WaveNet-LSTM soliton form switching prediction method based on feature fusion

Abstract

The invention provides a WaveNet-LSTM method based on feature fusion. The WaveNet-LSTM method is used for accurately predicting the switching process of soliton forms. According to the method, a data set is generated by building a tunable mode-locked laser and combining numerical simulation of a coupled nonlinear schrodinger equation. After normalization processing is carried out on original optical pulse data, the original optical pulse data are spliced and fused with the coded characteristic values. In order to process the data, a parallel deep learning model is further constructed; one branch is to capture transient sudden change characteristics during soliton form switching by using one-dimensional convolution; and the other branch is that a WaveNet module is adopted to efficiently extract long-range dynamic dependence in a soliton stable evolution stage. Features extracted by the two branches are fused again and then sent to an LSTM layer in a unified mode for time sequence modeling, and finally accurate prediction of soliton dynamics is achieved. The method provides an efficient new data driving tool for intelligent design and on-demand control of the ultrafast laser.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic information technology, and in particular to a method for predicting soliton mode switching in tunable fiber lasers based on feature fusion using WaveNet-LSTM. Background Technology

[0002] Ultrafast fiber lasers have important applications in many fields, and their core technology lies in the precise control of the dynamic behavior of internal optical solitons. Among them, the soliton mode switching process, which is actively controlled by external parameters (such as temperature and pump power), is a key link in understanding and utilizing its complex nonlinear dynamics, and is of great significance for realizing intelligent on-demand control of lasers.

[0003] Traditionally, the study of soliton dynamics has relied primarily on numerical simulations based on physical models such as the nonlinear Schrödinger equation. However, this approach requires massive iterative calculations, consuming enormous computational resources and time, and failing to meet the demands of real-time prediction applications. In contrast, machine learning methods, with their powerful nonlinear fitting capabilities and efficient inference speed, offer a new paradigm for bypassing complex numerical solutions and directly establishing an end-to-end mapping from external parameters to soliton states, demonstrating a significant advantage in computational efficiency. Although existing deep learning models (such as recurrent neural networks) have made some progress in predicting soliton evolution, they still have significant limitations. Most of these models passively learn their evolution patterns by using only the time-series data of the light pulses themselves as input, failing to establish a clear physical connection between external control parameters and soliton state evolution. This learning approach makes it difficult for models to accurately capture and predict the precise process of soliton state switching actively triggered by changes in external parameters in tunable lasers, limiting their practical application in the field of intelligent control.

[0004] Therefore, there is an urgent need in this field for a new method for predicting soliton dynamics that is computationally efficient, accurate in prediction, and can directly respond to the control of external parameters. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a system and method that can accurately and quickly predict the long-distance evolution and morphological switching of solitons in tunable lasers.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A laser soliton dynamics prediction method based on feature fusion deep learning is disclosed. The method includes: Step s1, constructing a tunable mode-locked laser device; Step s2, generating a dataset obtained through numerical simulation based on a coupled nonlinear Schrödinger equation; Step s3, data preprocessing and feature fusion, including: Step s3.1, performing min-max normalization on the optical pulse data; and Step s3.2, encoding the feature values ​​and concatenating them with the optical pulse data for further feature fusion; Step s4, model construction, training, and prediction, including: Step s4.1, a state switching detector: this branch consists of two one-dimensional convolutional layers; Step s4.2, a WaveNet module: this branch consists of causal convolutions and exponentially expanding dilated convolutions; and Step s4.3, LSTM layers: each LSTM unit includes a forget gate, an input gate, and an output gate.

[0008] Step s1, the tunable mode-locked laser device includes: a 980nm pump source, a 980 / 1550nm wavelength division multiplexer, a 0.4m long Liekki Er110-4 / 125 erbium-doped fiber as the gain medium, a polarization controller, a polarization-independent isolator, and a saturable absorber made of a novel two-dimensional material Bi2TeSe2.

[0009] Furthermore, the numerical simulation in step s2 is based on the coupled nonlinear Schrödinger equation, the expression of which is:

[0010]

[0011] Here, u and v represent the normalized envelopes of the optical pulse on the two orthogonal polarization axes of the fiber, respectively. β² is the group velocity dispersion, γ is the Kerr nonlinear coefficient, and Ω... g It refers to gain bandwidth.

[0012] The gain coefficient g describes the saturation effect of the gain medium, and its expression is:

[0013]

[0014] Here, g0 is the small-signal gain, E sat It is the gain saturation energy, which determines the maximum energy that the laser can output.

