In this paper we discuss the relation between ensemble learning, deterministic annealing and Markov chain sample and optimization methods on the one hand and the Fokker-Planck Machine on the other hand. The latter was introduced as an alternative method for high-dimensional non-convex optimization, as often encountered in training of neural networks. We demonstrate how the Fokker-Planck Machine...

We derive simple formulas connecting the generalized Wigner functions for s-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master equations with Fokker-Planck equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Planck equations, and finally for studying pos...

This article is concerned with maximal accretive realization of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible bou...

The Haida plank house is one of the most important models built by native American Indians. Built on southwest coast Canada, it adapts tradition ancient pit houses to requirements humid and cold climate characteristic Gwaii Islands. This construction composed two main pieces: central covered a wooden envelope. Both protect its dwellers their hearths. ventilation system based solutions: gaps bet...

On the basis of our Fokker-Planck code “FPI”, a new kernel for nonlocal electron transport in plasmas has been developed. Large scale simulations of plasma macroscopic characteristics have been made by using both this Fokker-Planck and a new Hydrodynamic code using the new kernel [1]. However, these simulations were made with the approximation of spherical Rosenbluth potentials. We have now add...

We consider a system coupling the incompressible Navier–Stokes equations to the Vlasov– Fokker–Planck equation. Such a problem arises in the description of particulate flows. We design a numerical scheme to simulate the behavior of the system. This scheme is asymptotic-preserving, thus efficient in both the kinetic and hydrodynamic regimes. It has a numerical stability condition controlled by t...

We study the existence and the uniqueness of a solution φ to the linear Fokker-Planck equation −∆φ+ div(φF) = f in a bounded domain of R when F is a “confinement” vector field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows. Equation de Fokker-Planck dans un domaine b...