An Adaptive Method for Solving Chemical Master Equations using a Sparse Wavelet Basis

In the stochastic formulation of reaction kinetics, the time evolution of the probability distribution for a system of interacting molecular species is governed by the Chemical Master Equation (CME). This equation can be seen as a large system of ODEs, but solving the CME using standard numerical methods is usually impossible due to the huge number of degrees of freedom involved. In this paper, we propose the use of a sparse wavelet basis belonging to the Daubechies wavelet family for approximating the CME. By adaptively representing the solution of the equation in a thresholded wavelet basis and propagating only the essential degrees of freedom in each time step, we avoid the “curse of dimensionality” that affects the Chemical Master Equation.