[0015] Furthermore, in step s3.1, the numerical simulation optical pulse data undergoes min-max normalization, the expression of which is:

[0016]

[0017] Here, y′ is the normalized data, and y is the original data. max It is the maximum value in this set of data, ymin That is the minimum value in this set of data.

[0018] Furthermore, in step s3.2, feature fusion encodes the physical parameters characterizing external regulation and splices them with the normalized optical pulse data.

[0019] Furthermore, in step s4, the model construction, training, and prediction involve inputting the feature fusion data into two parallel modules.

[0020] In step s4.1, the one-dimensional convolution formula in the state switching detector is:

[0021]

[0022] Here, y i It is the i-th element of the output sequence, weight k K is the convolution kernel, K is the kernel size, and bias is the deviation.

[0023] In step s4.2, the formula for the gated activation unit of the WaveNet module is:

[0024] z = tanh(W) f *x)⊙σ(W g *x)

[0025] Here, x is the input data, * is the convolution operation, and W f and W g These are two different weight matrices: tanh is the hyperbolic tangent activation function, σ is the sigmoid activation function, ⊙ is element-wise multiplication, and z is the final output calculated by the formula.

[0026] Furthermore, in step s4.2, the tanh hyperbolic tangent activation function and the sigmoid activation function are formulated as follows:

[0027]

[0028] Furthermore, to enable the model to converge quickly, this invention employs a mean squared error loss function, which is expressed as:

[0029]

[0030] Here, y i It is the actual value. N is the model's predicted value, and N is the batch size.

[0031] In step s4, during model training, the batch size of the training samples is 128, the number of neurons in the LSTM layer is 300, the number of layers is 2, the number of samples is 600, the optimizer Adam is selected for model training, the learning rate is 0.0001, and the number of training epochs is 160.

[0032] Furthermore, to verify the model performance, in step s4, the model training result can be measured using the normalized root mean square error (NRMSE), which is calculated using the following formula:

[0033]

[0034] The present invention has the following beneficial effects:

[0035] 1. Improved physical accuracy and causality of predictions: Traditional deep learning models fail to establish a physical connection between external control parameters and soliton states. This invention, through an innovative feature fusion step, concatenates parameters representing external control with optical pulse data, forcing the model to directly learn the physical causal relationship of "how external parameters affect pulse evolution," greatly improving the model's understanding of tunable systems and its prediction robustness.

[0036] 2. Comprehensive Capture of Complex Dynamic Processes: The parallel feature extraction framework constructed in this invention can simultaneously process features at different time scales. Its state-switching detector branch can keenly capture the transient and dramatic features during soliton morphological switching, while the WaveNet module efficiently extracts long-range dynamic dependencies in stable evolution stages. Finally, the two types of features are fused for prediction, enabling the model to completely and accurately reproduce the entire dynamic process.

[0037] 3. Excellent long-term prediction stability and high fidelity: Addressing the common problem of error accumulation in traditional autoregressive models for long-range prediction, the method of this invention exhibits extremely strong stability. In continuous predictions spanning up to 1500 intracavity cycles, the normalized root mean square error (NRMSE) remained at an extremely low level without divergence, strongly demonstrating its high fidelity and reliability in long-distance evolution prediction.

[0038] 4. Combining high computational efficiency and application potential: Compared to traditional numerical simulation methods that require massive iterative calculations and are extremely time-consuming, this invention, as a data-driven model, exhibits extremely high computational efficiency in the prediction stage, meeting the application requirements of real-time prediction and intelligent control. It provides a powerful and efficient new tool for the intelligent design and on-demand control of ultrafast lasers.

[0039] 5. Verification of robustness and practical applicability: The effectiveness of the method in this invention has been verified by both numerical simulation and real physical experimental data. Whether in an idealized simulation environment or in a real physical experiment filled with noise and uncertainty, the prediction results show extremely high consistency with the reference data, demonstrating the method's excellent prediction accuracy and strong robustness, and its enormous potential for practical application. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart illustrating the prediction method in this invention;

[0042] Figure 2 This is the tunable mode-locked laser device of the present invention;

[0043] Figure 3 This is a schematic diagram of the neural network structure in this invention.

