A method of constructing a reservoir platform based on coupled GaAs resonators

Abstract

The application discloses a construction method of a reserve pool platform based on coupled GaAs resonators, first introduces a coupling parameter, constructs a coupled resonator, and describes the dynamics of the resonator; then, a NARMA benchmark task is set to verify the performance of the constructed RC, to stimulate and drive the first resonator to drive the second resonator, and the amplitude of the second resonator is sampled as training data, and the output weight matrix W is obtained through a ridge regression algorithm out , and then the prediction value is obtained through the equation y(k) = W out S(k), and then the error between the prediction value and the true value is obtained by solving NMSE, and a heat map under different parameter configurations is drawn by NMSE. The application innovates the reservoir of the reserve pool, uses the coupled resonator as the reservoir, obtains the output weight matrix through the amplitude of the second resonator as the training data, and improves the performance of the reserve pool through rich nonlinearity.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of artificial intelligence and industrial control technology, in particular to a construction method of a reservoir pool platform based on coupled GaAs resonators. BACKGROUND

[0002] Reservoir computing can be used to process time series data, and is good at capturing complex time-dependent relationships and dynamic changes in data. However, with the extension of time series and the influence of early input information, traditional reservoir computing also has the problems of limited memory capacity and forgetting. In order to improve the performance of the reservoir, machine learning methods such as deep reservoir computing (Deep RC) and time-delay reservoir computing (TDRC) have emerged, but the most attractive RC model is to use a nonlinear element to replace a large number of neurons in the traditional reservoir.

[0003] So far, RC has been implemented using electronic self-selecting devices, memristors, and micro-electromechanical system (MEMS) resonators. It is crucial for the used nonlinear element, the "computing substrate", to exhibit sufficient nonlinear dynamics and decaying memory to implement the RC model. However, the current MEMS resonators and Duffing resonators lack sufficient nonlinearity required by RC and need additional circuit design. In addition, the input signal of the MEMS resonator is limited to electrical signals, which hinders RC from processing information carried by light. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides a construction method of a reservoir pool platform based on coupled GaAs resonators, which can utilize and process information carried by light and the optical signal can make the resonator exhibit more abundant nonlinearity, significantly improving the efficiency and application range of RC.

[0005] To achieve the above object, the present application provides the following technical scheme: a construction method of a reservoir pool platform based on coupled GaAs resonators, comprising the following steps:

[0006] S1, based on the parameter characteristics of the GaAs resonator, introducing a coupling parameter, constructing a coupled resonator, and characterizing the dynamics of the resonator;

[0007] S2, using the constructed coupled resonator as a reservoir to build an RC, setting an NARMA benchmark task to verify the prediction ability of the proposed RC, as follows:

[0008]

[0009] The input u(k) is uniformly generated from [0, 0.5], y is a function of u(k), n is a positive integer, indicating how many steps of delay to the current state at k, u(k) is regarded as the information carried by the laser;

[0010] S3, input an N-dimensional vector mask Mask, which is superimposed on the amplitude of the injected laser power;

[0011] S4, according to step S3, the response of the coupled resonator is periodically sampled to obtain an output sequence ;

[0012] S5, train by ridge regression with the expected signal as the target , obtain the output weight matrix ;

[0013] S6, on the basis of step S5, by the obtained output weight matrix , take the matrix used for training as input, obtain the output value , and then solve the normalized mean square error to obtain the error between the predicted value and the true value;

[0014] S7, study the influence of the hyperparameters of the node number, the training length, the sampling time and the delay parameter in NARMA, draw a heat map under different parameter configurations with NMSE, and then build a new reservoir of the reservoir;

[0015] Preferably, step S1 further comprises: the GaAs resonator dynamics model is described by a Duffing oscillator, defined as follows:

[0016] ;

[0017] ;

[0018]

[0019]

[0020] ;

[0021]

[0022] The amplitude is fixed at , .

[0023] Preferably, step S1 further comprises: the coupled GaAs resonator dynamics model is described by a coupled Duffing oscillator, defined as follows:

[0024]

[0025] Parameter setting:

[0026] , ;

[0027] Solve the above equations with MATLAB built-in function ode45 to obtain the amplitude of the coupled resonator;

[0028] Draw the bifurcation diagram of the coupled resonator with the change of the coupling coefficient, and select the coupling coefficient when the coupled resonator is in a synchronous state;

[0029] Draw the bifurcation diagram of the coupled resonator with the change of the injected laser power.

[0030] Preferably, step S2 further comprises: setting the initial state of the coupled resonator as 0, only providing laser excitation and voltage excitation to the first resonator to preheat the coupled resonator, and taking the amplitude of the coupled resonator in a stable periodic state as the next input; taking u(k) with a length of 100 from the set NARMA benchmark task as the training input, and taking the corresponding length of as the target output.

