A method for photonic crystal fiber two-dimensional parameter space compression and random structure automatic generation based on convolutional adversarial auto-encoding network

Abstract

To solve the problems of low degree of freedom and low flexibility in the inverse design and optimization of photonic crystal fiber, a method of two-dimensional parameter space compression and random structure automatic generation of photonic crystal fiber based on convolutional adversarial autoencoder network is proposed. Firstly, the two-dimensional free distribution of the refractive index of the fiber cross section is converted into a two-dimensional parameter matrix, and the two-dimensional matrix is compressed into a low-dimensional hyperparameter space obeying Gaussian distribution by convolutional adversarial autoencoder. Then, the random Gaussian hyperparameters are decoded into any two-dimensional cross-section structure parameters conforming to the characteristics of the fiber by combining the decoder. After training, the decoder can be used as a separate generation model to input a set of random Gaussian low-dimensional hyperparameters and automatically generate new two-dimensional structure parameter matrices conforming to the characteristics of photonic crystal fiber. This method can be combined with the prediction neural network to realize the automatic generation and iterative optimization of the two-dimensional free space parameters of the fiber cross section, and it is free from the constraints of fixed characteristic parameters, with high degree of freedom and flexibility. It provides a new way for the design and optimization of high degree of freedom parameter space fiber structure.

Description

Technical Field

[0001] This invention belongs to the field of optical fiber technology and relates to a method for two-dimensional parameter space compression of photonic crystal fibers and automatic generation of two-dimensional structures of random photonic crystal fiber cross sections based on convolutional adversarial autoencoders. Background Technology

[0002] The development of novel fiber optic structures is crucial for promoting innovation and development in fields such as fiber photonics. Currently, fiber optic structure design and optimization methods and processes mainly fall into two categories. One category is based on traditional mathematical and physical numerical simulation methods, such as the finite-difference time-domain method, beam propagation method, and finite element method, combined with manual trial and error and fine-tuning to achieve structural design and optimization. In this type of method and optimization design process, the optical properties output by numerical simulation serve as a reference, and the physical structural parameters of the fiber are repeatedly adjusted based on human experience. This method is computationally expensive, inefficient, and the parameter tuning process heavily relies on the researcher's physical intuition and design experience, resulting in a large amount of repetitive and redundant work.

[0003] The second type of method is the reverse design of fiber optic structures based on deep learning and various optimization algorithms. In this type of method, the optimization algorithm can randomly generate fiber optic structure parameters and perform parameter tuning based on the optical characteristics fed back by the neural network. Compared with traditional optimization design methods, this method reduces computational costs and greatly improves computational efficiency. However, the fiber optic structure optimization design methods based on deep learning and optimization algorithms reported so far are all based on fixed structural parameters. They require pre-assuming several characteristic parameters based on experience (for example, assuming that the structure of ultra-low dispersion few-mode fiber is a double-ring structure and pre-setting the parameters r1, r2, etc. of the double ring), and then using optimization algorithms to randomly generate these fixed characteristic parameter values ​​within a certain range, and optimizing each characteristic parameter based on the prediction feedback results of the neural network. These pre-assumed fixed structural features and parameter variables greatly limit the parameter design space of the optical structure and limit the design ideas, because it is often difficult to know the geometric characteristics of the optimal target structure in advance.

