A KAN-based distributed fiber raman amplifier forward and backward problem fitting method

Abstract

The application discloses a fitting method for forward and reverse problems of a distributed fiber Raman amplifier based on a Kolmogorov-Arnold neural network (KAN), and belongs to the technical field of fiber Raman amplifiers. The method generates an ideal data set under the condition of second-order pumping by establishing a mathematical model of the distributed fiber Raman amplifier, and designs three different KAN structure models for different use scenarios, which are respectively used for forward single gain point, gain spectrum prediction and reverse pump parameter prediction. By optimizing the hyperparameters and network structure, the trained KAN model can realize efficient and accurate forward and reverse fitting. The method can simplify the network structure, greatly reduce the demand for computing resources, improve the nonlinear fitting capability, quickly adapt to the needs of different scenarios, combine the cascade of forward and reverse models, and can observe the gain spectrum shape corresponding to the reverse predicted pump parameter in real time, thereby significantly improving the design and performance evaluation efficiency of the distributed fiber Raman amplifier, and having important practical application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical fiber Raman amplifier, and particularly relates to a forward and reverse problem fitting method for a distributed optical fiber Raman amplifier based on KAN. BACKGROUND

[0002] In optical fiber communication systems, especially long distance optical fiber communication systems, optical amplifiers are an indispensable optical compensation device, which can compensate for the loss of optical signals in the optical fiber transmission link. In the past few decades, due to the problem of pumping efficiency, erbium-doped fiber amplifiers (EDFA) are widely used in optical transmission systems. When the total power of the signal is only a few milliwatts, the erbium-doped fiber amplifier only needs a few tens of milliwatts of pump power to provide the required narrow-band gain. However, with the increase in the number of channels and the bit rate of channels in dense wavelength division multiplexing (DWDM) systems, the total power of the signal light entering the optical fiber also increases, which puts higher requirements on the pump power and gain bandwidth of the EDFA, and ordinary EDFA often cannot meet the optical transmission window outside the C band.

[0003] Distributed Raman amplifier (DRA) can utilize stimulated Raman scattering (SRS)

[0004] The transmission fiber is changed into its own distributed low-noise amplifier. Compared with EDFA, DRA allows the signal light entering the optical fiber to be at a low power level, thereby avoiding harmful nonlinear effects caused by high power; at the same time, DRA can perform distributed amplification on the signal light in the optical fiber for a long distance, so that the power fluctuation of the signal is in a small range, thereby reducing high noise caused by low power. In addition, the gain bandwidth and gain characteristics of DRA are only related to the pump wavelength and pump power used, which makes DRA can change the width of the gain spectrum and the corresponding gain level by changing the pump parameters. Therefore, DRA is gradually becoming an indispensable part of DWDM systems.

[0005] In the actual design and expected performance evaluation of DRA, two basic problems are often involved: how to obtain the corresponding gain spectrum from the current pump wavelength and power and how to obtain the corresponding pump wavelength and power from the current gain spectrum. After solving these two basic problems, the expected performance evaluation of the pump parameters of DRA can be further performed, and special-shaped gain spectrum can be obtained by fine control of the pump parameters.

[0006] The traditional method to solve the first problem generally needs to solve the Raman power coupling equations describing the power transfer in the fiber, which involves very complex nonlinear power transfer. Solving the equations requires a large amount of computing resources and time cost, especially when a large number of channels and a large number of pump lights are involved. Traditional numerical calculation methods such as average power method, Runge-Kutta method, finite difference method, etc. combined with shooting method will produce strong instability, which brings difficulties to the numerical solution of the equations.

[0007] The traditional method to solve the second problem is to use a global optimization algorithm, such as genetic algorithm, ant colony algorithm, particle swarm algorithm, etc. The current gain spectrum is set as the target value, starting from a set of initial pump parameter values, and after multiple iterations, the gain spectrum corresponding to the pump parameter value is approximated to the target value. When it converges to within a preset error, the pump parameters corresponding to the target value are obtained. This method needs to embed the solution of the Raman coupling equation, and has problems such as many iterations, long iteration time, and difficulty in converging to the global optimal solution.

[0008] With the development of artificial intelligence methods, some researches began to use the mapping function of neural network input to output to replace the numerical solution algorithm of Raman coupling equation and the group optimization algorithm of optimization problem. Through training the neural network, the bidirectional mapping relationship between the pump parameters and the gain spectrum can be obtained, so as to replace the traditional algorithm to obtain higher efficiency.

[0009] Even though neural networks provide a simple and efficient method for DRA design and performance evaluation, there are still some problems that are less concerned. For the research of applying neural networks to solve the forward coupling equations of DRA, generally, the mapping from pump parameters to the entire gain spectrum is directly performed. The ordinary neural network needs a large amount of calculation as support in this application, and the error performance is general. Moreover, in some practical scenarios, the gain performance in the entire gain spectrum range may not be concerned, but only one or several gain points. At this time, if the classical neural network is used to solve the problem, it will cause a large waste of computing resources, because the optimal neural network structure size for fitting a single gain point and the entire gain spectrum is similar, and separating a single gain point from the gain spectrum cannot effectively reduce the required operation amount of the trained network. In addition, in the reverse design problem of DRA, due to the complex and not obvious nonlinear relationship between the gain spectrum and the pump parameters, a large neural network structure is often needed to obtain a practical fitting effect, and the fitting effect is generally poor, with a large error between the predicted gain spectrum corresponding to the predicted pump parameters and the actual gain spectrum. In addition, in some cases, it is necessary to quickly obtain the actual gain spectrum corresponding to the predicted pump parameters. Therefore, how to obtain more accurate forward and reverse fitting under the premise of using less computing resources has become an important problem in DRA performance evaluation and system design. SUMMARY

