Construction method of reservoir platform based on coupled GaAs resonator

Abstract

The invention discloses a reservoir platform construction method based on a coupled GaAs resonator, which comprises the following steps: firstly introducing coupling parameters, constructing a coupled resonator, depicting the dynamics of the resonator, and then setting an NARMA reference task to verify the performance of the constructed RC so as to excite and drive a first resonator to drive a second resonator. The method comprises the steps that a first resonator and a second resonator are obtained, the amplitude of the second resonator is sampled to serve as training data, an output weight matrix Wout is obtained through a ridge regression algorithm, a predicted value is obtained through an equation y (k) = WoutS (k), then the NMSE is solved to obtain an error between the predicted value and a true value, and thermodynamic diagrams under different parameter configurations are drawn through the NMSE. The reservoir of the reservoir is innovated, the coupled resonator serves as the reservoir, the amplitude of the second resonator serves as training data to obtain the output weight matrix, and the performance of the reservoir is improved by enriching nonlinearity.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence and industrial control technology, and in particular to a method for constructing a reserve pool platform based on a coupled GaAs resonator. Background Art

[0002] Reservoir computing can be used to process time series data and is good at capturing complex time dependencies and dynamic changes in data. However, with the extension of time series and the influence of early input information, traditional reservoir computing also has limited memory capacity and forgetting problems. 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 nonlinear elements to replace the large number of neurons in the traditional reservoir.

[0003] So far, RC has been implemented using electronic self-selecting devices, memristors, and microelectromechanical system (MEMS) resonators. The key to realizing the RC model is to make the nonlinear element used, the "computational substrate", exhibit sufficient nonlinear dynamic characteristics and decay memory. However, the currently used MEMS resonator, the Duffing resonator, lacks sufficient nonlinearity required for RC and requires additional circuit design. In addition, the input signal of the MEMS resonator is limited to electrical signals, which prevents RC from processing the information carried by light. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a method for constructing a reservoir platform based on coupled GaAs resonators, which can utilize and process the information carried by light and the optical signal can make the resonator present richer nonlinearity, significantly improving the efficiency and application range of RC.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for constructing a reservoir platform based on a coupled GaAs resonator, comprising the following steps:

[0006] S1. Based on the parameter characteristics of GaAs resonator, introduce coupling parameters, construct coupled resonators, and characterize the dynamics of resonators;

[0007] S2. Build RC with the constructed coupled resonator as the reservoir and set the NARMA benchmark task to verify the prediction ability of the proposed RC, as shown in the following formula:

[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 are delayed from k to the current state, and u(k) is regarded as the information carried by the laser;

[0010] S3, input the N-dimensional vector mask Mask, and superimpose it 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 S;

[0012] S5. Train S with the expected signal y as the target through ridge regression to obtain the output weight matrix W out ;

[0013] S6, based on step S5, the output weight matrix W is obtained out , take the matrix S used for training as input, get the output value y(k), and then solve the normalized mean square error to get the error between the predicted value and the true value;

[0014] S7. Study the influence of hyperparameters such as the number of nodes, training length, sampling time and delay parameters in NARMA, draw heat maps under different parameter configurations with NMSE, and then build a new reservoir of the reserve pool.

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

[0016]

[0017]

[0018] ρ=5332,A=7.5×10 -15 , L = 3 × 10 -6 , I = 1.5625 × 10 -30 ;

[0019] E = 8.55 × 10 10 , T0=3×10 -9 , T1=T0×P ex0 sin(w p t);

[0020] Amplitude P ex0 Fixed at 1.24μW, w p =2, V dc =V ac =5,ε=8.85×10 -12 , h = 2 × 10 -7 , d = 5 × 10 -8 .

[0021] Preferably, step S1 further comprises: the coupled GaAs resonator dynamic model is described by coupled Duffing oscillators, which are defined as follows:

[0022]

[0023] Parameter settings:

[0024] m=1.2001×10 -16 ,c=4.3903×10 -10 , k1=3.0341, k2=2.5837, k3=2.0564×10 15 , f0=-2.2148×10 -9 ,ω=1;

[0025] Use MATLAB's built-in function ode45 to solve the above equation and obtain the amplitude of the coupled resonator;

[0026] Draw the bifurcation diagram of the coupled resonator as the coupling coefficient changes, and select the coupling coefficient when the coupled resonator is in the synchronous state;

[0027] The bifurcation diagram of the coupled resonator as the injected laser power varies is plotted.

[0028] Preferably, 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, 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 y with a corresponding length tar as target output.