[0004] If all possible two-dimensional structural parameters of the optical fiber cross-section can be transformed into a design optimization space, the design freedom and flexibility will be greatly improved. Therefore, for the inverse design and automatic iterative optimization of the high-degree-of-freedom parameter space of optical fiber structures, we propose a method for compressing the two-dimensional parameter space and automatically generating random structures of photonic crystal fibers based on convolutional adversarial autoencoders (CAEs) using the free distribution of the two-dimensional material refractive index of the optical fiber cross-section as the parameter space. Taking air-hole photonic crystal fibers as an example, we transform the free distribution of the two-dimensional material refractive index of the optical fiber cross-section into a two-dimensional parameter matrix, where the parameter value of each matrix point corresponds to the material refractive index. Since the diameter of the optical fiber cross-section is 125 micrometers, and the material and refractive index distributions have nanometer-level variation precision, theoretically, a matrix of at least 1000×1000 is needed to fully represent the structural details of the optical fiber. If a 1000×1000 parameter matrix is ​​directly generated randomly using a neural network, from the perspective of training the network model, this will lead to a large consumption of computational resources and will also greatly increase the learning difficulty of the network model. With too many parameters, the optimization algorithm will be difficult to generate effectively. Therefore, we use a convolutional adversarial autoencoder to reduce the dimensionality of the two-dimensional matrix of the free-distribution refractive index of the fiber cross-section into a low-dimensional hyperparameter space that follows a Gaussian distribution. Then, a decoder is used to decode the random Gaussian hyperparameters to generate arbitrary two-dimensional cross-sectional structural parameter matrices that conform to the characteristics of the fiber. Utilizing the randomness of the hyperparameters, we can generate fiber structures similar to but different from the dataset, avoiding the hassle of manual parameter tuning. This method can be combined with predictive neural networks to achieve automatic generation and iterative optimization of the two-dimensional free-space parameters of the fiber cross-section, breaking free from the constraints of fixed feature parameters and possessing high degrees of freedom and flexibility. This provides a new approach for the design and optimization of fiber structures with high degrees of freedom parameter spaces. Summary of the Invention

[0005] This invention addresses the problems of low degree of freedom and low flexibility in the reverse design and optimization of optical fibers by proposing a method for compressing the two-dimensional parameter space of photonic crystal fibers and automatically generating random structures based on a convolutional adversarial autoencoder network. The method transforms the freely distributed two-dimensional refractive index of the fiber cross-section into a two-dimensional parameter matrix. A convolutional adversarial autoencoder then compresses this matrix into a low-dimensional hyperparameter space following a Gaussian distribution. A decoder then decodes the random Gaussian hyperparameters to generate arbitrary two-dimensional cross-sectional structure parameters that conform to the characteristics of the optical fiber. This method can be further combined with a predictive neural network to randomly generate two-dimensional fiber structures through the autoencoder network and adjust them based on the optical characteristics fed back from the predictive neural network. This achieves automatic generation and iterative optimization of the fiber structure, and the optimized parameter space of the fiber, with its freely distributed two-dimensional refractive index across the cross-section, possesses extremely high degree of freedom and flexibility.

[0006] The purpose of this invention is to automatically and randomly generate different two-dimensional structures of photonic crystal fibers using a convolutional adversarial autoencoder (CAE) network. Taking an air-hole photonic crystal fiber as an example, the material of this fiber is pure silicon dioxide. Different parameters, such as the number, arrangement, spacing, number of layers, and size of each air hole, correspond to different two-dimensional cross-sectional structures of the photonic crystal fiber. These parameters collectively constitute the structural parameter space of the fiber. By changing the fiber's structural parameters, the transmission mode characteristics that the fiber can support will change. The proposed invention, based on a CAE network, can automatically and randomly generate different two-dimensional cross-sectional structures of photonic crystal fibers. This method first uses an encoder to compress the freely distributed two-dimensional refractive index matrix of the photonic crystal fiber cross-section into a low-dimensional hyperparameter space following a Gaussian distribution. Then, a decoder decodes the random Gaussian hyperparameters to generate an arbitrary two-dimensional cross-sectional structure parameter matrix that conforms to the characteristics of photonic crystal fibers. The decoder can act as an independent structure generation network, using the low-dimensional hyperparameters following a Gaussian distribution as input to randomly generate different air-hole photonic crystal fiber structures. This technical solution is also applicable to the prediction of other optical structure characteristics.

[0007] The technical solution adopted in this invention includes the following steps:

[0008] 1. Collect and generate a matrix of refractive index parameters for two-dimensional materials with different cross-sections of photonic crystal fibers;

[0009] 2. Construct a suitable convolutional adversarial autoencoder network structure;

[0010] 3. Train the convolutional adversarial autoencoder network model using the collected dataset and save the model;

[0011] 4. Use the test set to test the performance of the encoder and decoder in the convolutional adversarial autoencoder network model;

[0012] 5. Save the decoder from the best-performing convolutional adversarial autoencoder network model, and use random Gaussian hyperparameters to decode and generate an arbitrary two-dimensional cross-sectional structure parameter matrix that conforms to the characteristics of photonic crystal fiber.

