Waves and complexity, towards deep neural networks with light

Claudio Conti
ISC-CNR and University Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy
Complexity is a notion that has several denotations. When applied to wave propagation, firstly, we tackle with Anderson localization, then we consider statistical phenomena, as rare events, and lastly, we resort to strongly interacting systems, with frustration and nonlinearity, as in turbulence and spin glasses. Surprisingly - or not - nonlinear optics cover the whole aspects of this journey in complexity, leading to impressive results as the observation of replica-symmetry breaking. The tour also includes the more recent topological concepts, which are useful in classifying extreme waves, like shocks, rogues, and soliton gases. Nowadays, one reaches the world of machine learning and artificial intelligence, as the highly nonlinear and disordered models have a remarkable rule in large-scale deep neural networks. One can use waves to solve computationally demanding tasks, as in the optical Ising machines. Reservoir computing in multiple scattering media may open the way to new applications in quantum optics and biomedicine. In my talk, I will review all these aspects linking waves and complex systems.