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基于时延光子储备池计算的混沌激光短期预测

刘奇 李璞 开超 胡春强 蔡强 张建国 徐兵杰

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基于时延光子储备池计算的混沌激光短期预测

刘奇, 李璞, 开超, 胡春强, 蔡强, 张建国, 徐兵杰

Short-time prediction of chaotic laser using time-delayed photonic reservoir computing

Liu Qi, Li Pu, Kai Chao, Hu Chun-Qiang, Cai Qiang, Zhang Jian-Guo, Xu Bing-Jie
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  • 提出并证明了一种利用时延光子储备池计算短期预测混沌激光的时间序列. 具体来说, 建立基于光反馈和光注入半导体激光器的储备池结构, 通过选择合适的系统参数, 时延光子储备池计算可以有效地预测混沌激光约2 ns的动态轨迹. 此外, 研究了系统参数对预测结果的影响, 包括掩模类型、虚拟节点数、训练数据长度、输入增益、反馈强度、注入强度、岭参数和泄漏率. 作为一种具有全光实现潜力的机器学习方法, 时延光子储备池具有结构简单、训练成本低、易于硬件实现等优点.
    Prediction of chaotic laser has a wide prospect of applications, such as retrieving lost data, providing assists for data analysis, testing data encryption security in cryptography based on chaotic synchronization of lasers. We propose and demonstrate a new method of using time delayed photonic reservoir computing (RC) to forecast the continuous dynamical evolution of chaotic laser from previous measurements. Specifically, the time delayed photonic RC based on semiconductor laser with optical injection and feedback structure is established as a prediction system. Chaotic laser, as input signal, is generated by semiconductor laser with external disturbance.The time delayed photonic RC used in this stage is a novel implementation, which consists of three parts: the input layer, the reservoir and the output layer. In the input layer, the chaos laser from the semiconductor with an optical feedback needs to preprocess and multiply by a mask signal. The reservoir is the master-slave configuration consisting of a response laser with the optical feedback and light injection. In the feedback loop, there are N virtual nodes at each interval θ with a delay time of τ (N = τ/θ). The reservoir performs the mapping of the input signal onto a high-dimensional state space. In the output layer, the output of the reservoir is a linear combination of the reservoir state and the output weight. The output weight is optimized by minimizing the mean-square error between target value and output value through using the ridge regression algorithm.The results demonstrate that time delayed photonic RC based on semiconductor laser can forecast the trajectory of chaotic laser in about 2 ns. Moreover, we also investigate the influence of critical parameters on prediction result, including the type of the mask, the quantity of the virtual nodes, the length of the training data, the input gain, the feedback strength, the injection strength, the ridge parameter and the leakage rate.The method used here in this work has many attractive advantages, such as simple configuration, low training cost and eminently suitable for hardware implementation. Although the prediction length is limited, the significant innovation using time delayed photonic RC based on semiconductor lasers as the prediction system of chaotic laser presents a new opportunity for further developing a technique for predicting chaotic laser.
      通信作者: 李璞, lipu8603@126.com
    • 基金项目: 国家自然科学基金(批准号: 61775158, 61805168, 61961136002, 61927811, U19A2076, 11904057)、国家密码局“十三五”国家发展基金(批准号: MMJJ20170127)、中国博士后科学基金(批准号: 2018M630283, 2019T120197)、山西省自然科学基金(批准号: 201901D211116)和山西省高等学校优秀青年学术带头人计划资助的课题
      Corresponding author: Li Pu, lipu8603@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61775158, 61805168, 61961136002, 61927811, U19A2076, 11904057), the National Cryptography Development Fund, China (Grant No. MMJJ20170127), the China Postdoctoral Science Foundation (Grant Nos. 2018M630283, 2019T120197), the Natural Science Foundation of Shanxi Province, China (Grant No. 201901D211116), and the Program for the Top Young Academic Leaders of High Learning Institutions of Shanxi Province, China
    [1]

