi-marginal Schr{ö}dinger system
Guillaume Carlier, Maxime Laborde
We develop an elementary and self-contained differential approach, in an setting, for well-posedness (existence, uniqueness and smooth dependence with respect to the dat…
Nonlinear systems coupled through multi-marginal transport problems
Maxime Laborde
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A si…
Long-time behavior of the heterogeneous SIRS epidemiological model
Romain Ducasse, Maxime Laborde
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to…
An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems
Thomas Gallouët, Maxime Laborde, Léonard Monsaingeon
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a construc…
On cross-diffusion systemsfor two populations subject to a common congestion effect
Maxime Laborde
In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are…
Displacement smoothness of entropic optimal transport
Guillaume Carlier, Lénaïc Chizat, Maxime Laborde
The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schrödinger map. We prove that when the cost…