[0010] In view of the above-mentioned defects in the prior art, the present application provides a more efficient and more accurate fitting method for forward gain point, gain spectrum, reverse pump wavelength and pump power of a distributed fiber Raman amplifier based on Kolmogorov-Arnold neural network (KAN). The method can obtain stronger nonlinear learning ability, better error performance and smaller computing resource requirement than the classical neural network on the same fitting problem, and can be flexibly adjusted for different specific actual problems to obtain the optimal network structure of the corresponding problem and further provide a KAN fitting method for the actual problem.

[0011] The present application is realized by the following technical solutions:

[0012] A fitting method for forward and reverse problems of a distributed fiber Raman amplifier based on KAN, specifically comprising the following steps:

[0013] Step A: setting a pump parameter range for stable solution, obtaining an ideal data set for KAN network training in the pump parameter range, specifically comprising:

[0014] Step A1: establishing a mathematical model of a distributed fiber Raman amplifier, and the system structure is a two-order pump source and a two-order amplification model jointly pumped by five first-order pump sources;

[0015] Step A2: determining suitable pump wavelength range and power range, obtaining uniformly distributed data points by uniformly sampling in the above range, and randomly combining the uniformly distributed data points of each pump parameter to obtain an ideal uniformly distributed pump parameter data set;

[0016] Step A3: substituting the pump parameters in the uniformly distributed pump parameter data set into the mathematical model of the distributed fiber Raman amplifier one by one to solve, obtaining the gain spectrum corresponding to the pump parameters, and further obtaining a complete ideal data set containing the pump parameters and the corresponding gain spectrum;

[0017] Step B: establishing three different KAN structure models for different use scenarios, which are forward fitting single gain point output model, forward fitting gain spectrum output model and reverse fitting pump parameter output model;

[0018] Step C: training the three different KAN models respectively by using the complete ideal data set obtained in step A3 to obtain the corresponding evaluation models for predicting different output conditions;

[0019] Step D: using the different KAN models trained in step C to realize the fitting of the forward and reverse problems of the distributed fiber Raman amplifier for different scenarios.

[0020] Further, in step A3, the mathematical model of the distributed fiber Raman amplifier with the second-order pumping structure established in step A1 is solved by using the adaptive step Runge-Kutta method combined with the Newton-Raphson method to obtain the gain spectrum corresponding to the pump parameters. In the solving process, the divergent or long-time non-convergent data points are removed, and the missing data points are reasonably supplemented to avoid excessive data loss, so as to obtain a complete ideal data set.

[0021] Further, the gain spectrum is obtained by solving the nonlinear power coupling differential equation of the mathematical model of the distributed fiber Raman amplifier, specifically as follows:

[0022]

[0023] In the formula, P i , v i and a i are the power, frequency and attenuation coefficient of the i-th wave; z is the distance from the origin of the optical fiber; A eff is the effective area of the optical fiber; G R (v j -v i ) is the Raman gain coefficient from the j-th wave to the i-th wave; the frequency ratio v i / v j represents the vibration loss; and the left side - and + respectively represent the backward propagating pump light and the forward propagating signal light.

[0024] Further, in step B, the KAN structure model is based on the Kolmogorov-Arnold representation method, wherein the forward fitting single gain point output model adopts a simplified structure, and the forward fitting gain spectrum output model and the reverse fitting pump parameter output model adopt an extended structure to enhance the nonlinear fitting capability.

[0025] Further, the Kolmogorov-Arnold representation method is specifically as follows:

[0026]

[0027] In the formula, f is an n-ary continuous function to be represented; x represents the vector form of the input variables of f; n represents the number of input variables of the function f; x p represents the p-th input variable; φ q,p represents an inner single-variable continuous function, which maps the p-th variable x p to a real number; Ф q represents an outer single-variable continuous function, which maps the sum of the inner functions to a real number; for a smooth f: [0, 1] n →R, there are φ q,p : [0, 1] → R and Φ q: R→R; (2n+1) is the minimum number of outer function items guaranteed by the theorem, ensuring that any n-dimensional continuous function can be represented; the Kolmogorov-Arnold representation method shows that a multi-dimensional continuous function on a bounded domain can be represented as a finite combination of one-dimensional functions of each variable.

[0028] Further, in step C, specifically includes the following content:

[0029] First, normalize the complete data set described in step A3, wherein the pump parameter part adopts column normalization to avoid excessive order of magnitude difference, and the gain spectrum part is uniformly normalized;

[0030] Then, the normalized data set is divided into training set, validation set and final test set in the ratio of 8:1:1, the training set is used for parameter training of the network, the validation set is used for preliminary evaluation of the performance of each network training, and the test set is used for evaluating the final error performance of the optimal network selected by the validation set;

[0031] Then, a network hyperparameter optimization mechanism is added to search for the optimal network structure of the two multi-output models;

[0032] Finally, the KAN network model is established according to the optimal network hyperparameters, and the network is trained using the training set. Since the edge weight function in the KAN training process is initialized using different seeds from a Gaussian distribution, the performance of the model after each training is not the same, so the final evaluation model is obtained by training ten times and selecting the optimal one from the validation set. The evaluation model is used to test the error performance of the test set, and finally the prediction output of different scenes is realized.