[0013] This invention provides a method for two-dimensional parameter spatial compression and automatic generation of random structures in photonic crystal fibers based on convolutional adversarial autoencoders, the advantages of which are:

[0014] 1. This method can be combined with a predictive neural network to randomly generate a two-dimensional fiber structure through an autoencoder network and adjust it according to the optical characteristics fed back by the predictive neural network, thereby realizing the automatic generation and iterative optimization of the fiber structure. Moreover, the optimization parameter space of the fiber is a two-dimensional refractive index freely distributed in the cross section, which has extremely high degree of freedom and flexibility.

[0015] 2. Compared with traditional manual parameter tuning methods, this method does not rely on researchers' physical intuition and design experience, and can achieve automatic generation and iterative optimization, which greatly reduces manual time and computational costs and improves the efficiency of structural design optimization.

[0016] 3. Compared with previously reported fiber structure design methods based on neural networks and optimization algorithms, this method transforms all possible structural distributions of the cross-section of photonic crystal fiber into a parameter optimization space, freeing it from the constraints of fixed characteristic parameters. It directly generates and optimizes the parameters in the two-dimensional refractive index distribution matrix parameter space, without being limited to specific parameters, thus greatly improving the freedom and flexibility of the design.

[0017] 4. To address the issue of excessively large data volume in the optical fiber cross-section parameter space and two-dimensional matrix, an encoder is used to reduce the dimensionality of the optical fiber structure's two-dimensional matrix into a low-dimensional hyperparameter space that follows a Gaussian distribution. This removes potential redundant variables in the parameter space, significantly reducing the learning difficulty for the decoder, making the network easier to train, and saving computational resources.

[0018] 5. Convolutional layers were added to both the encoder and decoder, which improved the model's feature learning ability, effectively reduced the occurrence of overfitting problems, and accelerated the training speed of the model. Attached Figure Description

[0019] Figure 1 : A schematic diagram of an example photonic crystal fiber structure automatically and randomly generated by this invention;

[0020] Figure 2 A schematic diagram of the two-dimensional matrix corresponding to the refractive index distribution of the cross-section structure of a photonic crystal fiber;

[0021] Figure 3 The flowchart of the two-dimensional parameter space compression and random structure automatic generation method for photonic crystal fiber based on Convolutional Adversarial Autoencoder (CAAE) proposed in this invention is shown below.

[0022] Figure 4 : A schematic diagram of the convolutional adversarial autoencoder network topology used in this invention;

[0023] Figure 5 The flowchart of the proposed method combined with a prediction neural network (PNN) for optical fiber structure optimization is shown below.

[0024] Figure 6 The test set was used to perform the test, and the resulting reconstruction of the photonic crystal fiber structure is shown in the comparison diagram. The left column shows the original structure of the test dataset, and the right column shows the fiber structure generated by the network.

[0025] Figure 7 The reconstructed photonic crystal fiber structure diagram is obtained by inputting a random 36-dimensional Gaussian distribution hyperparameter into the decoder. Two typical examples are given here: the left side shows a better randomly generated fiber structure diagram, and the right side shows a poorly generated fiber structure diagram. Detailed Implementation

[0026] The present invention and technical solution will be further described in detail below with reference to the accompanying drawings.

[0027] A method for two-dimensional parameter spatial compression and automatic generation of random structures in photonic crystal fibers based on convolutional adversarial autoencoders (CAEs), taking a photonic crystal fiber with concentric circular gratings and air-hole structures as an example, such as... Figure 1 As shown, different parameters such as the number, arrangement, spacing, number of layers, and size of each air hole in an optical fiber correspond to different two-dimensional cross-sectional structures of photonic crystal fibers. These parameters together constitute the structural parameter space of the optical fiber. By changing the structural parameters of the optical fiber, the transmission mode characteristics that the optical fiber can support will change.

[0028] First, the free distribution of the refractive index of the two-dimensional material in the fiber cross-section is converted into a two-dimensional parameter matrix. By changing various parameters such as the number, arrangement, spacing, number of layers, and size of each air hole, different two-dimensional structural parameter matrices for the photonic crystal fiber cross-section can be obtained. In the example, the parameter matrix size is set to 640×640, and the matrix values ​​corresponding to the air holes are set to the number "0", while pure silica material is set to the number "1". Following this rule, a two-dimensional numerical matrix of size 640×640 is generated. To shorten the training time of the neural network, taking advantage of the symmetry of the fiber structure, the original fiber structure is cut by 1 / 4, changing the size to 320×320. Under these parameters, the two-dimensional cross-sectional structural parameter matrix of a photonic crystal fiber model with concentric circular grids and air holes is as follows. Figure 2 As shown.