    Amil P, Soriano M C, Masoller C 2019 Chaos 29 113111Google Scholar

    [2]

    Cunillera A, Soriano M C, Fischer I 2019 Chaos 29 113113Google Scholar

    [3]

    Meng Q F, Peng Y H 2007 Phys. Lett. A 370 465Google Scholar

    [4]

    Lin X W, Yang Z H, Song Y X 2009 Expert Syst. Appl. 36 7313Google Scholar

    [5]

    Pathak J, Wikner A, Fussell R, Chandra S, Hunt B R, Girvan M, Ott E 2018 Chaos 28 041101Google Scholar

    [6]

    Pathak J, Hunt B, Girvan M, Lu Z X, Ott E 2018 Phys. Rev. Lett. 120 024102Google Scholar

    [7]

    Covas E, Benetos E 2019 Chaos 29 063111Google Scholar

    [8]

    Appeltant L, Soriano M C, Van d S G, Danckaert J, Massar S, Dambre J, Schrauwen B, Mirasso C R, Fischer I 2011 Nat. Commun. 2 468Google Scholar

    [9]

    Hicke K, Escalona-Moran M A, Brunner D, Soriano M C, Fischer I, Mirasso C R 2013 IEEE J. Sel. Top. Quantum Electron. 19 4Google Scholar

    [10]

    Paquot Y, Duport F, Smerieri A, Dambre J, Schrauwen B, Haelterman M, Massar S 2012 Sci. Rep. 2 287Google Scholar

    [11]

    Duport F, Schneider B, Smerieri A, Haelterman M, Massar S 2012 Opt. Express 20 A20Google Scholar

    [12]

    Martinenghi R, Rybalko S, Jacquot M, Chembo Y K, Larger L 2012 Phys. Rev. Lett. 108 244101Google Scholar

    [13]

    Larger L, Soriano M C, Brunner D, Appeltant L, Gutierrez J M, Pesquera L, Mirasso C R, Fischer I 2012 Opt. Express 20 3241Google Scholar

    [14]

    Dejonckheere A, Duport F, Smerieri A, Fang L, Oudar J L, Haelterman M, Massar S 2014 Opt. Express 22 9Google Scholar

    [15]

    Appeltant L, Sande G V D, Danckaert J, Fischer I 2014 Sci. Rep. 4 3629Google Scholar

    [16]

    Nguimdo R M, Verschaffelt G, Danckaert J, Van der Sande G 2014 Opt. Express 22 8672Google Scholar

    [17]

    Nguimdo R M, Verschaffelt G, Danckaert J, Van der Sande G 2015 IEEE Trans. Neural Networks Learn. Syst. 26 3301Google Scholar

    [18]

    Vinckier Q, Duport F, Smerieri A, Vandoorne K, Bienstman P, Haelterman M, Massar S 2015 Optica 2 438Google Scholar

    [19]

    Larger L, Baylón-Fuentes A, Martinenghi R, Udaltsov V S, Chembo Y K, Jacquot M 2017 Phys. Rev. X 7 011015Google Scholar

    [20]

    Takano K, Sugano C, Inubushi M, Yoshimura K, Sunada S, Kanno K, Uchida A 2018 Opt. Express 26 29424Google Scholar

    [21]

    Vatin J, Rontani D, M Sciamanna 2018 Opt. Lett. 43 4497Google Scholar

    [22]

    Vatin J, Rontani D, M Sciamanna 2019 Opt. Express 27 018579Google Scholar

    [23]

    Tan X S, Hou Y S, Wu Z M, Xia G Q 2019 Opt. Express 27 026082Google Scholar

    [24]

    Guo X X, Xiang S Y, Zhang Y H, Lin L, Wen A J, Hao Y 2019 IEEE J. Sel. Top. Quantum Electron. 26 1700109Google Scholar

    [25]

    Li P, Cai Q, Zhang J, Xu B, Wang Y 2019 Opt. Express 27 017859Google Scholar

    [26]