[0044] Figure 4 This is a schematic diagram of the state switching detector in this invention;

[0045] Figure 5 This is a schematic diagram of the WaveNet module in this invention;

[0046] Figure 6 This is a schematic diagram of the LSTM neuron structure in this invention;

[0047] Figure 7 This is the predicted result of the spectral center wavelength in this invention;

[0048] Figure 8 This is the pulse energy evolution prediction result in this invention;

[0049] Figure 9 This refers to the spectral cross section prediction results in this invention;

[0050] Figure 10 The evolution results of NRMSE in this invention; Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the present invention will be further described below with reference to specific embodiments and the accompanying drawings. The embodiments of the present invention include, but are not limited to, the following embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application.

[0052] The purpose of this invention is to overcome the shortcomings of the prior art and provide a system and method that can accurately and quickly predict the long-distance evolution and morphological switching of solitons in tunable lasers.

[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Appendix Figure 1 This is a schematic diagram illustrating the overall workflow of the prediction method in this invention. The diagram shows four core stages: experimental setup, dataset generation, model training and prediction, and comparison of prediction results with experimental and simulation data. Specifically, it includes the following steps:

[0055] Step 1: The setup of the tunable mode-locked laser device is shown in the attached figure. Figure 2 As shown, this embodiment constructs an experimental platform for generating solitons and experimentally verifying a temperature-tunable ultrafast fiber laser. The device is an all-fiber ring cavity mode-locked laser, mainly comprising: a 980nm pump source, a 980 / 1550nm wavelength division multiplexer, a 0.4m long Liekki Er110-4 / 125 erbium-doped fiber as the gain medium, a polarization controller for adjusting the intracavity polarization state, a polarization-independent isolator to ensure unidirectional transmission, and a saturable absorber made of a novel two-dimensional material, Bi2TeSe2, as the mode-locking device. Intracavity energy is extracted through an output coupler. To achieve temperature control, a special structure composed of polarization-maintaining fiber is integrated into the cavity. External temperature changes alter its birefringence, thereby modulating intracavity loss and power, ultimately inducing soliton generation and mode switching. The purpose of this experimental setup is to obtain real physical data to ultimately verify the accuracy and reliability of the prediction method proposed in this invention.

[0056] Step Two: It should be noted that, considering the limitations of real physical experimental data acquisition—high cost, low signal-to-noise ratio, and difficulty in covering all dynamic processes on a large scale—this invention prioritizes numerical simulation based on coupled nonlinear Schrödinger equations to generate large-scale, high-fidelity, and diverse datasets, ensuring the sufficiency and effectiveness of model training. Compared to noisy and difficult-to-obtain experimental data on a large scale, simulated data has advantages such as high fidelity, low noise, precise and controllable parameters, and high sample diversity.

[0057] The numerical simulation in this embodiment is based on a coupled nonlinear Schrödinger equation. This model can accurately describe the pulse evolution in the optical fiber, and its mathematical form is as follows:

[0058]

[0059] The gain coefficient g describes the saturation effect of the gain medium, and its expression is:

[0060]

[0061] Here, g0 is the small-signal gain, E sat It is the gain saturation energy, which is determined in the simulation by precisely controlling the gain saturation energy E. sat This is used to equivalently simulate the changes in intracavity power caused by real temperature changes, thereby driving soliton mode switching.

[0062] To cover a variety of dynamic processes, two dispersive environments were set up for the simulation:

[0063] Anomalous dispersion region: The net dispersion within the cavity is set to a negative value to simulate the dynamic process of switching from a conventional soliton to a bound soliton.

[0064] Normal dispersion region: The net dispersion is adjusted to a positive value by introducing dispersion compensation fiber to simulate the behavior of soliton molecules transforming into dissipative solitons.

[0065] By systematically scanning E sat The parameters were adjusted and different random noises were used as the initial field to generate a large-scale, high-fidelity dataset containing 600 independent evolutionary samples.

[0066] Step 3: Data Preprocessing and Feature Fusion This step processes the generated raw data to adapt it to the model's input requirements. First, the complex field data representing soliton states is subjected to min-max normalization, scaling the data to the [0,1] interval to accelerate model convergence. The expression is:

[0067]

[0068] Where y′ is the normalized data, y is the original data, and y' is the normalized data. max It is the maximum value in this set of data, y min That is the minimum value in this set of data.

[0069] Subsequently, the core step of this invention, feature fusion, is performed. A series of control parameter values ​​characterizing external modulation are encoded and then concatenated with normalized optical pulse complex field data to form an enhanced fused feature vector, which serves as the final input to the subsequent model. The innovation of this step lies in forcing the model to directly learn the explicit physical causal relationship of "how external parameters affect pulse evolution," rather than passively inferring it. This significantly improves the model's understanding of tunable systems and its predictive robustness.

