Optical waveguide parameter optimization method and system based on Transform model and improved NSGA-II algorithm

Abstract

The invention relates to the technical field of optical waveguide parameter optimization, and particularly discloses an optical waveguide parameter optimization method and system based on a Transform model and an improved NSGA-II algorithm, and the method comprises the following steps: S1, preprocessing an optical waveguide structure parameter, inputting the preprocessed optical waveguide structure parameter into the Transform model, carrying out the coding and feature extraction, outputting a performance prediction value, carrying out the physical constraint cutting, and carrying out the optimization of the performance prediction value; the method is used as a basis for evaluating the advantages and disadvantages of individuals by the improved NSGA-II algorithm; s2, randomly generating an initial optical waveguide structure parameter population within a preset boundary constraint, inputting the initial optical waveguide structure parameter population into an improved NSGA-II algorithm, selecting and driving population evolution, and generating a current Pareto optimal solution set; s3, dynamically combining the historical Pareto frontier solution set and the current candidate solution set in each round of iteration, and updating the global optimal solution set through non-dominated sorting; s4, repeating the steps S1 to S3 until a preset number of iterations or convergence conditions are reached, and outputting a final Pareto optimal solution set; according to the method, the precision optimization of the optical waveguide parameters is realized by combining the Transform model and the improved NSGA-II multi-objective optimization algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical waveguide parameter optimization, and more particularly to an optical waveguide parameter optimization method and system based on a Transformer model and an improved NSGA-II algorithm. BACKGROUND

[0002] With the advent of the mobile internet era, the network traffic of communication systems grows exponentially, and optical interconnection technology emerges as the times require. In optical internet, signal amplification is crucial, and for this reason, researchers at home and abroad have successfully developed a new type of optical amplifier, namely, an erbium-doped optical waveguide amplifier.

[0003] However, in the development and application of EDWA optical waveguide parameter optimization algorithms, there are still some significant limitations. First, the optimization target is too single. Most existing algorithms only focus on gain equalization and gain improvement. This narrow optimization perspective leads to the inability to comprehensively improve the overall performance of the optical waveguide, and easily overlooks the influence of other key parameters (such as noise figure, bandwidth, etc.) on the actual working effect, making it difficult for the optimized device to achieve the best performance in actual application.

[0004] Second, the consideration of crosstalk is insufficient. The algorithm does not fully consider the influence of effective refractive index difference on solving the crosstalk problem during design, resulting in a lack of effective means for dealing with optical waveguide crosstalk and an inability to fundamentally reduce the interference of crosstalk on signal transmission quality, thereby affecting the stability and reliability of the entire communication system.

[0005] In addition, the algorithm itself also has the challenges of high computational complexity, difficult parameter tuning, and large memory consumption. High computational complexity means that powerful hardware support is needed, which not only increases cost and energy consumption, but also limits its application scenarios. At the same time, improper parameter tuning can easily lead to model overfitting or underfitting, making the algorithm less robust, and the accuracy and reliability of the optimization results are difficult to guarantee when facing different optical waveguide structures and working conditions. The huge memory consumption also puts higher requirements on the storage capacity of the device, further limiting the deployment and application of the algorithm in resource-constrained environments. SUMMARY

[0006] The purpose of the present application is to provide an optical waveguide parameter optimization method and system based on a Transformer model and an improved NSGA-II algorithm, which realizes efficient and high-precision optimization of optical waveguide structure parameters by combining a Transformer model and an improved NSGA-II multi-objective optimization algorithm.

[0007] To achieve the above purpose, the present application provides the following technical solutions: An optical waveguide parameter optimization method based on a Transformer model and an improved NSGA-II algorithm, comprising the following steps: S1, input the pre-processed optical waveguide structure parameters into the Transformer model, perform non-linear encoding and feature extraction, output performance prediction values, and perform physical constraint pruning as the basis for evaluating the performance of individuals in the improved NSGA-II algorithm; S2, randomly generate an initial population of optical waveguide structure parameters within the preset boundary constraints, input them into the improved NSGA-II algorithm, generate new individuals through crossover and mutation operations, combine non-dominated sorting, crowding degree calculation, and binary tournament selection to drive population evolution, and generate the current Pareto optimal solution set; S3, dynamically merge the historical Pareto front solution set and the current candidate solution set in each iteration, and update the global optimal solution set through non-dominated sorting; the double standards include: single-objective optimization and balanced solution; S4, repeat S1-S3 until the preset number of iterations or convergence conditions are reached, output the final Pareto optimal solution set to achieve optical waveguide parameter optimization.

