Introduction to Memristive Mechanisms and Models.

The increase in computational power demand led by the development of Artificial Intelligence is rapidly becoming unsustainable. New paradigms of computation, which potentially differ from digital computation, together with novel hardware architecture and devices, are anticipated to reduce the exorbitant energy demand for data-processing tasks. Memristive systems with resistive switching behavior are under intense research, given their prominent role in the fabrication of memory devices that promise the desired hardware revolution in our intensive data-driven era. They are suggested to provide the hardware substrate to scale up computational capabilities while improving their energy expenditure and speed. This work provides an orientation map for those interested in the vast topic of memristive systems with application to neuromorphic computing. We address the description of the most notable emerging devices and we illustrate models that capture the complex dynamical behavior of these systems under the dynamical-systems framework developed by Chua. We then review the memristive behavior under the perspective of statistical physics and percolation theory suited to describe fluctuations and disorder which are otherwise precluded in the dynamical-system approach. Percolation theory allows the investigation of these systems at the mesoscopic level, enabling material-independent modeling of non-linear conductance networks. We finally discuss recent and less recent successes in deep learning methods that bridge the field of physics-based and biological- inspired neuromorphic computing.