[0070] Step 4: Model Construction, Training, and Prediction This embodiment constructs an innovative WN-LSTM model, as shown in the attached diagram. Figure 3 As shown. The core advantage of this model lies in its ability to directly correlate external control physical quantities with the evolution of the soliton's internal state, and to efficiently capture transient switching events and long-term dynamic dependencies. The model mainly consists of two parallel feature extraction branches and a recurrent processing layer.

[0071] State transition detector: as attached Figure 4 As shown, this branch consists of two one-dimensional convolutional layers. Its design goal is to act as a "mutation event" monitor, utilizing the powerful local pattern recognition capabilities of the convolutional kernels to capture, in real-time and sensitively, the transient and dramatic waveform or phase change patterns unique to key switching events such as soliton collisions, energy redistribution, or mode jumps from the input sequence. The formula for calculating its one-dimensional convolution is:

[0072]

[0073] WaveNet module: as attached Figure 5 As shown, this branch consists of causal convolutions and exponentially expanding dilated convolutions. This structure can achieve a large temporal receptive field with fewer network layers, enabling it to efficiently focus on capturing the long-term dynamic dependencies of solitons during stable evolutionary phases or transitional periods. Its gating activation unit formula is:

[0074] z = tanh(W) f *x)⊙σ(W g *x)

[0075] x is the input data, * is the convolution operation, and W is the input data. f and W g These are two different weight matrices: tanh is the hyperbolic tangent activation function, σ is the sigmoid activation function, ⊙ is element-wise multiplication, and z is the final output calculated by the formula.

[0076] LSTM layer: as attached Figure 6As shown, the "long-range dependency features" extracted by the WaveNet module are fed into the LSTM layer for effective modeling and long-term memory. Each LSTM unit contains a forget gate, an input gate, and an output gate, enabling it to effectively process time-series information.

[0077] Finally, the "transient features" extracted by the state switching detector are concatenated and fused with the "long-range dependency features" processed by the LSTM layer to form a final feature vector that combines both types of information. This vector is then fed into a fully connected layer to accurately predict the long-range evolution of solitons.

[0078] During model training, the following parameters were used: batch training sample size of 128, LSTM layer neurons of 300, number of layers of 2, total number of training samples of 600, Adam optimizer selected, learning rate set to 0.0001, and number of training iterations of 160. During training, mean squared error was used as the loss function for backpropagation to update the network weights. Its expression is:

[0079]

[0080] During the model prediction phase, the model employs an autoregressive approach. That is, only the initial optical pulse complex field data and control parameter values ​​of the system need to be input, and the model will predict the state at the next time step. This prediction result is then used as a new input to predict the state at the next time step after that, and so on, thereby achieving rapid and accurate long-term prediction of soliton morphology evolution for thousands of subsequent intracavity cycles.

[0081] It should be understood that the parameters disclosed in this embodiment are a set of preferred configurations. Those skilled in the art can adjust these parameters according to the specific circumstances such as the computing resources used and the size of the dataset, and such adjustments will not depart from the scope of protection claimed by this invention.

[0082] Step 5: Implementation effect verification. The prediction effect of the method of the present invention was comprehensively and rigorously verified by comparing it with numerical simulation and real physical experimental data. The results confirmed the high accuracy, strong robustness and long-term stability of the method of the present invention.

[0083] To verify the predictive capability of the method of this invention in complex nonlinear dynamic scenarios, a representative soliton morphology switching process was selected for verification.

[0084] In the scenario of switching from conventional solitons to soliton molecules, the method of this invention successfully predicted the three key physical stages of the entire switching process: the initially stable conventional soliton, the intermediate period of violent oscillations and non-equilibrium transition, and the final stable bound state.

[0085] Prediction of key dynamic parameters such as energy and center wavelength: as attached. Figure 7As shown, the predicted curves of the method of this invention almost perfectly match the simulation data, accurately capturing the amplitude and rhythm of each energy exchange and wavelength drift, demonstrating the model's profound understanding and modeling ability of strongly nonlinear transient dynamics. (See attached image) Figure 8 As shown, during the transition period of switching, the intracavity mode undergoes dynamic reconstruction, superimposed with the laser's inherent relaxation oscillations, resulting in drastic fluctuations in pulse energy. Simultaneously, this dramatic energy change causes a rapid drift in the pulse center wavelength through self-phase modulation.

