Calculation Of The Reserve Pool Based On The Nonlinear Dynamics System Of The Semiconductor Laser

In order to solve complex tasks such as pattern recognition,chaotic time series prediction,classification,etc.,researchers strive to find new methods that are more efficient and more computational power than traditional digital computers.Reservoir computing?RC?is a novel method emerging in the field of machine learning.This method is completely different from traditional digital computers,and shows high efficiency and high precision when dealing with complex tasks.Although RC originates from recurrent neural network?RNN?,it eliminates the defect of training difficulty in RNN and so is easier to apply in practice.RC needs to map the input signal from low-dimensional space to high-dimensional space by using nonlinear feature mapping.It can be realized in two different ways:one is based on a large number of nonlinear nodes;the other is based on a single nonlinear node with an external feedback loop which outputs are equidistantly sampled and taken as virtual nodes.RC based on the latter named as delay-based RC and its structure is very simple,which can greatly reduce the implementation difficulty.In 2011,a delay-based RC system based on a chaotic circuit with a feedback loop was reported for the first time.In the test of 10th-order Nonlinear Auto-Regressive Moving Average 10?NARMA10?at a data processing rate of 0.1 KSa/s,the prediction error is as low as 2.3%.High speed and high accuracy are the eternal goals pursued by RC when dealing with time-dependent information.Optoelectronic or all-optical RC has more advantages than circuit-implemented delay-based RC.In particular,SLs exhibit rich dynamic behavior under optical injection and optical feedback,and its nonlinearity is controllable.By adjusting only a few parameters such as injection strength,feedback strength and frequency detuning one can obtain the optimal non-linearity required by the RC,which makes SLs very suitable for the nonlinear nodes in the reservoir.In2013,a delay-based RC system based on SL was experimentally implemented for the first time.The prediction error evaluated via Santa Fe chaotic time series is only 10.6%at a data processing rate of 13 MSa/s.Since then,new progress has been made in the research of delay-based RC system based on SLs,and it has shown great application prospects in task tests such as wireless channel equalization,time series prediction,optical packet head recognition,speech recognition,handwritten digit recognition.Although there have been some reports on delay-based RC system implemented by SLs,there are still some problems.For example,in order to improve the performance of the RC system,appropriate mask is needed to stimulate rich internal dynamics of the reservoir.At the same time,research is needed on how to design new structures to further improve the calculation accuracy and data processing rates.In addition,the ability of the reservoir to process information in parallel needs to be further explored.These are the core issues of extending delay-based RC to practical application.Therefore,this paper mainly theoretically investigates all-optical RC systems based on SL.Aiming at the generation of chaotic mask and its time-delay signature and complexity,the theoretical model of RC system,the influence of key parameters on prediction performance,classification performance and memory capacity,the reservoir based on a SL system with dual optical feedback loop,the reservoir based on a mutually coupled SLs system and the reservoir with two tasks processed in parallel are proposed.In details,the main works and results of our studies are summarized as follows:1.High quality chaotic signal generation in mutually coupled SLs system is theoretically investigated.Autocorrelation function?ACF?is utilized for quantitatively identifying the time-delay signature?TDS?of chaotic signal,and Kolmogorov-Sinai?KS?entropy and Kaplan-York?KY?dimension are applied to estimate the complexity of chaotic signal.The results show that,under suitable parameters,two sets of chaotic signals with weak TDS and high complexity can be obtained simultaneously.By analyzing the influences of the coupling strength and frequency detuning on the TDS of chaotic signals,the parameter regions of chaotic signals with weak TDS are determined in the parameter space of coupling strength and frequency detuning.On this basis,by further calculating the KS entropy and KY dimension of chaotic signals with weak TDS,the optimized parameter regions are specified for simultaneously generating two sets of high quality chaotic signals based on the mutually coupled SLs system.2.A RC system based on a SL subject to double optical feedback is proposed.Using high quality chaotic signals as masks,the prediction performance of such a system is numerically investigated via Santa Fe chaotic time series prediction task.In the simulation,de-synchronization scheme is adopted,that is,the delay time of the shorter feedback loop?₁ is equal to T+??T is the period of input data,and?is the interval time between virtual nodes?.The simulation results indicate that the RC system can yield a good prediction performance.Through optimizing some relevant operating parameters,ultra-fast information processing rates up to Gb/s level can be realized with a prediction error of less than 3%.Moreover,the prediction performance of the reservoir is better when the longer feedback loop delay?₂ is close to?₁+T_RO/2(T_RO is the relaxation oscillation period of the response SL).On this basis,the influence of phase fluctuation between-2?and 2?caused by the minute change of?₂on the performance of the reservoir is analyzed.It is concluded that phase fluctuation has a great influence on the prediction performance of the system,and the better prediction performance is located near 0 and±2?.In addition,the prediction performance of the RC systems based on a SL subject to single and double optical feedback is compared,and it is concluded that the RC system based on a SL subject to double optical feedback has better prediction performance under the same parameters conditions.Finally,by further comparing the states of the virtual nodes and memory capacity of their reservoirs,the reason that the RC system based on a SL subject to double optical feedback has better prediction performance is revealed.3.A RC system based on mutually coupled SLs is proposed.Using high quality chaotic signals as masks,the prediction performance and classification performance for such a system are numerically investigated via Santa Fe chaotic time series prediction task and waveform recognition task,respectively.The simulation results indicate that,when adopting this system to process ultra-fast data with rate up to 1GSa/s,the best prediction error 5.1?10^-5?5.2?10^-6 and classification error5.5?10^-4?8.8?10^-5 can be achieved under optimized operation parameters.On this basis,NARMA10 task is used to test the system's ability to handle relatively complex tasks.Compared with Santa Fe chaotic time series prediction task,waveform recognition task and nonlinear channel equalization task,NARMA10 task requires higher memory capacity of the system.In this test,the system achieves the best prediction error 0.077?0.002 at a data processing rate of 0.5 GSa/s,which is better than the results reported at the same data processing rate.Finally,the performance of the two reservoirs is compared in terms of the reservoir based on mutually coupled SLs and reservoir based on decoupled SLs.Through the comparative analysis of their virtual node state,memory capacity and memory quality,it is concluded that the reservoir based on mutually coupled SLs has higher memory capacity and memory quality.At the same time,compared with the memory capacity of the reservoir based on a SL subject to single or double feedback,the memory capacity of the reservoir based on mutually coupled SLs is significantly stronger,which reveals the reason why the RC system based on mutually coupled SLs can perform well for NARMA10 tasks.4.The parallel computing ability of RC system based on mutually coupled SLs is investigated via Santa Fe chaotic time series prediction task and non-linear channel equalization task.Considering that the coupling of two SLs results in interfering with each other in RC system when processing two independent tasks in parallel,we increase injection strength and decrease coupling strength to reduce this interference.And the system achieves good results in the tests of parallel processing two Santa Fe chaotic time series prediction tasks,two non-linear channel equalization tasks,one Santa Fe chaotic time series prediction task and one non-linear channel equalization task at a data processing rate of 0.5 GSa/s.The results demonstrate that this RC system has the ability of processing two independent tasks in parallel.In this system,there are higher requirements for parameter selection for processing two tasks simultaneously,such as coupling strength,injection strength and mask scaling factor.At the same time,the simulation results show that the mask scaling factor plays a crucial role in balancing system performance when dealing with two tasks.At the meantime,for two different pairs of tasks,the system does not need to change too many parameters and only needs to adjust mask scaling factor to make the amplitude of the masked data fall within the same interval,which can realize the switching of the system to different tasks.