[0029] Figure 3This is a flowchart illustrating the proposed method for two-dimensional parameter space compression and automatic random structure generation of photonic crystal fibers based on a Convolutional Adversarial Autoencoder (CAAE) network. First, this invention collects photonic crystal fiber structure models with different concentric circular grating air apertures to obtain the corresponding two-dimensional cross-sectional structure parameter matrices as the dataset for the CAAE network. Next, a suitable CAAE network model is constructed, and the collected training dataset is fed into the constructed CAAE network model for training, resulting in a network model with low loss and high reconstruction accuracy. This model is then saved. Finally, the performance of the encoder and decoder in the trained CAAE network is tested using a test dataset. By comparing the fiber structure in the test set with the reconstructed fiber structure, the accuracy of the network model is demonstrated.

[0030] Figure 4 The diagram shows the CAAE network topology proposed in this invention for compressing the two-dimensional parameter space of optical fibers and automatically generating random structures. The designed convolutional adversarial autoencoder (CAAE) network is a generative model consisting of an encoder, decoder, and discriminator. The encoder and decoder are coupled together, forming an autoencoder network. To improve the model's feature learning ability and effectively reduce overfitting, convolutional layers are added to both the encoder and decoder, working in conjunction with fully connected layers to perform compression encoding and decoding functions, respectively. The encoder's role is to extract features from the two-dimensional refractive index distribution structure parameter matrix of the optical fiber through convolutional layers, and then use fully connected layers to compress and encode the extracted features into low-dimensional hyperparameters (an example is a 36-dimensional hyperparameter, i.e., the 36-D Hyperparameter shown in the diagram). This ensures that while removing potentially redundant parameter variables, it still contains the important structural parameters of the two-dimensional parameter matrix of the optical fiber. The decoder then decodes the hyperparameters through fully connected layers, uses transposed convolutions for upsampling, and reconstructs a two-dimensional structural parameter matrix of the optical fiber that is similar to but different from the input.

[0031] To ensure the compressed hyperparameters conform to a Gaussian data distribution, a discriminator is added to the autoencoder, making the hyperparameters follow a predefined Gaussian distribution. Since the hyperparameters have few dimensions, the discriminator does not use convolutional layers but instead employs a simple fully connected neural network to perform binary classification. The discriminator and encoder undergo adversarial training, making the discriminator unable to distinguish whether the hyperparameters originate from the encoder's compressed encoding or from the pre-defined Gaussian distribution model (i.e., the Pre-defined Model distribution shown in the figure). Ultimately, this ensures the hyperparameters have the same data distribution as the pre-defined Gaussian distribution model. In this way, the pre-defined Gaussian distribution model contains the main features of all fiber 2D parameter matrices in the training set. To effectively avoid gradient vanishing during network training, the LeakyReLU activation function is used as the neuron activation function. During training, each iteration consists of two steps. First, the encoder and discriminator engage in a game-like interaction, updating their weights using an adversarial loss function. Second, the mean squared error loss between the reconstructed fiber 2D refractive index distribution structure and the original input is calculated, and the decoder's weights are updated using a backpropagation algorithm. Once the convolutional adversarial autoencoder network model is trained, the decoder can function as a standalone generative model. It can randomly select a set of low-dimensional hyperparameters from a predefined Gaussian distribution model as input to the decoder and use the decoder's decoding capabilities to generate a novel two-dimensional cross-sectional structure parameter matrix that conforms to the characteristics of photonic crystal fibers.

[0032] The method proposed in this invention can be further combined with predictive neural networks, such as... Figure 5 As shown, random 36-dimensional arbitrary hyperparameters are generated by a Gaussian data generator and input into a decoder to randomly generate a two-dimensional fiber structure. This fiber structure can be input into a prediction neural network (PNN) and adjusted according to the optical characteristics fed back by the prediction neural network, realizing the automatic generation and iterative optimization of the fiber structure. Moreover, the optimization parameter space of the fiber is a two-dimensional refractive index with free distribution in the cross section, which has extremely high degree of freedom and flexibility.

