Mathematical modeling of a self-learning neuromorphic network based on nanosized memristive elements with 1T1R crossbar architecture

Artificial neural networks play an important role in the modern world. Their main field of application is the tasks of recognition and processing of images, speech, as well as robotics and unmanned systems. The use of neural networks is associated with high computational costs. In part, it was this fact that held back their progress, and only with the advent of high-performance computing systems did the active development of this area begin. Nevertheless, the issue of speeding up the work of neural network algorithms is still relevant. One of the promising directions is the creation of analog implementations of artificial neural networks, since analog calculations are performed orders of magnitude faster than digital ones. The memristor acts as the basic element on which such systems are built. A memristor is a resistance, the conductivity of which depends on the total charge passed through it. Combining them into a matrix (crossbar) allows one layer of artificial synapses to be implemented at the hardware level. Traditionally, the STDP method based on Hebb’s rule has been used as an analog learning method. In this work, we are modeling a two-layer fully connected network with one layer of synapses. The memristive effect can manifest itself in different substances (mainly in different oxides), so it is important to understand how the characteristics of memristors will affect the parameters of the neural network. Two oxides are considered: titanium oxide (TiO₂) and hafnium oxide (HfO₂). For each oxide, a parametric identification of the corresponding mathematical model is performed to best fit the experimental data. The neural network is tuned depending on the oxide used and the process of training it to recognize five patterns is simulated.

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