Phd in MATHEMATICAL MODELS FOR ENGINEERING, ELECTROMAGNETICS AND
NANOSCIENCES

Thesis title: Solitonic Neural Networks Development of an innovative photonic neural network based on solitonic plastic interconnections

In recent years, the problem of managing and processing large quantities of data has led to the search for new methods that could guarantee high computation speed and efficiency.
In particular, research has begun to implement at the software level models capable of replicating the typical learning functions of the brain. In this context, Machine Learning (ML) methods have established themselves as the dominant tool to satisfy complex cognitive objectives (supervised learning, unsupervised learning and reinforcement learning). Software neural models suffer from problems related to large energy demand and low computational speed, if super computers are not available. Indeed, traditional computational architectures are characterized by a distinction between the computational memory functions and the processing activity. The most immediate consequences of this separation are found in a difficulty in achieving high computational speeds, efficiency and low energy consumption. In response to these needs, the neuromorphic approach has been developed which intends to replicate the fundamental functional blocks of the biological brain. Indeed, animal neural systems are the most efficient computers. Nothing is more efficient than a brain. Its functioning is not yet fully understood: however it is based on relatively simple processing per- formed by individual units, the neurons. The complexity derives from the network of synaptic interconnections that make up the complex processing map. A long line of research has developed around electronic neuromorphic hardware. Although excellent results have been achieved, this approach has clashed with the limits imposed by the physics of electrical conduction. These systems are characterized by a high energy loss due to energy dissipation caused by the Joule effect. The complexity required by a neuromorphic hardware is characterized by a very high number of interconnections, a difficult condition to achieve with the electronics. Furthermore, the electronic hardware systems have a static structure and a poor adaptability. Therefore, they are not suitable for the realization of complex networks. Moreover, one of the key words of biological neural learning is plasticity which is the ability to update its own structure according to the inputs to be processed and then stored in memory. Self-modification of geometries underlies learning in the biological brain. Information is processed and stored by tracing specific paths along the complexity of the neural network. The research I conducted during the three years of PhD was focused on the development of a new concept of photonic neuromorphic hardware system, fully operating in the optics domain, capable of recognizing input signals, processing them and simultaneously memorizing them. To achieve this result, I exploited the nonlinear properties of a photorefractive crystal, the lithium niobate (LiNbO3), which are characterized by a plastic refractive index, useful to create dynamical environment for neural processing. This research opens up a new road in neuromorphic research.