论文标题
神经元网络模型的有效隐式求解器
Efficient implicit solvers for models of neuronal networks
论文作者
论文摘要
我们介绍了专门针对神经网络的有效和准确模拟的标准隐式溶解器的经济版本。这些重新制定可以通过减小在每个时间步骤有效解决的代数系统的大小来大大提高网络模拟的效率。虽然我们在这里专门将重点放在明确的第一步上，但对角隐含的runge kutta方法（ESDIRK），也可以将类似的简化应用于任何隐式ode求解器。为了证明所提出的方法的功能，我们考虑基于具有缓慢快速动力学的三个不同单细胞模型的网络，包括经典的Fitzhugh-Nagumo模型，细胞内钙浓度模型和Hindmarsh-Rose模型。基于这些模型，对增加大小的网络的模拟网络的数值实验证明了所提出的经济方法的较高效率。
We introduce economical versions of standard implicit ODE solvers that are specifically tailored for the efficient and accurate simulation of neural networks. These reformulations allow to achieve a significant increase in the efficiency of network simulations, by reducing the size of the algebraic systems effectively solved at each time step. While we focus here specifically on Explicit first step, Diagonally Implicit Runge Kutta methods (ESDIRK), similar simplifications can also be applied to any implicit ODE solver. In order to demonstrate the capabilities of the proposed methods, we consider networks based on three different single-cell models with slow-fast dynamics, including the classical FitzHugh-Nagumo model, a Intracellular Calcium Concentration model and the Hindmarsh-Rose model. Numerical experiments on the simulation of networks of increasing size based on these models demonstrate the superior efficiency of the proposed economical methods.