    Nakayama J, Kanno K, Uchida A 2016 Opt. Express 24 8679Google Scholar

    [27]

    Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 3Google Scholar

    [28]

    Wieczorek S, Krauskopf B, Simpson T B, Lenstra D 2005 Phys. Rep. 416 1Google Scholar

    [29]

    Hoerl A E, Kennard R W 1970 Technometrics 12 1Google Scholar

    [30]

    Lukosevicius M, Jaeger H 2009 Comput. Sci. Rev. 3 127Google Scholar

  • 图 1  基于半导体激光器的时延储备池计算系统示意图

    Fig. 1.  Schematic diagram of reservoir computing system based on semiconductor laser.

    图 2  (a) 激光器输出强度的分岔图; (b) 混沌激光目标信号及其预测值

    Fig. 2.  (a) Bifurcation diagram of the output intensity of the laser; (b) chaotic laser target signal together with the predicted values.

    图 3  (a) 在不同掩模类型和不同节点数的情况下, 预测长度(PL)随训练长度(Ts)变化的趋势图; (b) 在使用混沌掩模信号且节点数为800的情况下, 预测长度(PL)随输入增益(Gin)变化的趋势图; 虚线为拟合曲线

    Fig. 3.  (a) PL as a function of the length of the training data (Ts) under different type of masks and the number of nodes; (b) PL as a function of the input gain (Gin) under N = 800 with the chaos mask signal. The dotted lines represent the associated fitting curves.

    图 4  (a)预测系统在不同反馈强度(kf)和注入强度(kinj)的参数空间中PL值的二维图; (b), (c) 在(kinj, kf) = (0.06, 0.18)的条件下, 无调制信号和有调制信号时R-laser的输出强度时序

    Fig. 4.  (a) Two-dimensional map of the PL values of prediction system in the parameter space of the different feedback strength (kf) and the injection strength (kinj); (b), (c) temporal traces of the R-laser under (kinj, kf) = (0.06, 0.18) without and with modulated input data.

    图 5  (a) 预测长度(PL)随泄漏率(δ)变化的趋势图; (b) 预测长度(PL)随岭参数(λ)变化的趋势图; 虚线为拟合曲线

    Fig. 5.  (a) PL as a function of the leakage rate (δ); (b) PL as a function of the Ridge parameter (λ). The dotted lines represent the associated fitting curves.

    表 1  数值模拟中使用的激光器参数值

    Table 1.  Laser parameter values used in numerical simulations.

    符号参数参考值
    q/C电子电荷量1.6 × 10–19
    α线宽增强因子5.0
    g/(m3·s–1)微分增益1.414 × 10–12
    N0/ m-3透明载流子密度1.4 × 1024
    ε增益饱和系数5.0 × 10–23
    τp/ps光子寿命1.92
    τs/ns载流子寿命2.04
    τin/ps内腔往返时间7.38
    kf反馈强度0.18
    kinj注入强度0.06
    ν/GHz频率失谐–10
    τ/ns外腔反馈延时8 (N = 800)
    θ/ns节点间隔0.01
    Id/IthD-laser的归一化偏置电流1.2
    Ir/IthR-laser的归一化偏置电流1.25
    Gin输入增益1.5
    λ岭参数10–6
    δ泄漏率0.25
    下载: 导出CSV
  • [1]

    Amil P, Soriano M C, Masoller C 2019 Chaos 29 113111Google Scholar

    [2]

    Cunillera A, Soriano M C, Fischer I 2019 Chaos 29 113113Google Scholar

    [3]

    Meng Q F, Peng Y H 2007 Phys. Lett. A 370 465Google Scholar

    [4]

    Lin X W, Yang Z H, Song Y X 2009 Expert Syst. Appl. 36 7313Google Scholar

    [5]

    Pathak J, Wikner A, Fussell R, Chandra S, Hunt B R, Girvan M, Ott E 2018 Chaos 28 041101Google Scholar

    [6]

