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A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universität Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus

Efficiency of a two-neuron simulation. Triangles show results with the single-step method, while circles indicate results obtained by the iterative method. Again solid curves indicate cubic interpolation and dashed curves were obtained with linear interpolation. The used communication scheme is indicated by open (h-step communication) and filled symbols (communication in intervals of the minimal delay). The iteration control was used with prelim_tol chosen as 10−6. (A) Shift of the spike times after 1 s of biological time plotted against used step size h. (B) RMSE ϵ measured over 1 s of biological time plotted against the step size h. (C) Simulation time of the different approaches for 1 s of biological time. (D) Simulation time vs. RMSE ϵ of the corresponding simulation.
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Figure 7: Efficiency of a two-neuron simulation. Triangles show results with the single-step method, while circles indicate results obtained by the iterative method. Again solid curves indicate cubic interpolation and dashed curves were obtained with linear interpolation. The used communication scheme is indicated by open (h-step communication) and filled symbols (communication in intervals of the minimal delay). The iteration control was used with prelim_tol chosen as 10−6. (A) Shift of the spike times after 1 s of biological time plotted against used step size h. (B) RMSE ϵ measured over 1 s of biological time plotted against the step size h. (C) Simulation time of the different approaches for 1 s of biological time. (D) Simulation time vs. RMSE ϵ of the corresponding simulation.

Mentions: Figure 7 compares the results of the iterative method with the results of the single step methods in terms of accuracy and simulation time. Panel B measures the error ϵ of both methods for different step sizes h. For any given step size h the RMSE of the iterative method is much smaller than the RMSE of the single-step approach, which does not even reach a satisfying accuracy for step size 0.001 ms. Within the iterative method a cubic interpolation leads to a higher accuracy. Figure 7A shows that the error relates to a shift in comparison to the reference solution. This shift can be reduced up to 10−6 ms for the iterative method with cubic interpolation and step size 0.01 ms. At given step size h and leaving accuracy considerations aside, the single step method is the fastest implementation for any given step size, since no additional iterations are needed to compute the results. The iterative approach with linear interpolation saves some time in comparison to the version with cubic interpolation since less interpolation data needs to be computed and communicated. For this simple test case h-step communication outperforms the communication strategy in intervals of the minimal delay by a factor of 1.5, due to the very low amount of communicated data and because the communication in the employed shared memory system is fast compared to the computation. Further simulation time results for simulations on supercomputers are presented in Section 3.3. Figure 7D compares the methods in terms of efficiency. We therefore analyze the simulation time as a function of the integration error (Morrison et al., 2007), measured through the RMSE. There are two ways of reading this graph: Horizontally, one can find the most accurate method for a given simulation time. Vertically one can find the fastest method for a desired accuracy. The results show that the iterative method delivers better results in shorter time than the single step method. Also the additional effort of the cubic simulation pays off, since the method computes more accurate results in the same simulation time and reaches an accuracy which cannot be reached with the linear interpolation.


A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Efficiency of a two-neuron simulation. Triangles show results with the single-step method, while circles indicate results obtained by the iterative method. Again solid curves indicate cubic interpolation and dashed curves were obtained with linear interpolation. The used communication scheme is indicated by open (h-step communication) and filled symbols (communication in intervals of the minimal delay). The iteration control was used with prelim_tol chosen as 10−6. (A) Shift of the spike times after 1 s of biological time plotted against used step size h. (B) RMSE ϵ measured over 1 s of biological time plotted against the step size h. (C) Simulation time of the different approaches for 1 s of biological time. (D) Simulation time vs. RMSE ϵ of the corresponding simulation.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4563270&req=5

Figure 7: Efficiency of a two-neuron simulation. Triangles show results with the single-step method, while circles indicate results obtained by the iterative method. Again solid curves indicate cubic interpolation and dashed curves were obtained with linear interpolation. The used communication scheme is indicated by open (h-step communication) and filled symbols (communication in intervals of the minimal delay). The iteration control was used with prelim_tol chosen as 10−6. (A) Shift of the spike times after 1 s of biological time plotted against used step size h. (B) RMSE ϵ measured over 1 s of biological time plotted against the step size h. (C) Simulation time of the different approaches for 1 s of biological time. (D) Simulation time vs. RMSE ϵ of the corresponding simulation.
Mentions: Figure 7 compares the results of the iterative method with the results of the single step methods in terms of accuracy and simulation time. Panel B measures the error ϵ of both methods for different step sizes h. For any given step size h the RMSE of the iterative method is much smaller than the RMSE of the single-step approach, which does not even reach a satisfying accuracy for step size 0.001 ms. Within the iterative method a cubic interpolation leads to a higher accuracy. Figure 7A shows that the error relates to a shift in comparison to the reference solution. This shift can be reduced up to 10−6 ms for the iterative method with cubic interpolation and step size 0.01 ms. At given step size h and leaving accuracy considerations aside, the single step method is the fastest implementation for any given step size, since no additional iterations are needed to compute the results. The iterative approach with linear interpolation saves some time in comparison to the version with cubic interpolation since less interpolation data needs to be computed and communicated. For this simple test case h-step communication outperforms the communication strategy in intervals of the minimal delay by a factor of 1.5, due to the very low amount of communicated data and because the communication in the employed shared memory system is fast compared to the computation. Further simulation time results for simulations on supercomputers are presented in Section 3.3. Figure 7D compares the methods in terms of efficiency. We therefore analyze the simulation time as a function of the integration error (Morrison et al., 2007), measured through the RMSE. There are two ways of reading this graph: Horizontally, one can find the most accurate method for a given simulation time. Vertically one can find the fastest method for a desired accuracy. The results show that the iterative method delivers better results in shorter time than the single step method. Also the additional effort of the cubic simulation pays off, since the method computes more accurate results in the same simulation time and reaches an accuracy which cannot be reached with the linear interpolation.

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universität Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus