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Spiking neural network simulation: numerical integration with the Parker-Sochacki method.

Stewart RD, Bair W - J Comput Neurosci (2009)

Bottom Line: The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models.We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods.Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, OX1 3PT, UK. Robert.Stewart@pharm.ox.ac.uk

ABSTRACT
Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. The method has been limited to polynomial equations, but we present division and power operations that expand its scope. We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.

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HH model results. (Top) Mean simulation time for 1 s benchmark simulation. (Middle) Mean accuracy, with accuracy values taken as the inverse of the mean absolute voltage difference between test and reference solutions. (Bottom) Overall performance (accuracy/time)
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Fig5: HH model results. (Top) Mean simulation time for 1 s benchmark simulation. (Middle) Mean accuracy, with accuracy values taken as the inverse of the mean absolute voltage difference between test and reference solutions. (Bottom) Overall performance (accuracy/time)

Mentions: Figure 5 shows the results of this performance analysis. The top panel shows how simulation time varied with the error tolerance condition. All methods became slower with decreasing error tolerance, as expected. RK was the slowest method in all conditions here. PS was the fastest method, with better than real-time speed in all conditions in the one-spike experiments. In the ten-spike simulations, PS was between 1.26 (c1) and 3.27 (c15) times slower than the equivalent one-spike simulations, but was still faster than RK and BS in all conditions. Fig. 5


Spiking neural network simulation: numerical integration with the Parker-Sochacki method.

Stewart RD, Bair W - J Comput Neurosci (2009)

HH model results. (Top) Mean simulation time for 1 s benchmark simulation. (Middle) Mean accuracy, with accuracy values taken as the inverse of the mean absolute voltage difference between test and reference solutions. (Bottom) Overall performance (accuracy/time)
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2717378&req=5

Fig5: HH model results. (Top) Mean simulation time for 1 s benchmark simulation. (Middle) Mean accuracy, with accuracy values taken as the inverse of the mean absolute voltage difference between test and reference solutions. (Bottom) Overall performance (accuracy/time)
Mentions: Figure 5 shows the results of this performance analysis. The top panel shows how simulation time varied with the error tolerance condition. All methods became slower with decreasing error tolerance, as expected. RK was the slowest method in all conditions here. PS was the fastest method, with better than real-time speed in all conditions in the one-spike experiments. In the ten-spike simulations, PS was between 1.26 (c1) and 3.27 (c15) times slower than the equivalent one-spike simulations, but was still faster than RK and BS in all conditions. Fig. 5

Bottom Line: The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models.We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods.Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.

View Article: PubMed Central - PubMed

Affiliation: Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, OX1 3PT, UK. Robert.Stewart@pharm.ox.ac.uk

ABSTRACT
Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. The method has been limited to polynomial equations, but we present division and power operations that expand its scope. We apply the Parker-Sochacki method to the Izhikevich 'simple' model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. Benchmark simulations demonstrate an improved speed/accuracy trade-off for the method relative to these established techniques.

Show MeSH