[0008] Further, in S1, the optical waveguide structure parameters include: outer layer width, inner layer width, outer layer concentration, and inner layer concentration.

[0009] Further, the workflow of the physical constraint Transformer model includes: perform StandardScaler standardization processing on the input optical waveguide parameters; extract the correlation between parameters through a multi-head self-attention mechanism and output performance prediction values.

[0010] Further, in S2, the improved NSGA-II algorithm includes: introducing a LayerNorm layer before the fully connected layer; using a GELU activation function instead of ReLU; and designing a stepwise dimension reduction structure at the output end; The stepwise dimension reduction structure includes: first-level dimension reduction: compressing high-dimensional features output by the Transformer to 16-dimensional hidden layers; second-level dimension reduction: mapping 16-dimensional features to a 3-dimensional target space.

[0011] Further, in S3, the single-objective optimization includes: selecting extreme solutions in the directions of minimizing gain difference, maximizing average gain, and maximizing effective refractive index difference, respectively; The balanced solution includes: based on the principle of minimum Euclidean distance ideal point, selecting a scheme that achieves the best trade-off between minimizing gain difference, maximizing average gain, and maximizing effective refractive index difference from the Pareto front.

[0012] Further, in S3, the dynamic merging of the historical Pareto front solution set and the current optical waveguide parameter population in each iteration, and updating the global optimal solution set through non-dominated sorting includes: In each iteration, the historical Pareto front solution set is merged with the current optical waveguide parameter population; The global Pareto front solution set is updated by non-dominated sorting, and the non-dominated solutions of the historical optimal solution and the current population are integrated; Representative solutions are selected from the updated archive solution set to guide the initialization of the next generation population or as final design scheme candidate solutions.

[0013] Further, the training strategy of the physical constraint Transformer model comprises: 5-fold K-fold cross-validation combined with early stopping mechanism is adopted; The optimizer adopts AdamW, combined with cosine annealing learning rate scheduling.

[0014] The application also provides a system for performing the optical waveguide parameter optimization method based on the Transformer model and the improved NSGA-II algorithm, comprising: The Transformer model is used to output the performance prediction value after nonlinear encoding and feature extraction of the preprocessed optical waveguide structure parameters, and to perform physical constraint pruning as the basis for evaluating the pros and cons of individuals by the improved NSGA-II algorithm; The improved NSGA-II module is used to input the initial optical waveguide structure parameter population randomly generated within the preset boundary constraint into the improved NSGA-II algorithm, generate new individuals through cross and mutation operations, combine non-dominated sorting, crowding degree calculation and binary tournament selection to drive population evolution, and generate the current Pareto optimal solution set; The multi-objective collaborative optimization module dynamically merges the historical Pareto front solution set and the current candidate solution set in each iteration, and updates the global optimal solution set by non-dominated sorting; wherein the double standards include single-objective optimization and balanced solution; The output module: output the final Pareto optimal solution set.

[0015] According to the specific embodiments provided by the application, the application has the following technical effects compared with the prior art: The application utilizes the improved NSGA-II algorithm, through its fast non-dominated sorting, congestion calculation and binary tournament selection mechanism, can systematically drive the population to conduct global exploration and accurate convergence in complex parameter space, effectively avoids the defects that the traditional optimization method is easy to fall into local optimum, ensures the diversity and Pareto optimality of the final solution set. Secondly, the Transformer model is introduced to predict the performance of the optical waveguide, replacing the traditional time-consuming and expensive physical simulation or experimental measurement, its strong nonlinear coding and feature extraction capability can quickly and accurately map the complex implicit relationship between the optical waveguide parameters and performance, greatly speed up the individual fitness evaluation process, so that the algorithm can iterate a large number of parameter combinations in a short time, significantly improve the optimization efficiency. Further, by merging the historical and current Pareto frontiers in each generation evolution and performing elite selection, and combining the double standards of "single target optimization" and "balanced solution" to select representative solutions, not only ensures the stability of the optimization process and the continuous improvement of the solution set, but also provides the decision maker with a full range of high-value candidate solutions from the extreme performance to the balanced performance, enhancing the practicality and interpretability of the results. Finally, the closed-loop iterative process can output a Pareto optimal solution set with breadth and depth after reaching the preset conditions, not only realizes the global optimal trade-off of the optical waveguide design in multiple conflicting targets (such as loss, bandwidth, mode purity, etc.), but also through the cooperation of intelligent prediction and efficient search, shortens the traditional design cycle from weeks or even months to hours or minutes, greatly promotes the automation and intelligentization process of photonic device design, and provides strong technical support for the rapid development and customization of high-performance and multi-functional optical waveguides. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without any creative labor.