[0033] Further, in searching for the optimal network structure of the two multi-output models in the network hyperparameter optimization mechanism, the maximum number of searches is 100, and the search space of the hyperparameters is: the search range of the network layer number is 2-4; the neuron number set of each network layer is {1, 16, 32, 64, 128}; the search range of the learning rate is 10 -4 ~ 10 -2 ; the search range of the weight decay is 10 -5 ~ 10 -3 ; the search range of the exponential decay parameter of the learning rate is 0.7-0.95.

[0034] Further, in step C, the edge weight function adopts B-spline function; the optimization algorithm adopts Adam and adds learning rate decay; and the loss function is MSE.

[0035] Further, in step D, using the three different optimal models trained in step C, the pump parameters and gain spectrum are input respectively to complete the fitting of the forward and reverse problems of the distributed fiber Raman amplifier in different scenarios.

[0036] Compared with the prior art, the present application has the following advantages:

[0037] The KAN-based fitting method for the forward and reverse problems of the distributed fiber Raman amplifier provided by the present application not only simplifies the network structure in the multi-output prediction scenario, but also greatly reduces the relative computing resource requirement in the simple output prediction scenario; it can flexibly establish different network structures for different prediction scenarios, and has stronger nonlinear fitting capability than the traditional neural network method, thereby obtaining better error performance. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the specific embodiments or the prior art, the drawings needed in the specific embodiments or the prior art description will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual proportions.

[0039] Figure 1 The flowchart of the KAN-based fitting method for the forward and reverse problems of the distributed fiber Raman amplifier provided by the present application embodiment;

[0040] Figure 2 The structure diagram of the distributed fiber Raman amplifier provided by the present application embodiment;

[0041] Figure 3 The ideal data set pump parameter data point range distribution diagram provided by the present application embodiment;

[0042] Figure 4 The KAN general model structure diagram provided by the present application embodiment;

[0043] Figure 5 The performance comparison diagram of the KAN fitting method and the classic MLP neural network at a single gain point output provided by the present application embodiment;

[0044] Wherein, (a) is the training loss change diagram of MLP and KAN over time, (b) is the comparison diagram of the predicted value and the true value R 2 of the single output KAN and the single output MLP in the test set at each gain point, and (c) is the comparison diagram of the predicted value and the true value MSE of the single output KAN and the single output MLP in the test set at each gain point;

[0045] Figure 6The KAN fitting method provided in this embodiment of the invention and the gain spectrum fitting effect and error diagram of the classic MLP neural network when the gain spectrum is output;

[0046] Among them, (a) is the KAN fitting result, and (b) is the MLP fitting result;

[0047] Figure 7 The following is a comparison of the gain spectrum corresponding to the pump parameters and the target gain spectrum of the KAN fitting method provided in this embodiment of the invention with those of the classic MLP neural network when the pump parameters are output in reverse.

[0048] Among them, (a) is the KAN prediction result, (b) is the MLP prediction result, and (c) is the KAN prediction result when the target gain spectrum is a flat gain spectrum.

[0049] Figure 8 Figure 1 shows the fitting results of the KAN fitting method provided in this embodiment of the invention for the forward and reverse problems of distributed fiber Raman amplifiers in three scenarios. Detailed Implementation

[0050] To clearly and completely describe the technical solution and its specific working process of the present invention, the specific embodiments of the present invention are as follows, in conjunction with the accompanying drawings:

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides a fitting method for the forward and inverse problems of a distributed fiber Raman amplifier based on KAN, specifically including the following steps:

[0053] Step A: Define a range of pump parameters that can be stably solved by most methods, and obtain an ideal dataset for training the KAN network within this range. Specifically, this includes:

[0054] Step A1: Establish a mathematical model of a distributed fiber Raman amplifier. The system structure is a second-order amplification model pumped by a second-order pump source and five first-order pump sources.

[0055] Step A2: Determine a reasonable range of pump light wavelength and power, perform uniform sampling within the range to obtain uniformly distributed data points, and randomly combine the data points to obtain an ideal uniformly distributed pump parameter dataset.

[0056] Step A3: Substitute the pump parameters in the dataset one by one into the mathematical model of the distributed fiber Raman amplifier to solve for the gain spectrum corresponding to the pump parameters, and then obtain a complete ideal dataset containing the pump parameters and their corresponding gain spectra.

[0057] Step B: Three different KAN structure models are established for different use scenarios, which are forward fitting single gain point output model, forward fitting gain spectrum output model, and reverse fitting pump parameter output model.

[0058] Step C: The complete ideal data set obtained in step A3 is used to train different KAN models to obtain corresponding evaluation models for predicting different output conditions.

[0059] Step D: The different KAN models trained in step C are used to realize the fitting of forward and reverse problems of distributed fiber Raman amplifier for different scenarios.