[0086] Prediction of spectral fine structure: as attached Figure 9 As shown, this embodiment compares the predicted and experimental transient spectra. The predicted spectra show extremely high consistency with the experimental data in terms of profile, peak position, and modulation depth, demonstrating the model's excellent ability to capture and resolve detailed features.

[0087] To test the limiting performance of the method of this invention in long-range prediction and its ability to avoid error accumulation, it was applied to the long-range evolution prediction of more complex two-color solitons. (See attached...) Figure 10 As shown, in autoregressive predictions spanning up to 1500 intracavitary cycles, the NRMSE remained consistently at an extremely low level without any accumulation or divergence trend. This result strongly demonstrates the superior long-term stability and high fidelity of the method presented in this invention, effectively overcoming the common error accumulation problem in long-range predictions of traditional autoregressive models.

[0088] In summary, whether facing idealized numerical simulations or real physical environments filled with noise and uncertainty, the method proposed in this invention demonstrates excellent prediction accuracy, robustness, and long-term stability, proving its great application potential as a reliable prediction tool in guiding and optimizing the design and control of ultrafast fiber lasers in the real world.

Claims

1. A method for predicting soliton morphological switching based on WaveNet-LSTM with feature fusion, characterized in that, Includes the following steps: Step s1: Assemble the tunable mode-locked laser device. Step s2, the generation of the dataset, characterized in that the dataset is obtained through numerical simulation based on the coupled nonlinear Schrödinger equation; Step s3, data preprocessing and feature fusion, includes: Step s3.1: Perform min-max normalization on the optical pulse data; Step s3.2 involves encoding the feature values ​​and then concatenating them with the optical pulse data for further feature fusion. Step s4, model construction, training, and prediction include: Step s4.1, State Switching Detector: This branch consists of two one-dimensional convolutional layers. Step s4.2, WaveNet module: This branch consists of causal convolutions and exponentially expanding dilated convolutions. Step s4.3, LSTM layer: Each LSTM unit contains a forget gate, an input gate, and an output gate.

2. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, The apparatus for step s1 includes: a 980nm pump source, a 980 / 1550nm wavelength division multiplexer, a 0.4m long Liekki Er110-4 / 125 erbium-doped fiber as a gain medium, a polarization controller, a polarization-independent isolator, and a saturable absorber made of a novel two-dimensional material Bi2TeSe2.

3. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, Step s2, based on the coupled nonlinear Schrödinger equation, is expressed as follows: u and v represent the normalized envelopes of the optical pulse along the two orthogonal polarization axes of the optical fiber. β² is the group velocity dispersion, γ is the Kerr nonlinear coefficient, and Ω... g It refers to gain bandwidth. The gain coefficient g describes the saturation effect of the gain medium, and its expression is: Here, g0 is the small-signal gain, E sat It is the gain saturation energy, which determines the maximum energy that the laser can output.

4. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, Step s3.1 involves performing min-max normalization on the optical pulse data, the expression of which is: Where y′ is the normalized data, y is the original data, and y' is the normalized data. max It is the maximum value in this set of data, y min That is the minimum value in this set of data.

5. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, In step s4.1, the one-dimensional convolution formula in the state switching detector is: y i It is the i-th element of the output sequence, weight k K is the convolution kernel, K is the kernel size, and bias is the deviation.

6. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, In step s4.2, the formula for the gated activation unit of the WaveNet module is: z = tanh(W) f *x)⊙σ(W g *x) x is the input data, * is the convolution operation, and W is the input data. f and W g These are two different weight matrices: tanh is the hyperbolic tangent activation function, σ is the sigmoid activation function, ⊙ is element-wise multiplication, and z is the final output calculated by the formula.

7. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 6, characterized in that, In step s4.2, the tanh hyperbolic tangent activation function and the sigmoid activation function are defined as follows:

8. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, In step s4, the loss function is expressed as: Where y i It is the actual value. N is the model's predicted value, and N is the batch size.

9. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, In step s4, the model training process, the batch size of the training samples is 128, the number of neurons in the LSTM layer is 300, the number of layers is 2, the number of samples is 600, the model training selects the Adam optimizer, the learning rate is 0.0001, and the number of training epochs is 160.

10. The method for predicting soliton morphological switching based on WaveNet-LSTM according to claim 1, characterized in that, The model training result in step s4 can be measured by NRMSE, and its calculation formula is as follows:

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