Time-driven simulation with fully asynchronous pulse coupling

Abstract

Event Abstract Back to Event Time-driven simulation with fully asynchronous pulse coupling Alexander Hanuschkin1*, Suzanne Kunkel1, Moritz Helias1, Abigail Morrison2 and Markus Diesmann1, 2 1 BCCN Freiburg, Germany 2 RIKEN Brain Science Institute, Japan Artificial synchrony can be introduced by discrete time simulation of neuronal networks, since they typically constrain spike times to a grid determined by the computational step size [1]. Event-driven algorithms avoid this problem but are computationally demanding, both with respect to calculating future spike times and to event management, particularly for large network sizes. To address this problem, Morrison et al. [2] developed a general method of handling off-grid spiking in combination with exact subthreshold integration in globally time-driven simulations [3,4] using interpolation to approximate threshold crossings. In the framework of event-driven simulations, Brette [5] presented an elegant method of calculating spike times of integrate-and-fire neurons with exponentially decaying currents. The prediction of the next threshold crossing of the membrane potential is reformulated into a root finding problem of the equivalent polynomial. Here, we show that this scheme can also be implemented in the time-driven environment of NEST [4]. Additionally, we extended the model of Morrison et al. [2] by replacing the interpolation of threshold crossings with the computationally more expensive, but numerically more exact, Newton-Raphson technique. We compare the accuracy of the three approaches in single-neuron simulations and the efficiency in a balanced random network of 12,000 neurons [6]. For small input and output rates the polynomial method is more efficient than the interpolated one whereas for high input or output rates the interpolated method is more efficient than the polynomial one. The direct numerical method based on Newton-Raphson root finding outperforms both the interpolation and the polynomial approach at all input/output rates. Partially funded by DIP F1.2, BMBF Grant 01GQ0420 to the BCCN Freiburg, and EU Grant 15879 (FACETS).