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Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations

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SDBW04 - Spatially Distributed Stochastic Dynamical Systems in Biology

Co-authors: Hepburn, Iain (OIST), Chen, Weiliang (OIST)

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either by particle tracking or voxel-based methods, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers. GPU parallel implementations have been described for particle tracking methods [1,2] and for voxel-based methods [3], where good parallel performance gain up to 2 order of magnitude have been demonstrated but this depends strongly on model specificity. MPI parallel implementations have gained less attention than GPU implementations to date but offer several advantages including a greater range of platform support from personal computers to advanced supercomputer clusters. An initial MPI implementation for irregular grids has been described and almost ideal speedup demonstrated but only up to 4 cores [4], which indicates the potential for good scalability of such implementations.

We describe an operator splitting implementation for irregular grids with a novel method to improve accuracy over Lie-Trotter splitting that is somewhat comparable to tau-reduction but without the performance cost. We systematically investigate parallel performance for a range of models and mesh partitionings using the STEPS simulation platform [5]. Finally we introduce a whole cell parallel simulation of a published reaction-diffusion model [6] within a detailed, complete neuron morphology and demonstrate a speedup of 3 orders of magnitude over serial computations. 

[1] L Dematte 2012. IEEE /ACM Trans. Comput. Biol. Bioinf. 9: 655-667 [2] DV Gladkov et al. 2011. Proc. 19th High Perf. Comp. Symp. 151-158 [3] E Roberts, JE Stone, Z Luthey-Schulten 2013. J. Comp. Chem. 34: 245–255 [4] A Hellander et al. 2014. J. Comput. Phys. 266: 89-100 [5] I Hepburn et al. 2012. BMC Syst. Biol. 6:36 [6] H Anwar et al. 2013. J. Neurosci. 33: 15848-15867

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