[0017] The application will be further described below in combination with the drawings, and a kind of optical waveguide parameter optimization method and system based on Transformer model and improved NSGA-II algorithm of the present application will be further described. Figure 1 It is the overall flow schematic diagram of the optical waveguide parameter optimization method based on Transformer model and improved NSGA-II algorithm in the embodiment 1 of the present application. Figure 2 It is the flow schematic diagram of the improved NSGA-II algorithm generating current Pareto optimal solution set in the optical waveguide parameter optimization method based on Transformer model and improved NSGA-II algorithm in the embodiment 1 of the present application. Figure 3 is a flowchart of the Pareto front processing in the optical waveguide parameter optimization method based on the Transformer model and the improved NSGA-II algorithm in embodiment 1 of the present application; Figure 4 is a data set including a training set and a validation set in embodiment 2 of the present application; Figure 5 is an optimized parameter result after training in embodiment 3 of the present application; Figure 6 is an optical field diagram of six modes in embodiment 3 of the present application; wherein (a) is an LP01 mode, (b) is an LP11a mode; (c) is an LP11b mode; (d) is an LP21a mode; (e) is an LP21b mode; and (f) is an LP02 mode; Figure 7 is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm, -5dBm and 0dBm at the DMG minimum in embodiment 3 of the present application, and the LP01, LP11a, LP11b, LP21a and LP21b graph lines overlap; wherein (a) is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm at the DMG minimum; (b) is a curve graph of the mode gain varying with the pump power when the signal light power is-5dBm at the DMG minimum; and (c) is a curve graph of the mode gain varying with the pump power when the signal light power is 0dBm at the DMG minimum; Figure 8 is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm, -5dBm and 0dBm at the maximum average gain, and the LP11a and LP11b graph lines overlap, and the LP21a and LP21b graph lines overlap; wherein (a) is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm at the maximum average gain; (b) is a curve graph of the mode gain varying with the pump power when the signal light power is-5dBm at the maximum average gain; and (c) is a curve graph of the mode gain varying with the pump power when the signal light power is 0dBm at the maximum average gain; Figure 9 is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm, -5dBm and 0dBm at the maximum effective refractive index, and the LP21a and LP21b graph lines overlap; wherein (a) is a curve graph of the mode gain varying with the pump power when the signal light power is-10dBm at the maximum effective refractive index; (b) is a curve graph of the mode gain varying with the pump power when the signal light power is-5dBm at the maximum effective refractive index; and (c) is a curve graph of the mode gain varying with the pump power when the signal light power is 0dBm at the maximum effective refractive index.

[0018] Figure 10 Fig. 3 is a diagram of mode gain varying with pump power when signal light power is-10 dBm, -5 dBm and 0 dBm respectively in the three parameter balance of embodiment 3 of the present application, and the graph of LP21a and LP21b overlaps; wherein (a) is a diagram of mode gain varying with pump power when signal light power is-10 dBm in the maximum effective refractive index; (b) is a diagram of mode gain varying with pump power when signal light power is-5 dBm in the maximum effective refractive index; (c) is a diagram of mode gain varying with pump power when signal light power is 0 dBm in the maximum effective refractive index. DETAILED DESCRIPTION

[0019] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the present application, but are not used to limit the scope of the present application.

[0020] In order to better understand the purpose, structure and function of the present application, the present application will be further described in detail below with reference to the accompanying drawings.

[0021] Example 1 As shown in Figure 1 The present application provides an optical waveguide parameter optimization method based on a Transformer model and an improved NSGA-II algorithm, as shown in Figure 1 The method comprises the following steps: S1, input the preprocessed optical waveguide structure parameters into the Transformer model, output the performance prediction value after nonlinear coding and feature extraction, and perform physical constraint clipping as the basis for evaluating the pros and cons of individuals by the improved NSGA-II algorithm; wherein the optical waveguide structure parameters include: outer layer width, inner layer width, outer layer concentration and inner layer concentration; The working process of the physical constraint Transformer model comprises: Standardizing the input optical waveguide parameters by StandardScaler; Extracting the correlation between parameters by multi-head self-attention mechanism, and outputting the performance prediction value.

[0022] In this embodiment, the training strategy of the physical constraint Transformer model comprises: 5-fold K-fold cross-validation combined with early stopping mechanism is adopted; The optimizer adopts AdamW, and cooperates with cosine annealing learning rate scheduling.