[0060] For different use scenarios, users can call different KAN models to realize gain point prediction, gain spectrum prediction, and reverse pump parameter prediction for special-shaped gain spectrum. For reverse pump parameter prediction, the reverse model can be cascaded with the forward model by combining the forward gain spectrum prediction to realize real-time observation of the gain spectrum shape corresponding to the reverse predicted pump parameter, thereby realizing more precise further regulation.

[0061] In this embodiment, step A1 is specifically as follows:

[0062] To avoid the RIN noise generated by coupling the rapid fluctuation of pump into the signal light, the Raman pumping method used in this embodiment is reverse pumping, as shown in Figure 2 wherein m-way pump light is coupled into the optical fiber through a wavelength division multiplexer and transmitted simultaneously with n-way signal light, and the transmission direction of the pump light is opposite to that of the signal light. To obtain the long-distance gain length of the distributed fiber Raman amplifier, 80km G.652 optical fiber is used as the gain medium to realize the amplification of C+L band signal light.

[0063] This embodiment establishes a second-order fiber Raman amplifier system model, the pump end is composed of 1-way second-order pump light and 5-way first-order pump light; the signal end contains 87-way signal light, i.e. m=6, n=87. Figure 2 wherein an isolator is connected after the signal source to avoid damage to the signal source by reflected light, the optical fiber is used as a transmission gain medium, and the spectrometer is used to calculate the gain spectrum.

[0064] Distributed fiber Raman amplifier is based on the stimulated Raman scattering (SRS) effect to realize the power amplification of signal light by pump light. The amplification process is to use the fiber itself as a gain medium, through the interaction of high-power pump light and molecular vibration in the fiber, to realize the amplification of signal light. By controlling the wavelength of signal light and pump light during transmission, the signal light can fully absorb the energy of pump light to realize its own amplification within a certain frequency difference range. When mainly considering the gain of the amplifier, the mathematical model of the distributed Raman fiber amplifier can be simplified as a set of nonlinear Raman coupled equations as shown in equation (1). The loss of signal light and pump light during transmission is considered, and the stimulated Raman scattering effect between different wavelengths (signal light and signal light, signal light and pump light, and pump light and pump light) is also considered.

[0065]

[0066] In the formula, P i , v i and α i are the power, frequency and attenuation coefficient of the i-th wave respectively; z is the distance from the origin of the optical fiber; A eff is the effective area of the optical fiber; Γ is the polarization factor, whose value is between 1 and 2; g R (v j -v i ) is the Raman gain coefficient of the j-th wave to the i-th wave; the frequency ratio v i / v j represents the vibration loss; the left side of-and + respectively represents backward propagating pump light and forward propagating signal light.

[0067] For the distributed fiber Raman amplifier, the definition of on-off gain is generally used to evaluate its gain performance. The on-off gain is defined as equation (2):

[0068]

[0069] In equation (2), P pumpon and P pumpoff are the optical power of signal light at the output end of the optical fiber when the pump is on and the optical power of signal light at the output end of the optical fiber when the pump is off respectively.

[0070] In this embodiment, step A2 is specifically as follows:

[0071] The formula (1) gives the power transfer relationship between different wavelengths of light in the optical fiber. According to the set of equations and in combination with the required gain bandwidth, the range of pump parameters (including wavelength and power) corresponding to the gain spectrum that meets most requirements can be roughly determined. Then, each pump parameter in the pump parameter range is uniformly sampled to obtain random data in each pump parameter sampling range. Finally, each data of the pump parameters is randomly combined into a pump parameter group, that is, the complete ideal random data set of the pump parameters is obtained. The specific signal light gain range and pump parameter sampling range are set as follows: the gain wavelength range of the signal light is 1523.6 nm-1626.8 nm in the C+L band, the power is 0.1 mW, the wavelength interval is 1.2 nm, and there are 87 channels in total; the pump light parameter range is λ1: 1350 nm-1370 nm, P1: 0.70 W-1.40 W, λ2: 1420 nm-1436 nm, P2: 0.15 W-0.65 W, λ3: 1434 nm-1449 nm, P3: 0.10 W-0.40 W, λ4: 1447 nm-1462 nm, P4: 0.10 W-0.30 W, λ5: 1460 nm-1476 nm, P5: 0.08 W-0.15 W, λ6: 1500 nm-1510 nm, and P6: 0.015 W-0.095 W. The data points in the ideal data set should be uniformly distributed in the sampling range. The frequency distribution of the sampling data points in the above range is shown in FIG. 6, and it can be seen that the obtained data set is approximately ideal. Figure 3

[0072] In this embodiment, step A3 is specifically as follows:

[0073] To establish the forward and reverse mapping relationship of the pump parameters to the gain spectrum, the gain spectrum data corresponding to the pump parameters in the data set also needs to be improved, so as to establish a complete database. Generally, there is no analytical solution to the Raman coupling equation, so numerical solution algorithms of differential equations need to be used for calculation, such as finite difference method, Runge-Kutta method, average power method, etc. When the pump mode is backward pumping, two-point boundary value problems are introduced for the solution of the differential equation, and a suitable shooting method needs to be used for the solution. The boundary value problem also introduces great solution instability related to the initial value. In this embodiment, the Runge-Kutta method with adaptive step size is used in combination with the Newton-Raphson method to solve the Raman coupling equation of the backward pumping. Each group of pump data in the obtained pump parameter data set is solved group by group to obtain the corresponding gain spectrum data, which is added to the data set. When the solution process encounters pump data that is difficult to converge or does not converge, the pump data is removed from the data set, and a new group of data is randomly obtained in the established pump parameter value range to ensure that the number of data in the overall data set is maintained at the required level.

