Fast Monte Carlo methodology for multivariate particulate systems-II: ττ-PEMC

The point ensemble Monte Carlo (PEMC) was introduced [Irizarry, R., 2007. Fast Monte Carlo methodology for multivariate particulate systems-I: point ensemble Monte Carlo. Chemical Engineering Science, in press, doi:10.1016/j.ces.2007.09.007.] as a method to accelerate the simulation speed of particulate processes solved by Monte Carlo methods. The PEMC method is a “constructed” jump Markov model that approximates the dynamics of the original particulate process without losing a detailed description of individual particles. The PEMC method is integrated using the stochastic simulation algorithm, which is exact in time. A natural extension of the PEMC algorithm is to consider a coarse-graining strategy for the time to further accelerate the MC simulation. In this work, the ττ-leap method is adapted to the PEMC. It is shown that when the ττ-parameter is selected properly, the ττ-PEMC can also give accurate results with faster computational speed than the PEMC method. Furthermore, similar to the PEMC, the dynamic of complex intra-particle phenomena can be represented accurately. Numerical experiments show that this algorithm can improve the computational load of the exact method by orders of magnitude without sacrificing computational accuracy. The methodology is useful especially in stochastic optimization applications where many function calls (simulations) are required.