## Abstract

To understand the mechanism of information processing by a biological neural network, computer simulation of a large-scale spiking neural network is an important method. However, because of a high computation cost of the simulation of a large-scale spiking neural network, the simulation requires high performance computing implemented by a supercomputer or a computer cluster. Recently, hardware for parallel computing such as a multi-core CPU and a graphics card with a graphics processing unit (GPU) is built in a gaming computer and a workstation. Thus, parallel computing using this hardware is becoming widespread, allowing us to obtain powerful computing power for simulation of a large-scale spiking neural network. However, it is not clear how much increased performance the parallel computing method using a new GPU yields in the simulation of a large-scale spiking neural network. In this study, we compared computation time between the computing methods with CPUs and GPUs in a simulation of neuronal models. We developed computer programs of neuronal simulations for the computing systems that consist of a gaming graphics card with new architecture (the NVIDIA GTX 1080) and an accelerator board using a GPU (the NVIDIA Tesla K20C). Our results show that the computing systems can perform a simulation of a large number of neurons faster than CPU-based systems. Furthermore, we investigated the accuracy of a simulation using single precision floating point. We show that the simulation results of single precision were accurate enough compared with those of double precision, but chaotic neuronal response calculated by a GPU using single precision is prominently different from that calculated by a CPU using double precision. Furthermore, the difference in chaotic dynamics appeared even if we used double precision of a GPU. In conclusion, the GPU-based computing system exhibits a higher computing performance than the CPU-based system, even if the GPU system includes data transfer from a graphics card to host memory.

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## Acknowledgements

This work was supported by JSPS KAKENHI Grant No. 15K07146.

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## Appendix Hodgkin–Huxley model

### Appendix Hodgkin–Huxley model

The Hodgkin–Huxley model consists of four differential equations. One equation denotes the dynamics of the membrane potential:

where *C* is the membrane capacitance, *I* is an applied current, \(g_{\mathrm {Na}}, g_{\mathrm {K}}\), and \(g_L\) are respectively the conductances of \(\hbox {Na}^+, \hbox {K}^+\), and leak channels, and \(E_{\mathrm {Na}}, E_{\mathrm {Na}}\), and \(E_L\) are respectively the reversal potentials of \(\hbox {Na}^+, \hbox {K}^+\), and leak channels. The model has terms derived from a sodium current, a potassium current, and a leak current. *m*, *n*, and *h* are gating variables denoted by

\(\alpha (V)\) and \(\beta (V)\) are voltage-dependent rates:

We set the parameters: \(I(t) \,{=}\, 20 \, \hbox {mA}, V_{\mathrm {K}} \,{=}\, -\,95 \,\hbox {mV}, V_{\mathrm {Na}} \,{=}\, 57 \,\hbox {mV}, V_L = -\, 50 \,\hbox {mV}, g_{\mathrm {K}} = 36 \,\hbox {mS}/\hbox {cm}^2, g_{\mathrm {Na}} = 120 \,\hbox {mS}/\hbox {cm}^2, g_L \,{=}\, 0.3 \,\hbox {mS}/\hbox {cm}^2, V_{\mathrm {K}} = -\,95 \,\hbox {mV}, V_\mathrm = 57 \,\hbox {mV}, V_L = -\, 50\, \hbox {mV},\, \hbox {and}\, C = 1 \,\upmu \hbox {F}/\hbox {cm}^2\).

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Fujita, K., Okuno, S. & Kashimori, Y. Evaluation of the computational efficacy in GPU-accelerated simulations of spiking neurons.
*Computing* **100**, 907–926 (2018). https://doi.org/10.1007/s00607-018-0590-0

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DOI: https://doi.org/10.1007/s00607-018-0590-0