[0023] S2, randomly generate an initial optical waveguide structure parameter population within a preset boundary constraint, input into the improved NSGA-II algorithm, generate new individuals through crossover and mutation operations, combine non-dominated sorting, congestion degree calculation and binary tournament selection to drive population evolution, and generate a current Pareto optimal solution set; In the S2, the improved NSGA-II algorithm comprises: adding layer normalization (LayerNorm) before each fully connected layer to enhance the training stability; the activation function is optimized from ReLU to GELU to improve the non-linear expression capability; a stepped progressive dimension reduction structure is adopted in the output layer to improve the feature compression effect; and the optimization parameter configuration is set as: d_model=32, nhead=2, num_layers=2. The stepped dimension reduction structure comprises: first-stage dimension reduction: compressing high-dimensional features output by the Transformer to 16-dimensional hidden layers; and second-stage dimension reduction: mapping the 16-dimensional features to a 3-dimensional target space. As shown in Figure 2 The improved NSGA-II algorithm in the application is based on a genetic algorithm framework, and multiple objective functions are optimized through population iterative evolution, and is widely used in complex multi-objective scenarios such as engineering design, scheduling optimization and machine learning. The core mechanism includes non-dominated sorting, congestion distance calculation and elite reservation strategy. First, the non-dominated sorting divides the individuals in the population into layers according to the dominance relationship: if one solution is not worse than another solution in all objectives, and is better in at least one objective, it is said to dominate the latter; the non-dominated solution (i.e. the solution that cannot be dominated by other solutions) constitutes the first layer of the Pareto front, the suboptimal solution constitutes the second layer, and so on. This layering ensures that solutions close to the Pareto front are preferentially selected. Second, the congestion distance calculation is used to evaluate the distribution density of solutions in the same layer. By comparing the proximity distance of individuals in the objective space, the solution with a sparse distribution is preferentially reserved to ensure the diversity and uniformity of the solution set. The evolution process of NSGA-II starts from the initialization of a random population, and generates a child population through selection (usually tournament selection), crossover (simulated binary crossover, etc.) and mutation (polynomial mutation, etc.); then, the parent and child populations are combined, and the next generation population is selected through non-dominated sorting and congestion comparison, and the elite reservation strategy ensures that high-quality solutions are not lost. Compared with the traditional NSGA, the improved NSGA-II algorithm improves the sorting efficiency (the time complexity is reduced from O(MN³) to O(MN²), where M is the number of objectives and N is the population size), and avoids the problem of needing to set shared parameters through the congestion mechanism. NSGA-II has become a benchmark algorithm in the field of multi-objective optimization with its fast convergence, solution diversity and high computational efficiency, and is particularly suitable for handling non-linear, non-continuous or high-dimensional objective functions.

[0024] In summary, the improved NSGA-II in this invention efficiently searches for Pareto optimal solutions within the framework of a genetic algorithm by employing non-dominated sorting, crowding distance, and elite retention strategies, balancing convergence and diversity, and is applicable to a variety of practical optimization problems.

[0025] The crossover and mutation operations are explained below: 1) The crossover operation simulates the transposition of chromosomes in nature to generate new individuals, determining the algorithm's global search capability. The standard NSGA-II algorithm uses a simulated binary crossover operator, and the formula for calculating the (k+1)th generation individual is as follows:

[0026] In the formula, p 1,k+1 and p2,k+1 It is the first generation generated after crossover. k +1 generation individual; p 1,k and p 2,k The selected number k Individual; β qi It is the uniform distribution factor, and its calculation method is as follows:

[0027] In the formula, u i It is a random number belonging to the range [0,1); η It is the cross-distribution index, generally defined as 20-30. η The size of the individual affects how far the resulting individual is from its parent.

[0028] 2) The mutation operation simulates gene mutation in organisms. Like the crossover operation, it is used to generate new individuals. The mutation operator in the standard NSGA-II algorithm is a polynomial mutation operator. The formula for calculating the individual in the (k+1)th generation is as follows:

[0029] In the formula, p k The selected number k Individual; p k+1 yes p k The first one obtained after mutation operation k +1 generation individual; and These are the upper and lower bounds of the decision variable, respectively; δ k The calculation formula is as follows:

[0030] wherein, r k is a uniform distribution random number in [0, 1]; η m is a variation distribution index.