[0031] Preferably, step S4 further comprises:

[0032] The beam of the first resonator is regarded as an active beam, and the beam of the second resonator is regarded as a passive beam; under the driving of the excitation, the second beam is driven to move by the first beam, and the sampling period is set as ;

[0033] Take the amplitude of the coupled resonator under the excitation driving of the last time as the initial state of the coupled resonator under the excitation driving of the next time;

[0034] Collect the amplitude of the second beam as the training set data , and take the first 100 rows and the first 100 columns as the training data matrix .

[0035] Preferably, step S5 further comprises:

[0036] An output weight matrix is obtained by using ridge regression operation, and the equation is as follows:

[0037] ;

[0038] Wherein is a bias parameter to avoid overfitting, which is set as 1e-8, is an identity matrix.

[0039] Preferably, step S6 further comprises:

[0040] According to the obtained output weight matrix , the matrix for training is obtained as input , and the equation is as follows:

[0041] ;

[0042] Further, the trained reservoir performance is qualitatively analyzed by using NMSE, and the equation is as follows:

[0043] ;

[0044] wherein is the real signal, i.e. , is the output signal;

[0045] By training the matrix , the output value corresponding to the training data is predicted, and the NMSE is solved to judge the training effect;

[0046] The 101st row to the 200th row and the first 100 columns in the training data set X are taken as the prediction data matrix D;

[0047] The equation is used to obtain the predicted output value ;

[0048] The corresponding is taken, and the prediction error value is obtained by using the above NMSE formula.

[0049] Preferably, step S7 further comprises:

[0050] The values of NMSE used in the heat map are all logarithmized ;

[0051] The length of the mask MASK is set to 20, 40, 80, 160, and 320;

[0052] The sampling time is set to ;

[0053] Taking the length of the mask as the horizontal axis and the sampling time as the vertical axis, the NMSE is solved to draw the heat map of NARMA task 2;

[0054] Taking the length of the mask as the horizontal axis and the sampling time as the vertical axis, the NMSE is solved to draw the heat map of NARMA task 10;

[0055] The delay parameter of the NARMA task is set to 1, 2, 4, 6, and 10;

[0056] Set the training length to 20, 40, 80, 160, 320, 640, 1280;

[0057] Solve NMSE to draw a heat map with delay parameters as the horizontal axis and training length as the vertical axis.

[0058] Compared with the prior art, the present application has the beneficial effects:

[0059] 1. The present application can utilize and process information carried by light, and the light signal can make the resonator exhibit more abundant nonlinearity, significantly improving the performance and application range of RC.

[0060] 2. The present application innovates the reservoir of the reservoir pool, uses the coupled resonator as the reservoir, and obtains the output weight matrix by using the amplitude of the second resonator as the training data , and improves the performance of the reservoir pool by abundant nonlinearity. BRIEF DESCRIPTION OF DRAWINGS

[0061] The accompanying drawings are used to provide a further understanding of the present application, and constitute a part of the specification, together with the embodiments of the present application, to explain the present application, and do not constitute a limitation of the present application.

[0062] In the drawings:

[0063] Figure 1 is a flowchart of an embodiment of a construction method of a reservoir pool platform based on a coupled GaAs resonator of the present application;

[0064] Figure 2 is a dynamic bifurcation diagram of the present application;

[0065] Figure 3 is a NARMA task diagram of the present application; wherein the training NMSE is 0.0027 and the test NMSE is 0.0033;

[0066] Figure 4 is a heat map of the present application solving NMSE to draw NARMA task 2;

[0067] Figure 5 is a heat map of the present application solving NMSE to draw NARMA task 10;

[0068] Figure 6 is a heat map drawn after solving NMSE of the present application. DETAILED DESCRIPTION

[0069] The preferred embodiments of the present application are described below in conjunction with the accompanying drawings, and it should be understood that the preferred embodiments described herein are only used to illustrate and explain the present application, and do not limit the present application.

[0070] Embodiment: The present application provides a construction method of a reserve pool platform based on coupled GaAs resonators, as shown in Figure 1 The implementation steps of the prediction method of the present embodiment are described as follows:

[0071] Step 1: Study GaAs resonators, understand the parameter characteristics of the resonators, and study the state in which the resonators are rich in nonlinearity, suitable for building RC with coupled resonators as reservoirs; based on the parameter characteristics of GaAs resonators, introduce coupling parameters to construct coupled resonators;

[0072] The coupled GaAs resonator dynamics model is described by a coupled Duffing oscillator, defined as follows:

[0073]

[0074] Parameter settings:

[0075] , ;

[0076] Solve the above equation using the MATLAB built-in function ode45 to obtain the amplitude of the coupled resonator;

[0077] As shown in Figure 2 , the dynamics bifurcation diagram of the coupled resonator with the coupling parameter is depicted, and the coupled resonator is analyzed to be in a synchronous state or an asynchronous state;

[0078] The dynamics bifurcation diagram of the coupled resonator with the injected laser power is depicted, and the coupled resonator is analyzed to be in a single-period state or a multiple-period state or a chaotic state.