[0074] In this embodiment, step B is specifically as follows:​

[0075] Generally, the forward gain solution and reverse design of distributed fiber Raman amplifier need to use traditional algorithms combined with a large number of solutions of Raman coupling equations. As mentioned earlier, there is no analytical solution to the Raman coupling equation, and the numerical algorithm used in reverse pumping is both time-consuming and unstable. Therefore, the present embodiment aims to replace the traditional numerical algorithm with a general KAN approximation fitting method, and can provide a more concise network structure and higher fitting accuracy compared to MLP.

[0076] The general structure of KAN is shown in Figure 4 Unlike MLP, the learnable weights of KAN are not at the neurons, but in the edges connecting the neurons, and the edge weights of KAN are composed of a learnable nonlinear function, rather than a constant. These characteristics greatly improve the learning ability of KAN for nonlinear relationships and greatly simplify the network structure. KANs established under different scenarios need to have a reasonable network structure design. A reasonable structure can make the network better adapt to the needs of specific tasks, improve the generalization ability of the model, reduce the computational cost, and optimize resource utilization. The Kolmogorov-Arno representation method gives a basic KAN structure in mathematics. For a smooth f: [0, 1] n →R, there is φ q,p : [0, 1]→R, Φ q : R→R, as shown in equation (3):

[0077]

[0078] But this structure only describes the case where the output of the multi-element function is a single output. For multi-dimensional output, there is no mathematical description of how to construct a KAN structure that can satisfy the fitting relationship, so a hyperparameter search optimization method is needed to find the optimal network structure.

[0079] In the present embodiment, the basic KAN network structure includes: input nodes, intermediate nodes, output nodes, and a learnable nonlinear function layer between each two layers of nodes. The input and output content of KAN can be divided into three cases according to the use scenario: K = [λ1, …, λ m , P1, …, P m ] is the input of KAN, and G = G n is the output of KAN, at this time the structure of KAN is given by the Kolmogorov-Arno representation method [2m, 4m+1, 1]; K = [λ1, …, λ m , P1, …, P m ] is the input of KAN, and G = [G1, G2, G3, …, G n] is the output of KAN, at this time the structure of KAN adopts the method of hyperparameter search to optimize; G = [G1, G2, G3, …, G n ] is the input of KAN, K = [λ1, …, λ m , P1, …, P m ] is the output of KAN, at this time the structure of KAN adopts the method of hyperparameter search to optimize.

[0080] In the embodiment, step C is specifically as follows:

[0081] The complete data set described in step A3 is normalized, wherein the pump parameter part adopts column normalization to avoid excessive order of magnitude difference, and the gain spectrum part is uniformly normalized; then, the normalized data set is divided into a training set, a validation set and a final test set in a ratio of 8:1:1, the training set is used for parameter training of the network, the validation set is used for preliminary evaluation of the performance of the network after each training is completed, and the test set is used for evaluating the final error performance of the optimal network selected by the validation set.

[0082] After the data set is normalized, a hyperparameter optimization mechanism can be added to search and optimize the hyperparameters of the KAN network model that needs to be optimized. The process of searching and optimizing the hyperparameters of KAN is specifically as follows:

[0083] The structures that need to be searched for hyperparameters include two kinds, i.e., the input is the pump parameter and the output is the gain spectrum, and the input is the gain spectrum and the output is the pump parameter. Furthermore, in the present application, the number of pump parameters is 12, and the gain spectrum is composed of 87 gain points. The complete data set obtained in step A3 is used to search for hyperparameters under two KAN structures, and the optimization target is to obtain the hyperparameter combination that makes the training loss of the network lowest. The hyperparameter search algorithm adopts Optuna, the maximum number of searches is 100 times, the learnable nonlinear function is a B-spline function, the loss function is MSE, the optimization algorithm is Adam, and the search space of the hyperparameters is: the search range of the network layer number is 2-4; the neuron number set of each network layer is {1, 16, 32, 64, 128}; the search range of the learning rate is 10 -4 -10 -2 ; the search range of the weight decay is 10 -5 -10 -3 ; and the search range of the exponential decay parameter of the learning rate is 0.7-0.95.

[0084] After 100 times of hyperparameter search are respectively performed, the final determined KAN network hyperparameters with the input of the pump parameter and the output of the gain spectrum are: the number of intermediate network layers is 3, the corresponding node numbers are {128, 128, 128}, the learning rate is 5.1038785685655515x10-3 , the exponential decay coefficient of the learning rate is 0.9022602567081367; the KAN network hyperparameters for inputting the gain spectrum and outputting the pump parameters are: the number of intermediate network layers is 3, the corresponding number of nodes is {128, 128, 32}, the learning rate is 9.976739696472904e-05, the weight decay is 1.2191574474336939e-04. -5 , the exponential decay coefficient of the learning rate is 0.9022602567081367; the KAN network hyperparameters for inputting the gain spectrum and outputting the pump parameters are: the number of intermediate network layers is 3, the corresponding number of nodes is {128, 128, 32}, the learning rate is 9.976739696472904e-05, the weight decay is 1.2191574474336939e-04. -3 , the exponential decay coefficient of the learning rate is 0.9022602567081367; the KAN network hyperparameters for inputting the gain spectrum and outputting the pump parameters are: the number of intermediate network layers is 3, the corresponding number of nodes is {128, 128, 32}, the learning rate is 9.976739696472904e-05, the weight decay is 1.2191574474336939e-04. -5 , the exponential decay coefficient of the learning rate is 0.9022602567081367; the KAN network hyperparameters for inputting the gain spectrum and outputting the pump parameters are: the number of intermediate network layers is 3, the corresponding number of nodes is {128, 128, 32}, the learning rate is 9.976739696472904e-05, the weight decay is 1.2191574474336939e-04.