[0031] S3, dynamically merging the historical Pareto front solution set and the current candidate solution set in each round of iteration, updating the global optimal solution set through non-dominated sorting; wherein the double standards include: single objective optimization and balanced solution; In the S3, the single objective optimization includes: selecting the extreme value solution in the three directions of minimizing gain difference, maximizing average gain, and maximizing effective refractive index difference, respectively; The balanced solution includes: based on the principle of minimum Euclidean distance ideal point, selecting a scheme that achieves the best trade-off between minimizing gain difference, maximizing average gain, and maximizing effective refractive index difference from the Pareto front.

[0032] In this embodiment, the improved NSGA-II algorithm first randomly generates an initial optical waveguide parameter population within the preset boundary constraints as the starting point of optimization; then calculates the objective function value of each individual to evaluate its advantages and disadvantages, and distinguishes the non-dominated front through non-dominated sorting, preparing for multi-objective optimization; then adds new non-dominated solutions to the historical front, updates the Pareto front solution set, and checks whether the early stopping condition (such as the number of iterations or convergence index) is met; if it is met, the result is output and the algorithm is ended, otherwise the parent generation is selected from the current population or the front, new individuals are generated through crossover and mutation, the new individuals form a new generation population, and the target function evaluation step is returned, and the iteration continues until the stopping condition is met.

[0033] In the updating mechanism, the historical front and the new population are merged in each round of iteration, the Pareto front is updated through non-dominated sorting, and the front size change is recorded (in the selection of solutions, for single objective optimal solution, the standards of minimizing gain difference, maximizing average gain, and maximizing effective refractive index difference are adopted; for balanced solution, the solution with the minimum Euclidean distance to the ideal point (original target value) is selected. In terms of result output, including data files: pareto_optimal_solutions.csv (complete solution set) and representative_solutions.csv (three types of representative solutions); and visualization contents: 3D Pareto front graph, parallel coordinate graph, training loss curve and front size change graph.

[0034] In the S3, dynamically merging the historical Pareto front solution set and the current optical waveguide parameter population in each round of iteration, updating the global optimal solution set through non-dominated sorting includes: In each round of iteration, the historical Pareto front solution set and the current optical waveguide parameter population are merged; The global Pareto front solution set is updated by non-dominated sorting, and the non-dominated solutions of the historical optimal solution and the current population are integrated; Representative solutions are selected from the updated archive solution set to guide the initialization of the next generation population or as the final design scheme candidate solution; The embodiment is specifically: the iterative process of the Pareto front processing: first, initialize and prepare to execute optimization, then generate an initial population as the starting point of optimization; then, calculate the objective function value of each individual to evaluate its advantages and disadvantages, and distinguish the non-dominated front by non-dominated sorting, to prepare for multi-objective optimization; then, add new non-dominated solutions to the historical front, update the Pareto front solution set, and check whether the early stopping condition (such as the number of iterations or convergence index) is met; if met, output the result and end the algorithm, otherwise, select the parent from the current population or the front, generate new individuals through crossover and mutation, the new individuals form a new generation population, return to the objective function evaluation step, and continue iteration until the stopping condition is met.

[0035] In the updating mechanism, the historical front and the new population are combined in each iteration, the Pareto front is updated by non-dominated sorting, and the front size change is recorded. In the selection of solutions, for single-objective optimal solutions, the maximum gain difference minimization, average gain maximization and effective refractive index difference maximization standards are adopted; for balanced solutions, the solution with the minimum Euclidean distance to the ideal point (original target value) is selected. In terms of result output, data files are included: pareto_optimal_solutions.csv (complete solution set) and representative_solutions.csv (three types of representative solutions); and visualization contents: 3D Pareto front graph, parallel coordinate graph, training loss curve and front size change graph.

[0036] S4, repeating S1-S3 until a preset number of iterations or convergence condition is reached, outputting the final Pareto optimal solution set to realize optimization of the optical waveguide parameters.

[0037] In summary, the main points of the application are as follows: 1. Improved NSGA-II multi-objective optimization algorithm The improved NSGA-II algorithm is adopted, and fast non-dominated sorting, crowding degree calculation and binary tournament selection are integrated to realize population evolution in multi-objective optimization. In the feature processing stage, the gradient stability and convergence speed are improved by introducing a LayerNorm layer before the fully connected layer; the non-linear fitting ability is improved by replacing ReLU with GELU activation function; a stepped dimension reduction structure is designed at the output end (first stage dimension reduction: compressing high-dimensional features output by the Transformer to 16-dimensional hidden layers; second stage dimension reduction: mapping 16-dimensional features to a 3-dimensional target space).

