Hierarchical Reaction-Diffusion Master Equation
This work addresses the computational bottleneck of simulating multiscale chemical reaction systems, offering a practical speedup for researchers in computational chemistry and biology.
The authors developed a hierarchical algorithm coupling mesoscopic simulations on different mesh levels, achieving up to three orders of magnitude speedup without significant accuracy loss for multiscale chemical reaction systems.
We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh, while others live on a coarse-grained mesh. By allowing molecules to transfer from the fine levels to the coarse levels when appropriate, we show that we can save up to three orders of magnitude of computational time compared to microscopic simulations or highly resolved mesoscopic simulations, without losing significant accuracy. We demonstrate this in several numerical examples with systems that cannot be accurately simulated with a coarse-grained mesoscopic model.