Tackling the Temporal Stiffness of Kinetic Monte CarloSimulations of Well-Mixed Chemical Systems via On-the-Fly Scalingand Cost-Error Optimization

Reaction kinetics in biological systems are often subject to stochastic effects due to the low populations of reacting molecules, necessitating the adoption of kinetic Monte Carlo methods for their study. Such methods, however, can be computationally expensive, especially in the case of stiff systems, where some reactions are executed at much higher frequencies than others. We present an algorithm that reduces the reaction rate constants of the fast processes on-the-fly, thereby saving computational time, while keeping the approximation error within desirable limits. The algorithm couples the Modified Next Reaction Method for simulating stochastic systems with the Common Random Number framework and calculates accurate metrics for both the computational cost and approximation error by generating multiple sets of trajectories that correspond to increasingly reduced (downscaled) reaction rate constants. The optimum downscale factor is chosen via optimization of two conflicting objectives: (a) maximizing the speedup and (b) minimizing the approximation error introduced, and it is straightforward to tune the performance of the method, favoring accuracy versus speed or vice versa. Our approach is demonstrated on a biology-inspired well-mixed stiff system and is shown to accelerate the stochastic simulation thereof from 66 h down to 90 min, achieving a speed-up factor of 44×, without distorting the dynamics of the system studied.