[0038] During the running process, the algorithm takes a randomly generated initial population of optical waveguide parameters as input, generates candidate solutions through operations such as crossover and mutation, then predicts performance indicators through a physically constrained Transformer model, calculates target values, and performs fast non-dominated sorting and congestion evaluation. The superior individuals are retained to enter the next generation until the termination condition is reached, achieving the collaborative optimization of minimizing the maximum gain difference, maximizing the average gain, and maximizing the effective refractive index difference.

[0039] 2. Physically constrained Transformer model Based on the Transformer regression structure, the optical waveguide design parameters (a: outer layer width, b: inner layer width, c: outer layer concentration, d: inner layer concentration) are processed. StandardScaler standardization and K-fold cross-validation strategy are adopted to ensure the model's generalization ability and prediction accuracy.

[0040] The core is to introduce a physical constraint function to force b < a, ensuring that the generated optical waveguide structure meets the semiconductor process rules. The working principle is as follows: during the model prediction phase, the input optical waveguide parameters are first standardized and sent to the Transformer model. Through multi-head self-attention, the correlation between parameters is extracted, and the performance prediction value is output as the basis for NSGA-II to evaluate the superiority of individuals. If an individual that does not satisfy b < a is found during the prediction process, it will be automatically excluded or corrected to ensure that the optimization process is always conducted within the physically feasible domain.

[0041] 3. Dynamic Pareto front management mechanism In each iteration, the historical Pareto front solution set is merged with the current population, and the non-dominated sorting is used to dynamically update the global optimal solution set. The updated Pareto front not only retains the historical superior solutions, avoiding forgetting, but also quickly responds to the improvement of the search results of the new generation.

[0042] When selecting representative solutions, a double standard is adopted: (1) Single-target optimization - select the extreme solutions in the directions of minimizing the maximum gain difference, maximizing the average gain, and maximizing the refractive index difference; (2) Balanced solution - based on the minimum Euclidean distance ideal point principle, select the best solution that balances the three objectives.

[0043] The updated representative solutions can be used to guide the initialization of the next generation population and as candidates for the final design scheme. The overall working principle is as follows: Improved NSGA-II algorithm generates and evolves optical waveguide design parameters → physically constrained Transformer model predicts performance indicators and excludes infeasible solutions → dynamic Pareto front management mechanism merges historical and current solutions, selects optimal and balanced solutions → feedback to NSGA-II for continued iteration search until a stable multi-objective optimal solution set is obtained.

[0044] Example 2 The present application provides a specific scheme for multi-objective optimization using the optical waveguide parameter optimization method based on the Transformer architecture and the improved NSGA-II algorithm in Example 1: First, set the data content: including structural data (such as geometric parameters, material properties, etc.) (as shown in Figure 4 ) and its corresponding virtual simulation results; data preprocessing: normalize or standardize the input features to improve training convergence speed and model stability. The following figure is a screenshot of part of the data set: The ratio of training set and validation set in data division: 80% for training and 20% for validation; the training set is used for model parameter optimization, and the validation set is used for model performance evaluation and early stopping judgment.

[0045] Multi-objective cross-validation: K-fold cross-validation (KFold, K=5) is a widely used technique in machine learning model performance evaluation. It ensures that the evaluation results of the model are more stable and reliable through multiple experiments, and maximizes the use of limited data resources. It divides the data into several subsets, alternately as training set and test set, thereby reducing the bias caused by data division contingency and providing a scientific basis for model selection and optimization. Specifically as follows: First, data segmentation: randomly divide the entire data set into five mutually exclusive subsets of approximately equal size (called "folds"). After five experiments: first experiment: use the first subset as the test set, and the remaining four subsets (80 samples) as the training set; second experiment: use the second subset as the test set, and the remaining four subsets (80 samples) as the training set; the remaining three experiments are done in the same way. Then, the results are summarized, that is, the evaluation indicators (such as accuracy, recall, F1 score, mean square error, etc.) of each experiment are recorded. The final evaluation indicator result is the average of the results of the five experiments. The standardization formula is: ; In the formula, X is the original feature value, μ is the feature mean, and σ is the standard deviation.

[0046] The overlap integral factor calculation formula is as follows:

[0047] where, describes the parameters of its coupling or interaction with two states (j and i).

[0048] In the multi-objective cross-validation process, each fold is used as the validation set in turn, and the rest are used as the training set, in order to fully evaluate the stability and generalization ability of the model under different data distributions.