[0085] In order to compare the network structure size difference required by KAN and MLP when completing the same fitting task, the present application also performs hyperparameter search on MLP with the same function, and finally determines that the MLP network hyperparameters for inputting pump parameters and outputting a single gain point are: the number of hidden layers is 2, the number of neurons in each hidden layer is 674, and the learning rate is 7.590357579627308e-04. -4 , the dropout rate is 0.259085135682076; the MLP network hyperparameters for inputting pump parameters and outputting gain spectrum are: the number of hidden layers is 2, the number of neurons in each hidden layer is 990, and the learning rate is 1.070073858542273e-04. -3 , the dropout rate is 0.1793240679407619; the MLP network hyperparameters for inputting gain spectrum and outputting pump parameters are: the number of hidden layers is 5, the number of neurons in each hidden layer is 972, and the learning rate is 1.123409544674642e-04. -4 , the dropout rate is 0.2352016576553314.

[0086] It can be found through comparison that for MLP, the number of neurons of the network does not differ much when the output is a single gain point and gain spectrum, which makes the two functions of MLP differ by 87 times in output quantity, but the computing resources consumed for training the network do not differ much, but KAN greatly reduces the number of network layers and nodes when the output is a single gain point, greatly saving computing resources. The number of nodes required by KAN and MLP with the same function also differs greatly, and MLP often needs a large number of neurons to complete strong nonlinear fitting, especially when the output is pump parameters, while KAN greatly reduces the number of nodes required due to the nonlinearity of the weight.

[0087] According to the hyperparameters obtained by the above process, a corresponding KAN network is established according to actual scene requirements, that is, the corresponding fitting task can be completed, and a prediction result is given. In order to evaluate and compare the performance of the KAN network, the present application establishes a corresponding KAN and MLP network according to the hyperparameter optimization results obtained by the above process for three different scenes.

[0088] When training several KAN and MLP networks using the training set, due to the randomness of KAN and MLP in initial weight assignment, the strategy of training 10 times and taking the optimal model is adopted for each network training. After each training is completed, the performance of the current model is evaluated using the validation set data, and the best model is selected. After obtaining the optimal model, the statistical performance indicators of the model are evaluated using the test set, including MSE and R 2 value, wherein MSE represents the mean square error between the predicted value and the actual value, and when the MSE value is closer to 0, the error is smaller, and R 2 value represents the closeness between the predicted value and the actual value, and when the R 2 value is closer to 1, the prediction correlation of the neural network model is higher. In addition, for a multi-output network, a set of pump parameter data is randomly generated within the value range of the pump parameter, and the corresponding gain spectrum data is calculated to evaluate the fitting ability of the multi-output network for random data within the training range.

[0089] The decline process of the training loss of the single gain point output KAN network and the MLP network with time is shown in Figure 5 (a), the KAN with simpler structure declines to a lower training loss value than the MLP in a shorter time, and maintains this trend throughout the time axis. Taking the gain point corresponding to the 1523.6 nm wavelength signal light as an example, the R 2 value of the KAN on the test set after training is 0.9988, and the MSE value is 0.0084; the R 2 value of the MLP on the test set is 0.9970, and the MSE value is 0.0217. The R 2 performance of KAN and MLP at each gain point is shown in Figure 5 (b), and the MSE performance is shown in Figure 5 (c), KAN is superior to MLP at most gain points and overall, and only performs worse than MLP at one gain point, but KAN always has the advantages of simpler network structure and faster training loss decline.

[0090] After the training of the gain spectrum output network is completed, the R 2 value of KAN on the test set is 0.9994, and the MSE value is 0.0081; the R 2The value is 0.9963, and the MSE value is 0.0535. In this scenario, the error performance of KAN is much better than that of MLP. It is worth noting that in the KAN hyperparameter optimization in this scenario, the optimized KAN network structure is the maximum value in the optimization parameter range, which means that the error performance may be further improved by further increasing the KAN network structure. However, based on the error performance obtained so far, the increase in computing resources brought by further increasing the network structure is unnecessary. In order to further verify the fitting performance of the two networks on random data, a set of pump parameters are randomly generated within the range of pump parameter values: pump wavelength is 1366.29 nm, 1422.03 nm, 1443.49 nm, 1451.18 nm, 1475.32 nm, 1501.58 nm, and pump power is 1.370 W, 0.550 W, 0.227 W, 0.258 W, 0.126 W, 0.083 W. The comparison chart and error chart between the fitting results given by the KAN network and the true value are as shown in Figure 6 (a), and the comparison chart and error chart between the fitting results given by the MLP network and the true value are as shown in Figure 6 (b). The maximum error between the predicted value given by KAN and the true value is 0.4936 dB, and the average error is 0.0655 dB; the maximum error between the predicted value given by MLP and the true value is 1.1774 dB, and the average error is 0.1855 dB. The above results prove the superiority of the fitting effect of KAN network in this scenario.