[0029] Preferably, step S4 further comprises:

[0030] 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 drive of the excitation, the first beam drives the second beam to move, and the sampling period is set to

[0031] The amplitude of the coupled resonator driven by the last excitation is taken as the initial state of the coupled resonator driven by the next excitation;

[0032] The amplitude of the second beam is collected as the training set data X, and the first 100 rows and the first 100 columns are taken as the training data matrix s.

[0033] Preferably, step S5 further comprises:

[0034] Using ridge regression operation, we get the output weight matrix w out, the equation is as follows:

[0035] w out =yS T (SS T +γI) -1 ;

[0036] Where γ is the bias parameter to avoid overfitting, set to 1e-8, and I is the identity matrix.

[0037] Preferably, step S6 further comprises:

[0038] According to the obtained output weight matrix W out , taking the matrix S used for training as input, we get y(k), and the equation is as follows:

[0039] y(k)=W out S(k);

[0040] NMSE is further used to conduct a qualitative analysis of the trained reservoir performance, and the equation is as follows:

[0041] NMSE = Σk(p(k)-y(k)) 2 / Σkp 2 (k);

[0042] Where p(k) is the real signal, i.e. y tar , y(k) is the output signal;

[0043] Through the training matrix S, predict the output value corresponding to the training data, and solve the NMSE to judge the training effect; take the 101st to 200th rows and the first 100 columns from the training data set X as the prediction data matrix D;

[0044] By equation y = W out D, get the predicted output value y;

[0045] Take the corresponding y tar , the prediction error value is obtained by the above NMSE formula.

[0046] Preferably, step S7 further comprises:

[0047] The NMSE values ​​used in the heat map are logarithmic (log 10 (NMSE));

[0048] Set the length of the mask MASK to 20, 40, 80, 160, or 320;

[0049] Set the sampling time to 2Π(2 -5 , 2 -4 , 2 -3 , 2 -2 , 2-1 , 2 0 , 2 1 , 2 2 , 2 3 );

[0050] With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 2;

[0051] With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 10;

[0052] Set the delay parameters of the NARMA task to 1, 2, 4, 6, 10;

[0053] Set the training length to 20, 40, 80, 160, 320, 640, 1280;

[0054] With the delay parameter as the horizontal axis and the training length as the vertical axis, solve NMSE and draw a heat map.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. The present invention can utilize and process the information carried by light, and the optical signal can make the resonator present richer nonlinearity, which significantly improves the performance and application range of RC.

[0057] 2. The present invention innovates the reservoir of the reserve pool, using the coupled resonator as the reservoir, and using the amplitude of the second resonator as training data to obtain the output weight matrix W out , improving the performance of the reserve pool by enriching nonlinearity. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0059] In the attached picture:

[0060] Figure 1 It is a flow chart of an embodiment of a method for constructing a reservoir platform based on a coupled GaAs resonator of the present invention;

[0061] Figure 2 is the kinetic bifurcation diagram of the present invention;

[0062] Figure 3 The present invention is a NARMA task graph; wherein the training NMSE is 0.0027 and the test NMSE is 0.0033;

[0063] Figure 4The present invention solves NMSE to draw the heat map of NARMA task 2;

[0064] Figure 5 The present invention solves NMSE to draw the heat map of NARMA task 10;

[0065] Figure 6 It is a thermal map drawn after solving NMSE in the present invention. DETAILED DESCRIPTION

[0066] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0067] Embodiment: The present invention provides a method for constructing a reservoir platform based on coupled GaAs resonators, such as Figure 1 As shown, the implementation steps of the prediction method of this embodiment are detailed as follows:

[0068] Step 1: Study the GaAs resonator, understand the parameter characteristics of the resonator, and study under what conditions the resonator has rich nonlinearity and is suitable for building RC with coupled resonators as reservoirs; based on the parameter characteristics of the GaAs resonator, introduce coupling parameters and build coupled resonators;

[0069] The coupled GaAs resonator dynamics model is described by coupled Duffing oscillators, which are defined as follows:

[0070]

[0071] Parameter settings:

[0072] m=1.2001×10 -16 ,c=4.3903×10 -10 , k1=3.0341, k2=2.5837, k3=

[0073] 2.0564×10 15 , F0=-2.2148×10 -9 ,ω=1;

[0074] Use MATLAB's built-in function ode45 to solve the above equation and obtain the amplitude of the coupled resonator;

[0075] like Figure 2 As shown, the dynamic bifurcation diagram of the coupled resonator as the coupling parameters change is depicted, and the coupled resonator is analyzed to be in a synchronous state or an asynchronous state;

[0076] The dynamic bifurcation diagram of the coupled resonator is depicted as the injected laser power changes, and it is analyzed whether the coupled resonator is in a single-period state, a double-period state, or a chaotic state.

