Translation. Region: Russian Federation –
Source: Novosibirsk State University –
An important disclaimer is at the bottom of this article.
A new multi-step approach for compensating for nonlinear distortions in fiber-optic communication lines based on digital backpropagation, which utilizes a sophisticated model of nonlinear effects using perturbation theory, has been developed by scientists from Novosibirsk State University. This approach was developed as part of a comprehensive research project aimed at overcoming the influence of nonlinear physical effects and random noise on optical sensors and fiber-optic communication lines. In this large-scale project, NSU scientists, in collaboration with colleagues from Ulyanovsk State University, combined photonics and machine learning, enabling the development of new methods for analyzing, optimizing, and controlling nonlinear processes, leveraging both the high-speed signal processing in optical systems and the ability of machine learning to discover and exploit hidden information. The project "Machine Learning for Applied Problems of Nonlinear Photonics," led by former NSU Rector, RAS Academician, and Doctor of Physical and Mathematical Sciences Mikhail Fedoruk, received grant support from the Russian Science Foundation last year after winning an interdisciplinary competition in the category "Conducting Fundamental Scientific Research and Exploratory Scientific Research on the Instructions (Directives) of the President of the Russian Federation."
Union of Mathematicians and Physicists
Particular attention is currently being paid to the development of "smart" lasers that can adapt to external conditions and dynamically control their parameters in real time. Such systems ensure more precise and reliable operation of optical fiber systems in challenging environments, opening up new possibilities for their application in telecommunications, industrial automation, sensors, medicine, and security systems. The project is relevant in light of the current challenges facing the telecommunications and laser industries. Optical communication lines form the foundation of digital infrastructure and support all areas related to digital technologies. Increasing volumes of transmitted data require the development of new technologies, which necessitates considering nonlinear and noise effects. The operation of many fiber laser systems is also associated with nonlinear effects, such as the Kerr effect, Raman scattering, and Brillouin scattering. On the one hand, these effects can be useful, for example, for mode locking in pulsed lasers, but on the other, they can lead to instability and destabilize the system. Machine learning methods, particularly new neural network algorithms of various architectures, can play a key role in managing this nonlinearity, said Mikhail Fedoruk.
The project aims to address the scientific challenge associated with the complexity of analyzing, modeling, and managing nonlinear and random processes in photonics, a key area of modern science and included in the list of cross-cutting technologies of the NTI Platform. Using machine learning methods to study nonlinear effects and their manifestations in the presence of random processes opens up new opportunities for improving the performance of photonic systems and creating new solutions.
"The 'Machine Learning for Applied Problems of Nonlinear Photonics' project is interdisciplinary. It was launched at the initiative of NSU and brought together the efforts of two research groups—applied mathematicians and laser physicists. The first group is affiliated with NSU, and the project's main contributors—Oleg Sidelnikov, Anastasia Bednyakova, and Alexey Redyuk—graduated from NSU's Faculty of Mathematics and Mechanics and defended their theses and then their PhD dissertations under my supervision. The second group represents Ulyanovsk State University. It is led by Andrey Fotiadi, a recognized expert in nonlinear fiber optics, fiber lasers, and sensors and a PhD candidate in physics and mathematics. Both groups are focused on modeling in two main areas. The first focuses on machine learning methods in lasers and nonlinear photonic systems, while the second focuses on machine learning methods and nonlinear technologies in optical communication lines," said Mikhail Fedoruk.
Interdisciplinary approach
Universal methods for analyzing nonlinear systems still lack a single approach, but solving many applied problems in this field requires new approaches, making the importance of this research increasingly relevant. Improving the performance of existing systems and developing new engineering concepts requires understanding and correctly interpreting nonlinear effects and their interaction with random noise. Using machine learning methods to study nonlinear effects and their manifestations in the presence of random processes opens up new opportunities for improving the performance of photonic systems and creating new solutions.
"Machine learning algorithms can adapt to changing conditions and efficiently process large volumes of data, extracting hidden dependencies and enabling real-time system performance improvement. This interdisciplinary approach, combining photonics and machine learning, enables the development of new methods for analyzing, optimizing, and controlling nonlinear processes, leveraging both the high-speed signal processing in optical systems and the ability of machine learning to discover and exploit hidden information," explained Mykhailo Fedoruk.
