Machine Learning Photonics

Lake Como School of Advanced Photonics

14 – 18 September 2020

The school brings together experts in emerging photonic technologies, machine learning techniques, and fundamental physics who will share with young researchers their knowledge and interdisciplinary approaches for understanding and designing complex photonic systems and their practical applications.  In the new era of artificial intelligence, algorithms and computational interfaces are broadly emerging as novel tools to do scientific research. The paradigms of machine learning also inspire interpretations and methodologies, in both theories and experiments. Nonlinear, quantum and bio-photonics, as well as optical communications, are surprisingly influenced by these new ideas. The summer school is aimed to explore machine learning applications in the specific fields of nonlinear optics and photonics.

The areas covered include, but are not limited to: machine learning methods and complexity of optical communication systems, including topics such as the nonlinear Fourier transform and transmission over multimode fibres; complexity in quantum systems emulated in photonics (including optical computing); complexity of emerging novel materials, device and components such as micro-resonators and plasmonic nanostructures. Importantly, the complexity in bio-medical photonic applications will be also considered as a high priority topic.

The summer school will focus on comprehensive review talks from major figures in complementary areas of photonics and machine learning. Invited speakers will deliver one or more 1-hour lectures over 5 days. We shall select up to 30 participants from the pool of most vibrant PhD students and postdocs, with a special focus on Marie Curie Fellows as future leaders of European photonics science and industry. 

Theory of neuromorphic computing by waves

Machine-learning by rogue waves, dispersive shocks, and solitons

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schroedinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.


Controlling rogue waves and soliton gases

Topological control of extreme waves

From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, transitions between extreme waves are allowed. However, these have never been experimentally observed because control strategies are still missing. We introduce the new concept of topological control based on the one-to-one correspondence between the number of wave packet oscillating phases and the genus of toroidal surfaces associated with the nonlinear Schrödinger equation solutions through Riemann theta functions. We demonstrate the concept experimentally by reporting observations of supervised transitions between waves with different genera. Considering the box problem in a focusing photorefractive medium, we tailor the time-dependent nonlinearity and dispersion to explore each region in the state diagram of the nonlinear wave propagation. Our result is the first realization of topological control of nonlinear waves. This new technique casts light on shock and rogue waves generation and can be extended to other nonlinear phenomena.

Nature Communications volume 10, Article number: 5090 (2019)

Optical spatial shock waves in nonlocal nonlinear media, a review paper

Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity in temporal pulses transmission and nonlocality in spatial beams propagation. Despite the rich and vast literature on nonlinear waves in optical Kerr media, spatial dispersive shock waves in nonlocal materials deserve further attention for their unconventional properties. Indeed, they have been investigated in colloidal matter, chemical physics and biophotonics, for sensing and control of extreme phenomena. Here we review the last developed theoretical models and recent optical experiments on spatial dispersive shock waves in nonlocal media. Moreover, we discuss observations in novel versatile materials relevant for soft matter and biology.

Review Paper in Advances in Physics X