    Pathak J, Hunt B, Girvan M, Lu Z X, Ott E 2018 Phys. Rev. Lett. 120 024102Google Scholar

    [7]

    Covas E, Benetos E 2019 Chaos 29 063111Google Scholar

    [8]

    Appeltant L, Soriano M C, Van d S G, Danckaert J, Massar S, Dambre J, Schrauwen B, Mirasso C R, Fischer I 2011 Nat. Commun. 2 468Google Scholar

    [9]

    Hicke K, Escalona-Moran M A, Brunner D, Soriano M C, Fischer I, Mirasso C R 2013 IEEE J. Sel. Top. Quantum Electron. 19 4Google Scholar

    [10]

    Paquot Y, Duport F, Smerieri A, Dambre J, Schrauwen B, Haelterman M, Massar S 2012 Sci. Rep. 2 287Google Scholar

    [11]

    Duport F, Schneider B, Smerieri A, Haelterman M, Massar S 2012 Opt. Express 20 A20Google Scholar

    [12]

    Martinenghi R, Rybalko S, Jacquot M, Chembo Y K, Larger L 2012 Phys. Rev. Lett. 108 244101Google Scholar

    [13]

    Larger L, Soriano M C, Brunner D, Appeltant L, Gutierrez J M, Pesquera L, Mirasso C R, Fischer I 2012 Opt. Express 20 3241Google Scholar

    [14]

    Dejonckheere A, Duport F, Smerieri A, Fang L, Oudar J L, Haelterman M, Massar S 2014 Opt. Express 22 9Google Scholar

    [15]

    Appeltant L, Sande G V D, Danckaert J, Fischer I 2014 Sci. Rep. 4 3629Google Scholar

    [16]

    Nguimdo R M, Verschaffelt G, Danckaert J, Van der Sande G 2014 Opt. Express 22 8672Google Scholar

    [17]

    Nguimdo R M, Verschaffelt G, Danckaert J, Van der Sande G 2015 IEEE Trans. Neural Networks Learn. Syst. 26 3301Google Scholar

    [18]

    Vinckier Q, Duport F, Smerieri A, Vandoorne K, Bienstman P, Haelterman M, Massar S 2015 Optica 2 438Google Scholar

    [19]

    Larger L, Baylón-Fuentes A, Martinenghi R, Udaltsov V S, Chembo Y K, Jacquot M 2017 Phys. Rev. X 7 011015Google Scholar

    [20]

    Takano K, Sugano C, Inubushi M, Yoshimura K, Sunada S, Kanno K, Uchida A 2018 Opt. Express 26 29424Google Scholar

    [21]

    Vatin J, Rontani D, M Sciamanna 2018 Opt. Lett. 43 4497Google Scholar

    [22]

    Vatin J, Rontani D, M Sciamanna 2019 Opt. Express 27 018579Google Scholar

    [23]

    Tan X S, Hou Y S, Wu Z M, Xia G Q 2019 Opt. Express 27 026082Google Scholar

    [24]

    Guo X X, Xiang S Y, Zhang Y H, Lin L, Wen A J, Hao Y 2019 IEEE J. Sel. Top. Quantum Electron. 26 1700109Google Scholar

    [25]

    Li P, Cai Q, Zhang J, Xu B, Wang Y 2019 Opt. Express 27 017859Google Scholar

    [26]

    Nakayama J, Kanno K, Uchida A 2016 Opt. Express 24 8679Google Scholar

    [27]

    Lang R, Kobayashi K 1980 IEEE J. Quantum Electron. 16 3Google Scholar

    [28]

    Wieczorek S, Krauskopf B, Simpson T B, Lenstra D 2005 Phys. Rep. 416 1Google Scholar

    [29]

    Hoerl A E, Kennard R W 1970 Technometrics 12 1Google Scholar

    [30]

    Lukosevicius M, Jaeger H 2009 Comput. Sci. Rev. 3 127Google Scholar

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出版历程
  • 收稿日期:  2021-02-23
  • 修回日期:  2021-03-23
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-08-05

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