Smart photonics
The project team combines the expertise of two research groups, which is essential for the successful implementation of the project, namely, the development of machine learning algorithms and the creation of smart photonic devices using them. As part of this collaboration, a group of laser physicists with expertise in developing modern nonlinear and microwave photonic devices will develop functional devices and control tools. These devices will serve as testbeds for new original mathematical algorithms being developed by a group of NSU applied mathematicians with experience in modeling physical systems and applying machine learning methods to their optimization and control. The synergy between these two areas will enable not only the development of new mathematical apparatus for machine learning but also the creation of new photonic devices for real-world applications, offering fundamentally new consumer characteristics over existing analogs.
The project partner's contribution will consist of conducting preliminary laser testing experiments with the aim of transferring the results necessary for the development and testing of machine learning algorithms to the NSU team, as well as developing and implementing additional electronic control systems for the lasers' operating mode, which are necessary for the joint operation of photonic devices with trained algorithms.
Machine learning
As part of the project, the NSU team, led by Mikhail Fedoruk, will conduct a wide range of theoretical and numerical studies, which will be divided into two main research areas: "Machine Learning Methods in Lasers and Nonlinear Photonic Systems" and "Machine Learning Methods and Nonlinear Technologies in Optical Communication Lines."
The first area of focus will involve the development of neural network algorithms based on recurrent neural network architectures, transformer architectures, and reinforcement learning algorithms for implementing optoelectronic feedback in fiber laser systems. To stabilize radiation generation and control its key frequency-temporal and spectral characteristics, optoelectronic feedback based on machine learning algorithms will be implemented in fiber laser configurations. Further analysis of laser radiation using the nonlinear Fourier transform (NFT) is planned. The second area of focus involves the development of a compensation scheme for dispersion and nonlinear effects based on deep convolutional neural networks. This will be followed by the integration of approaches based on digital backpropagation and signal processing algorithms based on perturbation theory to compensate for nonlinear distortions.
Neural network algorithms
During the first year of the project, the scientists achieved important results in both of its main areas. In developing machine learning methods for lasers and nonlinear photonic systems, they conducted a range of theoretical, numerical, and experimental studies aimed at creating neural network control algorithms for a single-frequency fiber laser with an external ring resonator. They developed and implemented models based on long-short-term memory (LSTM) and transformer neural network architectures, which allow predicting the control voltage of a thermo-optical phase shifter based on a photodetector signal, simulating the behavior of a classic PID controller.
"We continued exploring new applications of NFT for analyzing optical fields in dissipative media. We considered the House-Ginzburg-Landau equation (HGLE) as an important example used for modeling laser resonators. As a result, we investigated the dependence of the generation mode type on the HGLE parameters—saturation energy and saturation power. We identified the ranges of parameter values in which HGLE solitons are close to those of the nonlinear Schrödinger equation, and demonstrated that in this case, the dynamics of a field obeying the HGLE can be described with high accuracy using only a discrete spectrum. For single-pulse modes, we described in detail the stages of generating a single-soliton solution from noise, and demonstrated the relationship between these stages and qualitative changes in the discrete spectrum parameters," explained Mikhail Fedoruk.
Neural network
Equally effective were the studies conducted within the "Machine Learning Methods and Nonlinear Technologies in Optical Communication Lines" program. A deep, complex-valued convolutional neural network was developed for modeling the propagation of optical signals in a wavelength-division multiplexed fiber communication line.
"The architecture of this network simulates the method of splitting into physical processes and is based on coupled nonlinear Schrödinger equations. We also studied the impact of key neural network model parameters on modeling accuracy, including the width of convolutional and nonlinear filters, as well as the number of layers per fiber span. We developed and tested an effective approach to network training based on pre-optimization of convolutional filters to compensate for chromatic dispersion. The obtained results demonstrate high accuracy in modeling signal propagation over long communication lines and confirm the applicability of the proposed architecture to the analysis and optimization of fiber-optic systems with wavelength division multiplexing," explained Mikhail Fedoruk.
Prospects
The scientist emphasized that the practical application of the obtained results will improve the efficiency of fiber-optic communication lines, which forms the basis for the development of high-speed data transmission infrastructure, which is strategically important for the connectivity of the Russian Federation. The continuous implementation of new telecommunications and laser technologies, including the use of machine learning methods proposed in the project, facilitates the development of strategic areas such as the transition to advanced digital and intelligent manufacturing technologies, the creation of systems for processing large volumes of data, machine learning, and artificial intelligence. The project's results can find practical application in several strategically important sectors of the real economy. Solving the problem of transmitting growing volumes of information directly impacts the development of new government digital services, the advancement of science and new technologies, as well as many other areas of industry, business, and everyday life.
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