[0077] Step 2: Then, the RC is built with the coupled resonator as the reservoir, and the NARMA benchmark task is set to verify the prediction capability of the proposed new reservoir platform;

[0078]

[0079] 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 are delayed from k to the current state, and u(k) is regarded as the information carried by the laser;

[0080] The initial state of the coupled resonator is set to 0, and only the first resonator is provided with laser excitation and voltage excitation to preheat the coupled resonator. The amplitude of the decoupled resonator in the stable periodic state is used as the next input; u(k) with a length of 100 is taken from the set NARMA benchmark task as the training input.

[0081] Step 3: Input the N-dimensional vector mask Mask and superimpose it on the amplitude of the injected laser power.

[0082] Step 4: Based on step 3, periodically sample the response of the coupled resonator to obtain an output sequence S; specifically comprising:

[0083] The beam of the first resonator is considered as an active beam and the beam of the second resonator is considered as a passive beam;

[0084] Under the drive of excitation, the first beam drives the second beam to move, and the sampling period is set to

[0085] The amplitude of the coupled resonator driven by the last excitation is taken as the initial state of the coupled resonator driven by the next excitation; the amplitude of the second beam is periodically sampled to obtain the training set data X, and the first 100 rows and the first 100 columns of X are taken as the training data matrix S.

[0086] Step 5: Train S with the expected signal y as the target through ridge regression to obtain the output weight matrix:

[0087] W out =yS T (SS T +γI) -1 ;

[0088] Where γ is the bias parameter to avoid overfitting, set to 1e-8, and I is the identity matrix.

[0089] Step 6: According to the obtained output weight matrix W out , taking the matrix S used for training as input, we get y(k), and the equation is as follows:

[0090] y(k)=W out S(k);

[0091] NMSE is further used to conduct a qualitative analysis of the trained reservoir performance, and the equation is as follows:

[0092] NMSE = ∑k(p(k)-y(k)) 2 / ∑kp 2 (k);

[0093] Where p(k) is the real signal, i.e. y tar , y(k) is the output signal;

[0094] Through the training matrix S, predict the output value corresponding to the training data, and solve the NMSE to judge the training effect; take the 101st to 200th rows and the first 100 columns from the training data set X as the prediction data matrix D;

[0095] By equation y = W out D, get the predicted output value y; take the corresponding y tar , the prediction error value is obtained by the above NMSE formula.

[0096] Step 7: Figure 3 As shown in the figure, the influence of the hyperparameters of the number of nodes, training length, sampling time and delay parameters in NARMA is studied, and the heat map under different parameter configurations is drawn with NMSE, and then a new reservoir of the reserve pool is built; specifically, it includes:

[0097] The NMSE values ​​used in the heat map are logarithmic (log 10 (NMSE));

[0098] Set the length of the mask MASK to 20, 40, 80, 160, or 320;

[0099] Set the sampling time to 2Π(2 -5 , 2 -4 , 2 -3 , 2 -2 , 2 -1 , 2 0 , 2 1 , 2 2 , 2 3 );

[0100] With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 2, as shown in Figure 4 As shown;

[0101] With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 10, as shown in Figure 5 As shown;

[0102] Set the delay parameters of the NARMA task to 1, 2, 4, 6, 10;

[0103] Set the training length to 20, 40, 80, 160, 320, 640, 1280;

[0104] With the delay parameter as the horizontal axis and the training length as the vertical axis, solve the NMSE and draw a heat map, such as Figure 6 shown.

[0105] The present invention is implemented by MATLAB software design and deployed on a personal computer based on a 64-bit Windows operating system.

[0106] Specific working principle: First, introduce coupling parameters, construct coupled resonators, characterize the dynamics of resonators, and study under what conditions the resonator is rich in nonlinearity, which is suitable for building RC with coupled resonators as reservoirs. Then set the NARMA benchmark task to verify the performance of the built RC, set the training length to 100, and the test length to 100 to excite the first resonator to drive the second resonator, and sample the amplitude of the second resonator as training data, and obtain the output weight matrix W through the ridge regression algorithm. out , and then through the equation y(k) = W out S(k) is used to obtain the predicted value, and then the NMSE is solved to obtain the error between the predicted value and the true value. In order to build a reservoir with better performance, its hyperparameters are studied, and the thermal map under different parameter configurations is drawn with NMSE. The present invention innovates the reservoir of the reserve pool, uses the coupled resonator as the reservoir, and uses the amplitude of the second resonator as the training data to obtain the output weight matrix W out , improving the performance of the reserve pool by enriching nonlinearity.

