Automatic Histogram and Variogram Reproduction in Simulated Annealing Simulation

Simulated annealing simulation (SAS) is a flexible tool for generating stochastic simulations conditioned to data at various scales and precision. However, a number of important drawbacks exists: (1) SAS requires considerable CPU time, (2) it requires experience in setting the so-called cooling schedule to obtain convergence, and (3) its space of uncertainty is not well understood. In this paper, I propose a new simulated annealing method that guarantees histogram and variogram reproduction through the implementation of a novel perturbation mechanism. The novel perturbation method is based on the Metropolis–Hastings sampler for a Markov-type random field. This new annealing method allows removal of the histogram and variogram from the objective function in the simulated annealing procedure. Furthermore, for the proposed method one finds that (1) the uncertainty space can be quantified, (2) the convergence properties can be linked to convergence of stationary Markov chains, and (3) the convergence speed is improved over traditional simulated annealing.