As mathematical models and computational tools become more sophisticated and powerful to accurately depict system dynamics, numerical methods that were previously considered computationally impractical started being utilized for large-scale simulations. Methods that characterize a rare event in biochemical systems are part of such phenomenon, as many of them are computationally expensive and require high-performance computing. In this paper, we introduce an enhanced version of the doubly weighted stochastic simulation algorithm (dwSSA) (Daigle et al. in J Chem Phys 134:044110, 2011), called dwSSA, that significantly improves the speed of convergence to the rare event of interest when the conventional multilevel cross-entropy method in dwSSA is either unable to converge or converges very slowly. This achievement is enabled by a novel polynomial leaping method that uses past data to detect slow convergence and attempts to push the system toward the rare event. We demonstrate the performance of dwSSA on two systems—a susceptible–infectious–recovered–susceptible disease dynamics model and a yeast polarization model—and compare its computational efficiency to that of dwSSA.
