Global weak error control for the tau-leap method

Jesper Karlsson
Mathematical and Computer Sciences and Engineering Division
King Abdullah University of Science and Technology
Thuwal, Saudi Arabia


This work presents novel, tau-leap based, algorithms for the discretization of pure jump processes arising in kinetic Monte Carlo models. A typical example of such a pure jump process is to model the time evolution of a reacting chemical network. Today, two algorithms are commonly used: (1) The SSA algorithm by Gillespie, that simulates a single trajectory exactly, but can be time consuming when many reactions take place during a short time interval. (2) The approximate tau-leap method, that can be used to reduce computational time, but introduces a time discretization error and may also lead to negative particle populations. The tau-leap based methods presented in this talk aim to estimate and control the global weak error. First, I will present a time-adaptive tau-leap method, controlling the global weak error using discrete duals, and using a post-leap check to prevent negative populations. Finally, instead of using a post-leap check, another approach is to devise a computationally less expensive and simpler to implement pre-leap check, using a Chernoff-type bound on the one-step exit probability for the tau-leap method. This allows to control the exit probability of a simulated trajectory using a hybrid SSA/tau-leap method, and to obtain accurate computable estimates for the global weak error associated with the exit event, and the corresponding total computational work.