[0091] After the network training of the pump parameter output is completed, the R 2 value of KAN on the test set is 0.8373, and the MSE value is 0.7822; the R 2 value of MLP on the test set is 0.7961, and the MSE value is 0.9272. In this application scenario, the error performance of KAN is still better than that of MLP, although the MLP network structure is very large at this time. However, sometimes the error performance of evaluating the pump parameters cannot represent the error performance between the gain spectrum corresponding to the predicted pump parameters and the true gain spectrum. Therefore, the pump parameter and gain spectrum data randomly obtained in the gain spectrum output scenario are still used to evaluate the error between the gain spectrum corresponding to the predicted pump parameters and the true gain spectrum, and the results are as shown in Figure 7 (a) and Figure 7(b) shown. The maximum error between the gain spectrum corresponding to the pump parameters given by KAN and the real gain spectrum is 0.8612 dB, and the average error is 0.2852 dB; the maximum error between the gain spectrum corresponding to the pump parameters given by MLP and the real gain spectrum is 0.9220 dB, and the average error is 0.3350 dB. It can be seen that due to the particularity of the reverse pump parameter prediction, the performance of the results fitted by the two networks has decreased, but KAN still slightly leads MLP in performance due to its strong nonlinear learning ability with the learnable nonlinear weight function. Finally, aiming at the demand for special gain spectrum in many cases, the effect of KAN network in the reverse design of flat gain spectrum is tested, and when the gain level of the required flat gain spectrum is 27.5 dB, the pump parameters given by KAN are as follows: the wavelengths are 1357.66 nm, 1422.94 nm, 1437.65 nm, 1456.57 nm, 1472.91 nm, and 1508.27 nm, and the powers are 1.439 W, 0.555 W, 0.205 W, 0.132 W, 0.094 W, and 0.018 W. The gain spectrum shape corresponding to the pump parameters is as shown in Figure 7 (c) shown, the average gain is 27.5071 dB, the gain ripple is 4.0648 dB, and the minimum gain value reaches 25.8378 dB, which is sufficient to meet the general flat high gain demand.

[0092] In the present embodiment, step D is specifically as follows:

[0093] After obtaining the optimal model parameters of the three different KAN structures in step C, the fitting of the forward problem and the reverse problem of the distributed fiber Raman amplifier can be realized for unobserved data in actual situations. The present application gives the corresponding KAN forward and reverse problem fitting results under a group of random pump parameters in the simulation of actual situations, as shown in Figure 8The pump parameters are as follows: wavelength is 1366.29 nm, 1434.49 nm, 1435.90 nm, 1460.70 nm, 1470.12 nm, 1500.98 nm, and power is 0.895 W, 0.423 W, 0.387 W, 0.293 W, 0.091 W, 0.093 W. Then, the maximum error and average error between the fitting result and the true result are further calculated: in the fitting result of all gain points of the single-output KAN structure, the maximum error is 0.4354 dB, and the average error is 0.1302 dB; in the gain spectrum fitting result of the gain spectrum output KAN structure, the maximum error is 0.1302 dB, and the average error is 0.0426 dB; the pump parameters output by the pump parameter output KAN structure are as follows: wavelength is 1365.34 nm, 1434.73 nm, 1435.59 nm, 1460.55 nm, 1469.87 nm, 1500.92 nm, and power is 1.132 W, 0.431 W, 0.264 W, 0.249 W, 0.082 W, 0.096 W, and the maximum error between the gain spectrum corresponding to the pump parameters and the actual gain spectrum is 0.4966 dB, and the average error is 0.1687 dB.

[0094] The preferred embodiments of the present application are described in detail above with reference to the drawings, but the present application is not limited to the specific details in the above-described embodiments. Within the technical concept of the present application, various simple modifications can be made to the technical solution of the present application, and these simple modifications all belong to the protection scope of the present application.

[0095] In addition, it should be noted that each specific technical feature described in the above-described specific embodiments can be combined in any appropriate manner without contradiction, and in order to avoid unnecessary repetition, the present application will not further describe various possible combinations.

[0096] Furthermore, various different embodiments of the present application can also be combined in any appropriate manner, as long as it does not deviate from the idea of the present application, and it should be considered as disclosed content of the present application.

Claims

1. A fitting method for the forward and backward problems of distributed fiber Raman amplifier based on KAN, characterized in that, Specifically comprising the following steps: Step A: setting the majority stable solution pump parameter range, obtaining the ideal data set of KAN network training in the pump parameter range, specifically comprising: Step A1: establishing a mathematical model of distributed fiber Raman amplifier, the system structure is a two-order pump source and five one-order pump sources combined to pump a two-order amplification model; Step A2: determining the suitable pump wavelength range and power range, uniformly sampling in the above range to obtain uniformly distributed data points, and randomly combining the uniformly distributed data points of each pump parameter to obtain an ideal uniformly distributed pump parameter data set; Step A3: substituting the pump parameters in the uniformly distributed pump parameter data set into the mathematical model of the distributed fiber Raman amplifier one by one to solve, obtaining the gain spectrum corresponding to the pump parameters, and further obtaining a complete ideal data set containing the pump parameters and the corresponding gain spectrum; Step B: for different use scenarios, three different KAN structure models are established, which are forward fitting single gain point output model, forward fitting gain spectrum output model and reverse fitting pump parameter output model; Step C: using the complete ideal data set obtained in step A3 to train the three different KAN models respectively to obtain the corresponding evaluation models for predicting different output conditions; Step D: using the different KAN models trained in step C, the forward and reverse problems of the distributed fiber Raman amplifier are fitted for different scenarios.

