Euler method can outperform more complex ODE solvers in the numerical implementation of the Izhikevich artificial Spiking Neuron Model given the allocated FLOPS

Abstract

The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in embedded systems. It is important therefore to realize a compromise between error and computational expense to solve numerically the model’s equations. Here we investigate the effects of discretization and we study the solver that realizes the best compromise between accuracy and computational cost, given an available amount of Floating Point Operations per Second (FLOPS). We considered three fixed-step solvers for Ordinary Differential Equations (ODE), commonly used in computational neuroscience: Euler method, the Runge-Kutta 2 method and the Runge-Kutta 4 method. To quantify the error produced by the solvers, we used the Victor Purpura spike train Distance from an ideal solution of the ODE. Counterintuitively, we found that simple methods such as Euler and Runge Kutta 2 can outperform more complex ones (i.e. Runge Kutta 4) in the numerical solution of the Izhikevich model if the same FLOPS are allocated in the comparison. Moreover, we quantified the neuron rest time (with input under threshold resulting in no output spikes) necessary for the numerical solution to converge to the ideal solution and therefore to cancel the error accumulated during the spike train; in this analysis we found that the required rest time is independent from the firing rate and the spike train duration. Our results can generalize in a straightforward manner to other spiking neuron models and provide a systematic analysis of fixed step neural ODE solvers towards an accuracy-computational cost tradeoff.

A Raspberry Pi Based Hardware Implementations of Various Neuron Models

“…In literature, although there are several implementations of neuron models on various platforms such as discrete elements, VLSI, FPAA, and FPGA as mentioned above, no study has been encountered using RPi. In other studies, for numerical solutions of neuron models, the RK4 method has been generally preferred, because it is easier to simulate than the other methods (Alteriis et al 2021;Behdad et al 2015;De Alteriis and Oddo 2021;Momani et al 2014;Rostami et al 2018;Skocik and Long 2014;Tuckwell and Jost 2009;Valadez-Godínez et al 2020;Xu et al 2018;Zhang et al 2011). A few studies about RKN, AB, AM, and ABM methods have been presented (Ramadoss et al 2021;Sweilam and Assiri 2016;V.…”