Accelerating the Gillespie τ-Leaping Method Using Graphics Processing Units

Abstract

The Gillespie τ-Leaping Method is an approximate algorithm that is faster than the exact Direct Method (DM) due to the progression of the simulation with larger time steps. However, the procedure to compute the time leap τ is quite expensive. In this paper, we explore the acceleration of the τ-Leaping Method using Graphics Processing Unit (GPUs) for ultra-large networks ( reaction channels). We have developed data structures and algorithms that take advantage of the unique hardware architecture and available libraries. Our results show that we obtain a performance gain of over 60x when compared with the best conventional implementations.

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“…At the time of this writing, the most recent algorithm to parallelize stochastic simulations on GPUs is [38]. It parallelizes well-mixed -leaping on GPUs with the help of the NVIDIA Thrust library, which provides convenient parallel operations on vectors.…”

“…The algorithm in [38] also includes a parallel version of SSA (direct method), used when -leaping must fall back to SSA. At each time step, this parallel SSA performs the reaction selection procedure, the update of propensities, and the update of the molecule counts in parallel.…”

“…This method is therefore efficient in systems with large numbers of reactions and molecular species, in cases where -leaping cannot be applied due to a violation of the leap condition. However the performance of the parallel DM part in isolation is not reported in [38].…”