[0049] The multi-objective optimization strategy is to train the final model using the full data after completing cross-validation and parameter tuning, that is, using all available training data (not just part of the data or a subset of cross-validation) to train the final model to improve the generalization ability and performance of the model.

[0050] Optimization goal: minimize the training loss function while ensuring the balance of each target (such as prediction accuracy and model stability).

[0051] Embodiment 3 The application also provides another specific scheme for multi-objective optimization using the optical waveguide parameter optimization method based on the Transformer architecture and the improved NSGA-II algorithm in Embodiment 1 Multiple iterations are performed to obtain the parameter values corresponding to the maximum gain, and COMSOL and MATLAB are used to jointly simulate to obtain the optical field image and pump light power image.

[0052] The maximum number of training rounds is set to 300 rounds in this training configuration, and the early stopping mechanism with patience = 20 is adopted, that is, the training is terminated when there is no performance improvement in the validation set for 20 consecutive rounds to prevent overfitting; the AdamW optimizer is selected with weight decay, the learning rate is set to 1e-4, and the MSELoss (Mean Squared Error) loss function suitable for regression tasks is used to measure the deviation between the predicted value and the true value. The Transformer model structure is designed for single-target regression tasks, with an output dimension of 1, a hidden layer dimension d_model = 32, a number of multi-head attention heads nhead = 2, an encoder layer number num_layers = 2, and a Dropout ratio of 0.3 to enhance the model's generalization ability. The training process includes data loading and preprocessing (including normalization / standardization), training set and validation set division, and parameter tuning through K-fold cross-validation. Finally, the model is trained using the full data, and the validation set loss is monitored in real time during the training process, and the early stopping mechanism is enabled. After training is completed, the model performance is evaluated and the best weights are saved, and the optimization parameter results during the training process are recorded, such as Figure 5 as shown.

[0053] Then, the optical field distribution map and the corresponding pump light power and gain image are obtained by COMSOL and MATLAB, as follows: A group of experiments without layering (P00) and without multi-objective optimization design are performed to highlight the advantages of our multi-layer structure and multi-objective optimization design. Six mode optical signals (LP01, LP11a, LP11b, LP21a, LP21b, LP02) are input, and G, DMG, and crosstalk are calculated. The six signal light images are as follows: Figure 6As shown; wherein the LP01 mode is a central bright spot, circularly symmetric; the LP11a mode is a horizontal double lobe; the LP11b is a vertical double lobe; the LP21a is a four-lobed, along the diagonal; the LP21b mode is a four-lobed, along the horizontal / vertical direction; the LP02 mode is a central bright spot + one concentric bright ring Based on the above optimized results, the gain curve of different signal light DB number is calculated by matlab, the horizontal axis is pump power, and the vertical axis is gain; as shown in Figure 7 As shown, the maximum gain difference is very small, and the LP01, LP11a, LP11b, LP21a and LP21b graphs overlap; Figure 8 As shown, the LP11a and LP11b graphs overlap, and the LP21a and LP21b graphs overlap; Figure 9 As shown, the LP21a and LP21b graphs overlap.

[0054] Example 4 The application provides a system for performing the optical waveguide parameter optimization method based on the Transformer model and the improved NSGA-II algorithm in example 1, comprising: The Transformer model is used for outputting performance prediction values after nonlinear coding and feature extraction of the preprocessed optical waveguide structure parameters, and performing physical constraint clipping, so as to serve as a basis for evaluating the advantages and disadvantages of individuals by the improved NSGA-II algorithm; The improved NSGA-II module is used for inputting an initial optical waveguide structure parameter population randomly generated within a preset boundary constraint into the improved NSGA-II algorithm, generating new individuals through cross and mutation operations, combining non-dominated sorting, crowding degree calculation and binary tournament selection to drive population evolution, and generating a current Pareto optimal solution set; The multi-objective collaborative optimization module dynamically combines a historical Pareto front solution set and a current candidate solution set in each round of iteration, and updates a global optimal solution set through non-dominated sorting; wherein the double standards include: single-objective optimization and balanced solution; The output module: outputs the final Pareto optimal solution set.

[0055] In this embodiment, first, the Transformer model performs nonlinear encoding of the features of the data and extracts key feature information. At the same time, the NSGA-II improved algorithm generates a Pareto front to provide multiple potential solutions for the optimization process. The results of the two are jointly input into the multi-objective collaborative optimization module, where multiple optimization objectives are balanced to find the best solution that meets all the objectives. In this process, the constraint clipping function always constrains the optimization results for physical feasibility to ensure that the output optical waveguide parameters meet the actual physical conditions. Finally, the optical waveguide parameters optimized through the above steps are determined and can be used to guide the design and manufacture of the optical waveguide to achieve the expected performance indicators.

