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Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks

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Abstract

With the various simulators for spiking neural networks developed in recent years, a variety of numerical solution methods for the underlying differential equations are available. In this article, we introduce an approach to systematically assess the accuracy of these methods. In contrast to previous investigations, our approach focuses on a completely deterministic comparison and uses an analytically solved model as a reference. This enables the identification of typical sources of numerical inaccuracies in state-of-the-art simulation methods. In particular, with our approach we can separate the error of the numerical integration from the timing error of spike detection and propagation, the latter being prominent in simulations with fixed timestep. To verify the correctness of the testing procedure, we relate the numerical deviations to theoretical predictions for the employed numerical methods. Finally, we give an example of the influence of simulation artefacts on network behaviour and spike-timing-dependent plasticity (STDP), underlining the importance of spike-time accuracy for the simulation of STDP.

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Notes

  1. The original Crank–Nicolson method solves semi-discretized partial differential equation systems by replacing the derivatives with respect to both independent dimensions in a particular way by finite difference ratios and evaluating the solution numerically using the trapezoidal rule, cf. Crank and Nicolson (1947). However, in the literature the phrase “Crank–Nicolson method” is used unspecifically, sometimes even indicating just the trapezoidal rule or the midpoint rule.

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Acknowledgements

The research leading to these results has received funding from the European Union 7th Framework Programme (FP7/2007-2013) under grant agreement no. 269921 (BrainScaleS).

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Authors and Affiliations

  1. Endowed Chair for Parallel VLSI Systems and Neural Circuits Institute of Circuits and Systems, University of Technology Dresden, Dresden, Germany

    Stephan Henker, Johannes Partzsch & René Schüffny

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  1. Stephan Henker
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  2. Johannes Partzsch
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  3. René Schüffny
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Correspondence to Johannes Partzsch.

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Action Editor: Alain Destexhe

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Henker, S., Partzsch, J. & Schüffny, R. Accuracy evaluation of numerical methods used in state-of-the-art simulators for spiking neural networks. J Comput Neurosci 32, 309–326 (2012). https://doi.org/10.1007/s10827-011-0353-9

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