[0079] Step 2: Then build RC with coupled resonators as reservoirs, and set NARMA benchmark tasks to verify the prediction ability of the proposed new reserve pool platform;

[0080]

[0081] The input u(k) is uniformly generated from [0, 0.5], y is a function of u(k), n is a positive integer representing how many steps of delay to the current state at k, and u(k) is considered as the information carried by the laser;

[0082] The initial state of the coupled resonator is set to 0, only the first resonator is provided with laser excitation and voltage excitation to preheat the coupled resonator, and the amplitude of the decoupled resonator in the stable periodic state is used as the next input; take u(k) with a length of 100 from the set NARMA benchmark task as the training input.

[0083] Step 3: Input an N-dimensional vector mask Mask, which is superimposed on the amplitude of the injected laser power.

[0084] Step 4: Periodically sampling the response of the coupled resonators to obtain an output sequence based on step 3 ; Specifically comprising:

[0085] Regarding the first resonator beam as the active beam and the second resonator beam as the passive beam;

[0086] Under the driving of the excitation, the second beam is driven by the first beam to move, and the sampling period is set to ;

[0087] Taking the amplitude of the coupled resonator under the last excitation driving as the initial state of the coupled resonator under the next excitation driving, periodically sampling the amplitude of the second beam to obtain training set data X, and taking the first 100 rows and the first 100 columns of X as the training data matrix .

[0088] Step 5: Training by ridge regression with the expected signal as the target to obtain the output weight matrix:

[0089] ;

[0090] Wherein is a bias parameter to avoid overfitting, which is set to 1e-8, is an identity matrix.

[0091] Step 6: According to the obtained output weight matrix , taking the matrix used for training as input to obtain , the equation is as follows:

[0092] ;

[0093] Further qualitative analysis of the trained reservoir performance is carried out by using NMSE, and the equation is as follows:

[0094] ;

[0095] Wherein is the true signal, i.e. , is the output signal;

[0096] By training the matrix , the output value corresponding to the training data is predicted, and the NMSE is solved to judge the training effect;

[0097] Taking the 101st row to the 200th row and the first 100 columns of the training data set X as the prediction data matrix D;

[0098] ​Equation , get the predicted output value ; take the corresponding , get the prediction error value through the above NMSE formula.

[0099] Step 7: as Figure 3 shown, the influence of the hyperparameters of the node number, the training length, the sampling time and the delay parameter in NARMA is studied, and the heat map of NMSE under different parameter configurations is drawn, and then the new reservoir of the reservoir is built; Specifically, it includes:

[0100] The value of NMSE used in the heat map is logarithmized ;

[0101] The length of the mask MASK is set to 20, 40, 80, 160, 320;

[0102] The sampling time is set to ;

[0103] Taking the length of the mask as the horizontal axis and the sampling time as the vertical axis, the NMSE is solved to draw the heat map of NARMA task 2, as shown in Figure 4 ;

[0104] Taking the length of the mask as the horizontal axis and the sampling time as the vertical axis, the NMSE is solved to draw the heat map of NARMA task 10, as shown in Figure 5 ;

[0105] The delay parameter of the NARMA task is set to 1, 2, 4, 6, 10;

[0106] The training length is set to 20, 40, 80, 160, 320, 640, 1280;

[0107] Taking the delay parameter as the horizontal axis and the training length as the vertical axis, the NMSE is solved and the heat map is drawn, as shown in Figure 6 .

[0108] Among them, the design and implementation in the application are realized by MATLAB software, and are deployed on a personal computer based on a 64-bit Windows operating system.

[0109] The specific working principle is: first, introduce the coupling parameter, build the coupled resonator, depict the dynamics of the resonator, and study the state of the resonator under which the nonlinearity is rich and suitable for building RC with the coupled resonator. Then set the NARMA benchmark task to verify the performance of the built RC, set the training length to 100, and set the test length to 100, drive the second resonator with the first resonator through the excitation, and sample the amplitude of the second resonator as training data, and get the output weight matrix , and then through the equation The predicted value is obtained, and then the NMSE is solved to obtain the error between the predicted value and the true value, in order to build a better reservoir, the hyperparameters are researched, and a heat map under different parameter configurations is drawn according to the NMSE. The reservoir of the reservoir pool is innovated, the coupling resonator is used as the reservoir, the amplitude of the second resonator is used as the training data to obtain the output weight matrix , and the performance of the reservoir pool is improved by enriching the nonlinearity.

