Approximate accelerated stochastic simulation of chemically reacting systems

TLDR

The stochastic simulation algorithm (SSA) is an essentially exact method for simulating well‑stirred chemical systems, but its computational cost remains high despite recent efficiency improvements. This work introduces the τ‑leap method, an approximate algorithm that can accelerate simulations with acceptable accuracy loss. The authors describe primitive strategies for selecting control parameters and mitigating errors in τ‑leap, and present simulation results on two simple model systems. With further refinement, τ‑leap offers a viable transition from exact SSA to the chemical Langevin equation and ultimately to deterministic rate equations as system size increases.

Abstract

The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.