2. The KAN-based distributed fiber Raman amplifier forward and backward problem fitting method of claim 1, wherein, In step A3, the mathematical model of the distributed fiber Raman amplifier with two-order pump structure established in step A1 is solved by using adaptive step Runge-Kutta method combined with Newton-Raphson method to obtain the gain spectrum corresponding to the pump parameters. In the solving process, the divergent or long-time non-convergent data points are removed, and the missing data points are reasonably supplemented to avoid excessive data loss, and a complete ideal data set is obtained.

3. A KAN-based distributed fiber Raman amplifier forward and backward problem fitting method according to claim 2, characterized in that, The gain spectrum is obtained by solving the nonlinear power coupling differential equation of the mathematical model of the distributed fiber Raman amplifier, specifically as follows: In the formula, P i v i and α i These represent the power, frequency, and attenuation coefficient of the i-th wave, respectively; z is the distance from the origin of the optical fiber; A eff Γ is the effective area of ​​the optical fiber; Γ is the polarization factor, whose value is between 1 and 2; g R (v j -v i ) is the Raman gain coefficient from wave j to wave i; frequency ratio v i / v j The symbol represents vibration loss; the "-" and "+" on the left represent the pump light propagating backward and the signal light propagating forward, respectively.

4. The KAN-based distributed fiber Raman amplifier forward and backward problem fitting method of claim 1, wherein, In step B, the KAN structure model is based on Kolmogorov-Arnold representation method, wherein the forward fitting single gain point output model adopts a simplified structure, and the forward fitting gain spectrum output model and the reverse fitting pump parameter output model adopt an extended structure to enhance the nonlinear fitting capability.

5. A KAN-based distributed fiber Raman amplifier forward and backward problem fitting method according to claim 4, characterized in that, The Kolmogorov-Arnold representation method is as follows: In the formula, f is an n-ary continuous function to be represented; x represents a vector form of input variables of f; n represents the number of input variables of function f; x p represents the pth input variable; φ q,p denotes an inner single variable continuous function mapping the pth variable x p to a real number; Ф q denotes an outer single variable continuous function mapping the sum of the inner functions to a real number; for smooth f: [0, 1] n → R, there exists φ q,p : [0, 1]→ R, Φ q : R→ R; (2n+1) is the minimum number of terms guaranteed by the theorem for the outer function to ensure that any n-ary continuous function is represented; the Kolmogorov-Arnoed representation states that a multi-variable continuous function on a bounded domain can be represented as a finite combination of one-variable functions for each variable.

6. The KAN-based distributed fiber Raman amplifier forward and backward problem fitting method of claim 1, wherein, In step C, specifically comprising the following contents: Firstly, the complete ideal data set in step A3 is normalized, wherein the pump parameter part is normalized by column to avoid large order difference, and the gain spectrum part is uniformly normalized; Then, the normalized data set is divided into three parts of training set, validation set and final test set according to the ratio of 8:1:1, the training set is used for parameter training of the network, the validation set is used for preliminary evaluation of the performance of each network training, and the test set is used for evaluating the final error performance of the optimal network selected by the validation set; Then, a network hyperparameter optimization mechanism is added to search for the optimal network structure of the two kinds of multi-output models; Finally, the KAN network model is established according to the optimal network hyperparameters, and the network is trained using the training set. Since the edge weight function in the KAN training process is initialized with different seeds from the Gaussian distribution, the performance of the model after each training is not the same. Therefore, the final evaluation model is obtained by training ten times and taking the optimal one from the validation set. The error performance of the test set is tested using the evaluation model, and the prediction output of different scenarios is finally realized.

7. The fitting method of a KAN-based distributed fiber Raman amplifier forward and backward problem according to claim 6, characterized in that, The network hyperparameter optimization mechanism is added, the maximum search number is 100 times in searching the optimal network structure of the two multi-output models, the search space of the hyperparameters is that the search range of the network layers is 2-4, the neuron number set of each network layer is {1, 16, 32, 64, 128}, the search range of the learning rate is 10 -4 -10 -2 , the search range of the weight decay is 10 -5 -10 -3 , and the search range of the exponential decay parameter of the learning rate is 0.7-0.

95.

8. The KAN-based distributed fiber Raman amplifier forward and backward problem fitting method of claim 1, wherein, In step C, the edge weight function uses B-spline function; the optimization algorithm uses Adam with learning rate decay; and the loss function is MSE.

9. The KAN-based distributed fiber Raman amplifier forward and backward problem fitting method of claim 1, wherein, In step D, three different optimal models trained in step C are used to input the pump parameters and gain spectrum, respectively, to complete the fitting of the forward and reverse problems of the distributed fiber Raman amplifier in different scenarios.

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