2,804 research outputs found
Characterization of the convergence of stationary Fokker-Planck learning
The convergence properties of the stationary Fokker-Planck algorithm for the
estimation of the asymptotic density of stochastic search processes is studied.
Theoretical and empirical arguments for the characterization of convergence of
the estimation in the case of separable and nonseparable nonlinear optimization
problems are given. Some implications of the convergence of stationary
Fokker-Planck learning for the inference of parameters in artificial neural
network models are outlined
q-Gaussian based Smoothed Functional Algorithm for Stochastic Optimization
The q-Gaussian distribution results from maximizing certain generalizations
of Shannon entropy under some constraints. The importance of q-Gaussian
distributions stems from the fact that they exhibit power-law behavior, and
also generalize Gaussian distributions. In this paper, we propose a Smoothed
Functional (SF) scheme for gradient estimation using q-Gaussian distribution,
and also propose an algorithm for optimization based on the above scheme.
Convergence results of the algorithm are presented. Performance of the proposed
algorithm is shown by simulation results on a queuing model.Comment: 5 pages, 1 figur
Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling
We investigate the performance of the recently proposed stationary
Fokker-Planck sampling method considering a combinatorial optimization problem
from statistical physics. The algorithmic procedure relies upon the numerical
solution of a linear second order differential equation that depends on a
diffusion-like parameter D. We apply it to the problem of finding ground states
of 2d Ising spin glasses for the +-J-Model. We consider square lattices with
side length up to L=24 with two different types of boundary conditions and
compare the results to those obtained by exact methods.
A particular value of D is found that yields an optimal performance of the
algorithm. We compare this optimal value of D to a percolation transition,
which occurs when studying the connected clusters of spins flipped by the
algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has
more and more problems to find the exact ground states. This means that the
approach, at least in its standard form, seems to be inferior to other
approaches like parallel tempering.Comment: v1: 13 pages, 7 figures; v2: extended tex
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows
at high Reynolds numbers is one of the last open problems of classical physics.
In this review we discuss recent developments related to the application of
instanton methods to turbulence. Instantons are saddle point configurations of
the underlying path integrals. They are equivalent to minimizers of the related
Freidlin-Wentzell action and known to be able to characterize rare events in
such systems. While there is an impressive body of work concerning their
analytical description, this review focuses on the question on how to compute
these minimizers numerically. In a short introduction we present the relevant
mathematical and physical background before we discuss the stochastic Burgers
equation in detail. We present algorithms to compute instantons numerically by
an efficient solution of the corresponding Euler-Lagrange equations. A second
focus is the discussion of a recently developed numerical filtering technique
that allows to extract instantons from direct numerical simulations. In the
following we present modifications of the algorithms to make them efficient
when applied to two- or three-dimensional fluid dynamical problems. We
illustrate these ideas using the two-dimensional Burgers equation and the
three-dimensional Navier-Stokes equations
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