[0056] The foregoing description of the embodiments disclosed above enables one of ordinary skill in the art to make or use the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing parameters of an optical waveguide based on a Transformer model and an improved NSGA-II algorithm, characterized in that, The method comprises the following steps: S1, input the pre-processed optical waveguide structure parameters into the Transformer model, perform nonlinear coding and feature extraction, output performance prediction values, and perform physical constraint clipping as the basis for evaluating the performance of the improved NSGA-II algorithm; S2, randomly generate an initial optical waveguide structure parameter population within the preset boundary constraints, input it into the improved NSGA-II algorithm, generate new individuals through crossover and mutation operations, combine non-dominated sorting, crowding degree calculation and binary tournament selection to drive population evolution, and generate a current Pareto optimal solution set; S3, dynamically combine the historical Pareto front solution set and the current candidate solution set in each iteration, and update the global optimal solution set through non-dominated sorting; The double standard includes: single target optimization and balanced solution; S4, repeat S1-S3 until the preset iteration number or convergence condition is reached, output the final Pareto optimal solution set, and realize optical waveguide parameter optimization.

2. The method of claim 1, wherein the method is based on a Transformer model and an improved NSGA-II algorithm. In S1, the optical waveguide structure parameters include: outer layer width, inner layer width, outer layer concentration and inner layer concentration.

3. The method of claim 1, wherein the method is characterized in that, The workflow of the physical constraint Transformer model includes: perform StandardScaler standardization processing on the input optical waveguide parameters; extract the correlation between parameters through a multi-head self-attention mechanism, and output performance prediction values.

4. The method of claim 1, wherein the method is characterized in that, In S2, the improved NSGA-II algorithm includes: introducing a LayerNorm layer before the fully connected layer; using a GELU activation function instead of ReLU; and designing a stepped dimension reduction structure at the output end; The stepped dimension reduction structure includes: first-level dimension reduction: compressing high-dimensional features output by the Transformer to 16-dimensional hidden layers; and second-level dimension reduction: mapping 16-dimensional features to a 3-dimensional target space.

5. The method of claim 1, wherein the method is characterized in that, In S3, the single target optimization includes: selecting extreme solutions in the directions of minimizing gain difference, maximizing average gain and maximizing effective refractive index difference, respectively; The balanced solution includes: based on the minimum Euclidean distance ideal point principle, selecting a scheme that achieves the best trade-off between minimizing gain difference, maximizing average gain and maximizing effective refractive index difference from the Pareto front.

6. The method of claim 1, wherein the method is based on a Transformer model and an improved NSGA-II algorithm. In S3, dynamically combining the historical Pareto front solution set and the current optical waveguide parameter population in each iteration, and updating the global optimal solution set through non-dominated sorting includes: In each iteration, combine the historical Pareto front solution set and the current optical waveguide parameter population; Update the global Pareto front solution set through non-dominated sorting, and integrate the historical optimal solution and the non-dominated solution of the current population; Select representative solutions from the updated archive solution set to guide the initialization of the next generation population or as candidate solutions for the final design scheme.

7. The method of claim 1, wherein the method is characterized by, The training strategy of the physical constraint Transformer model includes: Use 5-fold K-fold cross-validation combined with early stopping mechanism; Optimizer uses AdamW, combined with cosine annealing learning rate scheduling.

8. A system for optimizing parameters of an optical waveguide based on a Transformer model and an improved NSGA-II algorithm, configured to perform the method for optimizing parameters of an optical waveguide based on a Transformer model and an improved NSGA-II algorithm according to any one of claims 1-7. It includes: a Transformer model for performing nonlinear coding and feature extraction on pre-processed optical waveguide structure parameters, outputting performance prediction values, and performing physical constraint clipping as the basis for evaluating the performance of the improved NSGA-II algorithm; The improved NSGA-II module is used for inputting an initial optical waveguide structure parameter population randomly generated within preset boundary constraints into the improved NSGA-II algorithm, generating new individuals through cross and mutation operations, combining non-dominated sorting, crowdedness calculation and binary tournament selection to drive population evolution, and generating a current Pareto optimal solution set; The multi-objective collaborative optimization module dynamically combines a historical Pareto front solution set and a current candidate solution set in each round of iteration, and updates a global optimal solution set through non-dominated sorting; The double standards include single-objective optimization and balanced solution; The output module outputs a final Pareto optimal solution set.

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