Chaotic behavior in an algorithm to escape from poor local minima in lens design

Turnhout, Maarten van; Bociort, Florian

doi:10.1364/oe.17.006436

Cited by 44 publications

(4 citation statements)

References 16 publications

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“…The visualization method was implemented by constructing a "portrait" of the numerical search for the roots of systems of equations [32]. For this, the surface scanning method [33] implemented in the Mathcad package was used to construct special visual graphic (animation) objects, which are demonstrated within the lecture activities (see Section 3.2).…”

Section: Methodsmentioning

confidence: 99%

“…In order to answer this question, students are offered the following visualization prepared in advance by the teacher, which can be called a "portrait" of the roots of the system of Equation ( 2). This kind of visualization is used to evaluate numerical methods [32]. The visualization was obtained by scanning the area of the plane according to the graph in Figure 9.…”

Section: Application Of the Visualization Methods By Creating A "Port...mentioning

confidence: 99%

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Visualization in Mathematical Packages When Teaching with Information Technologies

et al. 2022

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A method has been obtained for the use of visualization in computer mathematical packages, which is an effective means of overcoming difficult situations that arise for students when mastering such packages and solving computational problems. Depending on the complexity of the problem being solved, either the teacher or the students themselves can create special visual graphic (animation) objects. Such objects allow, initially without going into the intricacies of the functioning of the package and the mathematical apparatus used, to competently describe a complete picture of a difficult situation for students and indicate ways to resolve it. The method is considered through the example of the process of solving systems of equations using the mathematical package Mathcad and the WolframAlpha online resource. Graphical and animated objects are presented that clearly demonstrate the areas of the location of initial approximations, allowing you to numerically obtain all the real roots of systems of trigonometric and nonlinear equations. Similar objects are built to find the critical points of the Himmelblau’s special test function. Visualization materials are confirmed by the presented computational calculations. The proposed method is implemented in the form of plans for lectures and practical classes on mathematical modeling using computer technologies. The method was tested with university students at the National Research University Moscow Power Engineering Institute.

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Section: Methodsmentioning

confidence: 99%

Section: Application Of the Visualization Methods By Creating A "Port...mentioning

confidence: 99%

Visualization in Mathematical Packages When Teaching with Information Technologies

et al. 2022

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“…Each span is followed by an FM-EDFA amplifier to compensate for the span loss. In the simulations, each signal consists of 2 18 symbols with 10% training symbols, created from the random bit stream, and each symbol is represented by 8 samples. Next, each signal is modulated with the 16QAM format, with a symbol rate of R s = 28 Gbaud/ s, resulting in the bit rate of 200 Gb/s per spatial mode.…”

Section: Spatial Division Multiplexing Transmission Systemmentioning

confidence: 99%

Physical Layer Security Based on Chaotic Spatial Symbol Transforming in Fiber-Optic Systems

Zhang

Gao

et al. 2018

IEEE Photonics J.

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We propose a chaotic spatial symbol transforming encryption method for enhancing the physical layer security in fiber-optic systems based on space-division multiplexed (SDM) transmission. The designed 3-D chaotic sequences are used to scramble the real and imaginary part of quadrature amplitude modulation (QAM) symbols, permute the symbolto-space mapping, and control iteration times between the two processes. The encrypted transmission of 200 Gb/s per mode polarization-division-multiplexed 16QAM signals has been simulated over 1000-km two-mode fiber. The results show that the eavesdropper cannot recover the original information with a part of the security keys or a part of the transmitted signals when the iteration times are beyond 5. We found the error spreading phenomenon can be combined with the mode-dependent loss (MDL) to realize the system security enhancement. When eavesdroppers coupled signals out from SDM waveguide by bending-induced fiber tapping, they need reduce the bend radius to receive more spatial leak modes. The bending-induced fiber tapping inherently causes MDL. Although the error spreading phenomenon leads to bit-error-rate increasing by 1.3 dB than conventional 16QAM transmission, it will be a promising solution to overcome the weakness that the huge amount of data can be compromised by taping out the portion of the signal in single-mode transmission.

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“…In addition to traditional optical design, automated optical design methods are becoming more prevalent, shortening the design cycle and striving for global optimization of the optical design. In particular, evolutionary algorithms (EA) [1][2][3] and extensions of local search algorithms [4][5][6][7] with, for example, saddle point constructions 4,6,8 are used to design optical systems.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of action spaces for reinforcement learning in optical design

Fu,

Onyszkiewicz,

Kemmerling

et al. 2024

Machine Learning in Photonics

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Nowadays, sophisticated ray tracing software packages are used for the design of optical systems, including local and global optimization algorithms. Nevertheless, the design process is still time-consuming with many manual steps, taking days or even weeks until an optical design is finished. To address this shortcoming, with reinforcement learning, an agent can be trained to use ray tracing and optimization software designing an optical system. In this setting, the agent can modify the current state of the system with a predefined set of actions. One of the primary challenges is the selection of an appropriate action space. Different types of discrete and continuous action spaces are compared and their advantages and disadvantages in terms of the cumulated reward, convergence rate and resulting optical design are examined.

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Chaotic behavior in an algorithm to escape from poor local minima in lens design

Cited by 44 publications

References 16 publications

Visualization in Mathematical Packages When Teaching with Information Technologies

Visualization in Mathematical Packages When Teaching with Information Technologies

Physical Layer Security Based on Chaotic Spatial Symbol Transforming in Fiber-Optic Systems

Evaluation of action spaces for reinforcement learning in optical design

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