[0110] Finally, it should be noted that: the above only for the preferred examples of the present application, and not for limiting the present application, although the foregoing embodiments of the present application are described in detail, for those skilled in the art, it still can be modified, or equivalent replacement of part of the technical features recorded in the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for constructing a reservoir platform based on coupled GaAs resonators, characterized in that, Includes the following steps: S1. Based on the parametric characteristics of GaAs resonators, coupling parameters are introduced to construct coupled resonators and characterize the dynamics of the resonators. S2. Using the constructed coupled resonator as the reservoir to build an RC, the NARMA benchmark task is set up to verify the predictive capability of the proposed RC, as shown in the following equation: ； The input u(k) is generated uniformly from [0, 0.5], y is a function of u(k), n is a positive integer representing how many steps are delayed to the current state at k, and u(k) is regarded as the information carried by the laser. S3. Input an N-dimensional vector mask Mask and superimpose it onto the amplitude of the injected laser power; S4. According to step S3, the response of the coupled resonator is periodically sampled to obtain the output sequence. ; S5, using ridge regression to obtain the desired signal Training for the goal The output weight matrix is ​​obtained. ; S6. Based on step S5, the output weight matrix is ​​obtained. The matrix used for training As input, the output value is obtained. Then, the normalized mean square error is calculated to obtain the error between the predicted value and the true value. S7. Investigate the influence of hyperparameters such as the number of nodes, training length, sampling time, and latency parameters in NARMA, and use NMSE to draw heat maps under different parameter configurations, thereby constructing the reservoir of a new reserve pool. Step S1 further includes: the dynamic model of the GaAs resonator is described using a Duffing oscillator, defined as follows: ； ； ； ； ； ； amplitude Fixed in , .

2. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S1 further includes: the dynamic model of the coupled GaAs resonator is described using a coupled Duffing oscillator, defined as follows: ； Parameter settings: ， ； The amplitude of the coupled resonator can be obtained by solving the equation using the built-in MATLAB function ode45. The bifurcation diagram of the coupled resonator as a function of the coupling coefficient is plotted, and the coupling coefficient of the coupled resonator in the synchronous state is selected. The bifurcation diagram of the coupled resonator as a function of injected laser power is depicted.

3. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S2 further includes: setting the initial state of the coupled resonator to 0; providing laser excitation and voltage excitation only to the first resonator to preheat the coupled resonator; taking the amplitude of the coupled resonator in its stable periodic state as the next input; taking u(k) of length 100 from the set NARMA benchmark task as the training input; and taking the corresponding length of... As the target output.

4. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S4 further includes: The beam of the first resonator is considered the active beam, and the beam of the second resonator is considered the passive beam. Under the drive of excitation, the first beam drives the second beam to move. The sampling period is set to... ; The amplitude of the coupled resonator under the previous excitation drive is taken as the initial state of the coupled resonator under the next excitation drive. Collect the amplitude of the second beam as training set data. The first 100 rows and the first 100 columns are taken as the training data matrix. .

5. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S5 further includes: The output weight matrix is ​​obtained using ridge regression. The equation is as follows: ； in This is a bias parameter to avoid overfitting, set to 1e-8. It is an identity matrix.

6. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S6 further includes: Based on the obtained output weight matrix The matrix used for training As input, we get The equation is as follows: ； The NMSE was further used to perform a qualitative analysis of the trained reservoir performance, and the equation is as follows: ； in It is a real signal, that is , It is the output signal; Through training matrix Predict the output value corresponding to the training data and solve the NMSE to judge the training effect; Take rows 101 to 200 and the first 100 columns from the training dataset X as the prediction data matrix D; Through equation To obtain the predicted output value ; Take the corresponding The prediction error value is obtained using the NMSE formula described above.

7. The method for constructing a reservoir platform based on a coupled GaAs resonator according to claim 1, characterized in that: Step S7 further includes: The NMSE values ​​in all used heatmaps were logarithmically converted. ; Set the length of the mask to 20, 40, 80, 160, or 320. Set the sampling time as follows: ; Using the length of the mask as the horizontal axis and the sampling time as the vertical axis, solve the NMSE to plot the heatmap of NARMA task 2; Using the length of the mask as the horizontal axis and the sampling time as the vertical axis, solve the NMSE to plot the heatmap of NARMA task 10. Set the delay parameters for the NARMA task to 1, 2, 4, 6, 10; Set the training length to 20, 40, 80, 160, 320, 640, 1280; Plot a heatmap by solving the NMSE with the delay parameter on the horizontal axis and the training length on the vertical axis.

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