Zheng G, Tonnelier A, Martinez D
INRIA, Inovallée 655 Avenue de l'Europe Montbonnot, 38334, Saint Ismier, France.
J Comput Neurosci. 2009 Jun;26(3):409-23. doi: 10.1007/s10827-008-0119-1. Epub 2008 Nov 26.
The numerical simulation of spiking neural networks requires particular attention. On the one hand, time-stepping methods are generic but they are prone to numerical errors and need specific treatments to deal with the discontinuities of integrate-and-fire models. On the other hand, event-driven methods are more precise but they are restricted to a limited class of neuron models. We present here a voltage-stepping scheme that combines the advantages of these two approaches and consists of a discretization of the voltage state-space. The numerical simulation is reduced to a local event-driven method that induces an implicit activity-dependent time discretization (time-steps automatically increase when the neuron is slowly varying). We show analytically that such a scheme leads to a high-order algorithm so that it accurately approximates the neuronal dynamics. The voltage-stepping method is generic and can be used to simulate any kind of neuron models. We illustrate it on nonlinear integrate-and-fire models and show that it outperforms time-stepping schemes of Runge-Kutta type in terms of simulation time and accuracy.
脉冲神经网络的数值模拟需要特别关注。一方面，时间步长方法是通用的，但它们容易产生数值误差，并且需要特定处理来应对积分发放模型的不连续性。另一方面，事件驱动方法更为精确，但它们仅限于有限类别的神经元模型。我们在此提出一种电压步长方案，该方案结合了这两种方法的优点，由电压状态空间的离散化组成。数值模拟简化为一种局部事件驱动方法，该方法会导致一种隐式的依赖活动的时间离散化（当神经元变化缓慢时，时间步长会自动增加）。我们通过分析表明，这样的方案会产生一种高阶算法，从而能够精确地逼近神经元动态。电压步长方法是通用的，可用于模拟任何类型的神经元模型。我们在非线性积分发放模型上对其进行了说明，并表明在模拟时间和准确性方面，它优于龙格 - 库塔类型的时间步长方案。
