噪声积分与火神经元网络的同步捕捉多尺度求解器

Ziyu Du, Yantong Xie, Zhennan Zhou
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摘要

多尺度建模与仿真》,第 22 卷第 1 期,第 561-587 页,2024 年 3 月。 摘要噪声渗漏积分发射(NLIF)模型在微观层面上描述了多粒子系统相互作用的神经元网络的电压配置。在模拟大型神经元网络时,计算粗粒度均场福克-普朗克方程求解宏观层面的网络电压密度实际上是一种可行的替代方法,因为当网络内的相互作用相对较低时,该方法具有高效率和可信的准确性。然而,当模拟具有主动点火事件的同步网络时,宏观模型无法得出有效的网络结果。本文继承了宏观求解器的低成本和微观求解器的高可靠性,提出了一种 NLIF 网络的多尺度求解器。在每个时间步长内,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,则切换到微观求解器。此外,宏观求解器和微观求解器还集成了高精度切换算法,以确保多尺度求解器的精度。我们从两个方面分析了多尺度求解器的有效性:首先,我们提供了保证宏观模型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,通过仿真几个大型神经元网络,包括具有瞬时或周期性输入电流的网络,验证了多尺度求解器的数值性能。
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A Synchronization-Capturing Multiscale Solver to the Noisy Integrate-and-Fire Neuron Networks
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.
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