Stationary Fokker – Planck Learning for the Optimization of Parameters in Nonlinear Models

Ground states of 2D ±JIsing spin glasses obtained via stationary Fokker–Planck sampling

“…Here, we briefly describe the stationary Fokker-Planck sampling algorithm as introduced in [13] and further detailed in [14,11,12], where also more details about the general framework can be found. SFP sampling is based on the interrelation between the Langevin and Fokker-Planck equations that allow for the stochastic description of a given system.…”

“…Moreover, the influence of the cost function on the search process therein depends on a diffusion-like parameter D. Upon its introduction in [13], the approximation of a stationary probability density via the SFP algorithm was illustrated for the two-parameter Michalewicz function, an unconstrained test function for global optimization. In [14] the authors presented an implementation of the SFP algorithm and showed its applicability to the five-parameter Levy No. 5 function, again a test function for global optimization, and the XOR problem, a fundamental problem relevant e.g.…”

Characterization of the convergence of stationary Fokker–Planck learning

“…This information can then be used in connection with a locally adaptive stochastic or deterministic algorithm. Preliminary applications of this density estimation method in the improvement of nonlinear optimization algorithms can be found in [23]. Theoretical aspects on the foundations of the method, its links to statistical mechanics and possible use of the density estimation procedure as a general diversification mechanism are discussed in [3].…”