Parallel implementation of simulated annealing to reproduce multiple-point statistics

7 This paper shows an innovative implementation of simulated annealing in the 8 context of parallel computing. Details regarding the use of parallel computing 9 through a cluster of processors, as well as the implementation decisions, 10 are provided. Simulated annealing is presented aiming at the generation 11 of stochastic realizations of categorical variables reproducing multiple-point 12 statistics. 13 The procedure starts with the use of a training image to determine the 14 frequencies of occurrence of particular configurations of nodes and values. 15 These frequencies are used as target statistics that must be matched by the 16 stochastic images generated with the algorithm. The simulation process con17 siders an initial random image of the spatial distribution of the categories. 18 Email addresses: [email protected] (Oscar Peredo A.), [email protected] (Julián M. Ortiz) Preprint submitted to Computers & Geosciences November 8, 2010 Nodes are perturbed randomly and after each perturbation the mismatch 19 between the target statistics and the current statistics of the image is calcu20 lated. The perturbation is accepted if the statistics are closer to the target, 21 or conditionally rejected if not, based on the annealing schedule. 22 The simulation was implemented using parallel processes with C++ and 23 MPI. The message passing scheme was implemented using a speculative com24 putation framework, by which prior to making the decision of acceptance or 25 rejection of a proposed perturbation, processes already start calculating the 26 next possible perturbation at a second level; one as if the perturbation on 27 level one is accepted, and another process as if the proposed perturbation is 28 rejected. Additional levels can start their calculation as well, conditional to 29 the second level processes. Once a process reaches a decision as to whether 30 accept or reject the suggested perturbation, all processes within the branch 31 incompatible with that decision are dropped. This allows a speed up of up 32 to logn(p + 1), where n is the number of categories and p the number of 33 processes simultaneously active. 34 Examples are provided to demonstrate improvements and speed ups that 35 can be achieved. 36