[0107] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing a reservoir platform based on coupled GaAs resonators, characterized in that: The following steps are involved: S1. Based on the parameter characteristics of GaAs resonator, introduce coupling parameters, construct coupled resonators, and characterize the dynamics of resonators; S2. Build RC with the constructed coupled resonator as the reservoir and set the NARMA benchmark task to verify the prediction ability of the proposed RC, as shown in the following formula: 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 are delayed from k to the current state, and u(k) is regarded as the information carried by the laser; S3, input the N-dimensional vector mask Mask, and superimpose it on the amplitude of the injected laser power; S4, according to step S3, the response of the coupled resonator is periodically sampled to obtain an output sequence S; S5. Train S with the expected signal y as the target through ridge regression to obtain the output weight matrix W out ; S6, based on step S5, the output weight matrix W is obtained out , take the matrix S used for training as input, get the output value y(k), and then solve the normalized mean square error to get the error between the predicted value and the true value; S7. Study the influence of hyperparameters such as the number of nodes, training length, sampling time and delay parameters in NARMA, draw heat maps under different parameter configurations with NMSE, and then build a new reservoir of the reserve pool.

2. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S1 further includes: the GaAs resonator dynamic model is described by a Duffing oscillator, which is defined as follows: p=5332, A=7.5×10 -15 ,L=3×10 -6 ,I=1.5625×10 -30 ; E=8.55×10 10 ,T0=3×10 -9 ,T1=T0×P ex0 sin(w p t); Amplitude P ex0 Fixed at 1.24μW, w p =2, V dc =V ac =5,ε=8.85×10 -12 , h = 2 × 10 -7 , d = 5 × 10 -8 .

3. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S1 further includes: the coupled GaAs resonator dynamic model is described by a coupled Duffing oscillator, which is defined as follows: Parameter settings: m=1.2001×10 -16 ,c=4.3903×10 -10 ,k1=3.0341,k2=2.5837,k3=2.0564×10 15 ,f0=-2.2148×10 -9 ,ω=1; Use MATLAB's built-in function ode45 to solve the above equation and obtain the amplitude of the coupled resonator; Draw the bifurcation diagram of the coupled resonator as the coupling coefficient changes, and select the coupling coefficient when the coupled resonator is in the synchronous state; The bifurcation diagram of the coupled resonator as the injected laser power varies is plotted.

4. The method for constructing a reservoir platform based on coupled GaAs resonators 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 the 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, taking the corresponding length y tar as target output.

5. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S4 further comprises: 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 drive of the excitation, the first beam drives the second beam to move, and the sampling period is set to The amplitude of the coupled resonator driven by the last excitation is taken as the initial state of the coupled resonator driven by the next excitation; The amplitude of the second beam is collected as the training set data X, and the first 100 rows and columns are taken as the training data matrix S.

6. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S5 further comprises: Using ridge regression operation, we get the output weight matrix W out , the equation is as follows: W out =yS T (SS T +γI) -1 ; Where γ is the bias parameter to avoid overfitting, set to 1e-8, and I is the identity matrix.

7. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S6 further comprises: According to the obtained output weight matrix W out , taking the matrix S used for training as input, we get y(k), and the equation is as follows: y(k)=W out S(k); NMSE is further used to conduct a qualitative analysis of the trained reservoir performance, and the equation is as follows: NMSE=∑k(p(k)-y(k)) 2 / ∑kp 2 (k); Where p(k) is the real signal, i.e. y tar , y(k) is the output signal; Through the training matrix S, predict the output value corresponding to the training data, and solve the NMSE to judge the training effect; take the 101st to 200th rows and the first 100 columns from the training data set X as the prediction data matrix D; By equation y = W out D, get the predicted output value y; Take the corresponding y tar , the prediction error value is obtained by the above NMSE formula.

8. The method for constructing a reservoir platform based on coupled GaAs resonators according to claim 1, characterized in that: Step S7 further comprises: The NMSE values ​​used in the heat map are logarithmic (log 10 (NMSE)); Set the length of the mask MASK to 20, 40, 80, 160, or 320; Set the sampling time to 2Π(2 -5 , 2 -4 , 2 -3 , 2 -2 , 2 -1 , 2 0 , 2 1 , 2 2 , 2 3 ); With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 2; With the length of MASK as the horizontal axis and the sampling time as the vertical axis, solve NMSE to draw the heat map of NARMA task 10; Set the delay parameters of the NARMA task to 1, 2, 4, 6, 10; Set the training length to 20, 40, 80, 160, 320, 640, 1280; With the delay parameter as the horizontal axis and the training length as the vertical axis, solve NMSE and draw a heat map.

Images