Research On Stochastic Simulation Approaches For Spatially Inhomogeneous Chemical Reaction Systems Based On PDES

Experiments indicate that stochasticity and spatial heterogeneity are important characteristics of chemical reaction systems, which have an important impact on the dynamics of the systems. Recent studies on these systems are based on the ISSA (Inhomogeneous stochastic simulation algorithm). However, the stochastic simulation algorithm is computing-intensive, and a sequential implementation of the stochastic simulation is extremely time-consuming. Nowadays, regarded as one of the most prevalent techniques for efficient simulation, PDES (Parallel Discrete Event Simulation) has not yet been fully deployed in current study of stochastic simulation. To fill the gap, the study of stochastic simulation based on PDES for spatially inhomogeneous reaction systems is of critical theoretical and practical importance.According to the characteristics of stochastic simulation of spatially inhomogeneous reaction systems, we study the current challenges in parallelizing the stochastic simulation of the systems and many key techniques of research on stochastic simulation approaches for Spatially Inhomogeneous Chemical Reaction systems based on PDES, the main contributions and innovations are made as follows:Firstly, NSM (the Next Sub-volume Method) presented by Elf etc. is the most prevalent method for stochastic simulation of spatially inhomogeneous chemical reaction systems. However, the method is essentially sequential and has a single common data structure, which is not conducive for parallel execution. To access this issue, we proposed ANSM (the Abstract NSM). The ANSM releases the NSM from the sequential semantic by introducing the event retraction mechanism; secondly, it minimized the costs of synchronous accessing of the one common data structure in the NSM by dividing it into many distributed ones.Secondly, the modified Poisson tau-leaping stochastic simulation method (MPtau-leapingSSA) proposed by Cao etc. is one of the most widely used and efficient methods for stochastic simulation. However, it can not capture the heterogeneity of many real-life systems. To tackle the problem, we proposed the space Poisson tau-leap stochastic simulation method (SMPtau-leapSSA). We introduced the space-partition scheme into the MPtau-leapingSSA to explore the parallelization of the inhomogeneous systems and then process all sub-volumes in the synchronous parallel manner. The test got remarkable speed-ups.Thirdly, based on speculative execution, optimistic time management algorithms in PDES can bring significantly speedup. But the Global Virtual Time (GVT) reduction algorithms used in current studies are either too complex to implement or very costly in the message acknowledgement for remote communication. To address this issue, we proposed the Twice-Notification GVT reduction (TN-GVT) algorithm based on synchronous communication method. On one hand, the acknowledgement mechanism is not used in the TN-GVT algorithm anymore, to reduce the cost of remote communication; on the other hand, it combines the synchronous and asynchronous GVT reduction algorithms, to not only improve the efficiency of the algorithm but also make it easy to implement.Finally, we designed and implemented a parallel discrete event stochastic simulation platform based on the discrete event framework JAMES II. We modeled and simulated the classical Predator-Prey Reaction System. Under parallel execution, the speed-up of nearly 2 for the SMPtau-leapSSA and the highest speed-up of over 6 for the ANSM are achieved.