Adaptive aggregation method for the Chemical Master Equation.

One important aspect of biological systems such as gene regulatory networks and protein-protein interaction networks is the stochastic nature of interactions between chemical species. Such stochastic behaviour can be accurately modelled by the Chemical Master Equation (CME). However, the CME usually imposes intensive computational requirements when used to characterise molecular biological systems. The major challenge comes from the curse of dimensionality, which has been tackled by a few research papers. The essential goal is to aggregate the system efficiently with limited approximation errors. This paper presents an adaptive way to implement the aggregation process using information collected from Monte Carlo simulations. Numerical results show the effectiveness of the proposed algorithm.