Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 561-587, March 2024.
Abstract. The noisy leaky integrate-and-fire (NLIF) model describes the voltage configurations of neuron networks with an interacting many-particles system at a microscopic level. When simulating neuron networks of large sizes, computing a coarse-grained mean-field Fokker–Planck equation solving the voltage densities of the networks at a macroscopic level practically serves as a feasible alternative in its high efficiency and credible accuracy when the interaction within the network remains relatively low. However, the macroscopic model fails to yield valid results of the networks when simulating considerably synchronous networks with active firing events. In this paper, we propose a multiscale solver for the NLIF networks, inheriting the macroscopic solver’s low cost and the microscopic solver’s high reliability. For each temporal step, the multiscale solver uses the macroscopic solver when the firing rate of the simulated network is low, while it switches to the microscopic solver when the firing rate tends to blow up. Moreover, the macroscopic and microscopic solvers are integrated with a high-precision switching algorithm to ensure the accuracy of the multiscale solver. The validity of the multiscale solver is analyzed from two perspectives: first, we provide practically sufficient conditions that guarantee the mean-field approximation of the macroscopic model and present rigorous numerical analysis on simulation errors when coupling the two solvers; second, the numerical performance of the multiscale solver is validated through simulating several large neuron networks, including networks with either instantaneous or periodic input currents which prompt active firing events over some time.

中文翻译：

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针对噪声集成和激发神经元网络的同步捕获多尺度求解器

多尺度建模与仿真，第 22 卷，第 1 期，第 561-587 页，2024 年 3 月。
摘要。噪声泄漏积分激发 (NLIF) 模型在微观层面描述了具有相互作用的多粒子系统的神经元网络的电压配置。当模拟大尺寸的神经元网络时，计算粗粒度平均场福克-普朗克方程在宏观层面上求解网络的电压密度实际上是一种可行的替代方案，因为当网络内相互作用时，其效率高且精度可靠仍然相对较低。然而，当模拟具有主动触发事件的相当同步的网络时，宏观模型无法产生有效的网络结果。在本文中，我们提出了一种用于 NLIF 网络的多尺度求解器，继承了宏观求解器的低成本和微观求解器的高可靠性。对于每个时间步骤，当模拟网络的发射率较低时，多尺度求解器使用宏观求解器，而当发射率趋于爆炸时，它切换到微观求解器。而且，宏观和微观求解器集成了高精度切换算法，保证了多尺度求解器的精度。从两个角度分析多尺度求解器的有效性：首先，我们提供了保证宏观模型平均场近似的实际充分条件，并对两个求解器耦合时的仿真误差进行了严格的数值分析；其次，通过模拟几个大型神经元网络来验证多尺度求解器的数值性能，包括具有瞬时或周期性输入电流的网络，这些电流在一段时间内提示主动放电事件。