Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting

Abstract

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

References in corpus (2)

• Spatio-temporal correlations can drastically change the response of a MAPK pathway
• Simulation of stochastic reaction-diffusion processes on unstructured meshes

Cited by in corpus (5)

• Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
• Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations
• Hierarchical Reaction-Diffusion Master Equation
• Strong convergence for split-step methods in stochastic jump kinetics
• Information metrics for long-time errors in splitting schemes for stochastic dynamics and parallel KMC