Mathematical Modeling of an Analogue Self-Learning Neural Network Based on Memristive Elements Taking into Account Stochastic Switching Dynamics

Abstract

In this paper, we consider the issues of modeling an analog self-learning pulsed neural network based on memristive elements. One of the important properties of a memristor is the stochastic switching dynamics, which is mainly due to the stochastic processes of generation/recombination and the movement of ions (or oxygen vacancies) in a dielectric film under the effect of an electric field. The stochastic features are taken into account by adding a term responsible for the additive (Gaussian) noise to the memristor-state equation. The effect of noise on the functioning of an element is demonstrated using the dynamic model of a memristor as an example. The switching of a memristor from the high-resistance state to low-resistance state and vice versa is shown to occur from cycle to cycle in different ways, which is consistent with experimental data. We formulate a stochastic model that describes the hardware analog implementation of a pulsed neural network with memristive elements as synaptic weights and a learning mechanism based on the spike timing dependent plasticity (STDP) method. The operation of two neural networks consisting of one neuron with 64 synapses and two neurons with 128 synapses, respectively, is modeled. The recognition of 8 × 8 images is performed. The stochastic component in the memristor model is shown to have an effect on the fact that the templates from implementation to implementation are distributed among the neurons in different ways and the adaptation of weights (network training) occurs at different rates. In both cases, the network successfully learns to recognize the specified images.