[0033] Figure 6The image shows the prediction results of the convolutional adversarial autoencoder network tested using the test dataset, verifying the accuracy of the network model. Since the values ​​in the reconstructed 2D matrix from the decoder are between 0 and 1, we set a transformation threshold to convert each value in the reconstructed 2D matrix to either "0" or "1", which is then displayed as an image. The dataset used to build and train the example network contains 2050 fiber optic structures, with 1845 in the training set and 205 in the test set. After training, the network model was saved and tested using the test set (205 structures). 191 structures were reconstructed well, and 14 structures were reconstructed poorly, resulting in a reconstruction efficiency of 93.17%. Figure 6 The left column shows the original structure of the test dataset, and the right column shows the fiber optic structure generated by the network. The first row of images shows an example of a well-reconstructed fiber optic structure, and the second row shows an example of a poorly reconstructed fiber optic structure, where the air holes are irregularly shaped.

[0034] Once the convolutional adversarial autoencoder network model is trained, the decoder can function as a standalone generative model. Figure 7 The diagram shows randomly generated air-hole photonic crystal fiber structures obtained through a decoder using random 36-dimensional hyperparameters following a Gaussian distribution. Only two typical examples are shown here: the left side displays a well-generated fiber structure, while the right side shows a poorly generated one. We randomly input 7200 hyperparameters (200 sets × 36 dimensions), obtaining 200 fiber structures. Of these, 167 structures were reconstructed well, and 33 were reconstructed poorly, resulting in a reconstruction efficiency of 83.5%.

[0035] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for two-dimensional parameter spatial compression and automatic generation of random structures in photonic crystal fibers based on convolutional adversarial autoencoders, characterized in that: The designed convolutional generative adversarial auto-encoder network for automatic generation of photonic crystal fiber structure is a generative model composed of an encoder, a decoder and a discriminator. The encoder extracts features from the two-dimensional refractive index distribution structure parameter matrix of the fiber through convolutional layers, and uses a fully connected layer to compress and encode the extracted features into a low-dimensional hyperparameter. This allows the fiber two-dimensional parameter matrix to contain important structural parameters while removing redundant parameter variables. The decoder decodes the hyperparameters through a fully connected layer and uses transposed convolution for upsampling to reconstruct a two-dimensional structural parameter matrix similar to the input but different. The role of the discriminator is to conduct adversarial training with the encoder so that the discriminator cannot distinguish whether the hyperparameters come from the encoder compression encoding or from the pre-set Gaussian distribution model. Finally, the hyperparameters have the same data distribution as the pre-set Gaussian distribution model. Specifically, the method comprises the following steps: Step 1: Collect and generate different fiber cross-sectional two-dimensional material refractive index parameter matrices; Step 2: Build a suitable convolutional generative adversarial auto-encoder network structure; Step 3: Train the convolutional generative adversarial auto-encoder network model using the collected data set and save the model; Step 4: Test the performance of the encoder and decoder in the convolutional generative adversarial auto-encoder network model using the test set; Step 5: Save the decoder in the convolutional generative adversarial auto-encoder network model with the best test effect, and use random Gaussian hyperparameters to decode to generate an arbitrary two-dimensional cross-sectional structural parameter matrix that meets the characteristics of photonic crystal fibers. 2.The method of generating photonic crystal fiber two-dimensional parameter space compression and random structure automatically based on convolutional adversarial auto-encoding network according to claim 1, wherein: The data set for training and testing the convolutional generative adversarial auto-encoder network is the two-dimensional structural parameter matrix of the photonic crystal fiber cross section, and the value of each point in the matrix corresponds to the refractive index of the fiber material. 3.The method of photonic crystal fiber two-dimensional parameter space compression and random structure automatic generation based on convolutional adversarial auto-encoding network according to claim 1, wherein: In step 4, for the encoder, the Kolmogorov-Smirnov test method is used to determine whether the hyperparameters obtained after compression and encoding of the encoder conform to the pre-set Gaussian distribution, and the mean square error loss between the hyperparameters and the Gaussian distribution is calculated to measure the fitting degree of the hyperparameters to the Gaussian distribution. 4.The method of generating photonic crystal fiber two-dimensional parameter space compression and random structure automatically based on convolutional adversarial auto-encoding network according to claim 1, wherein: In step 5, after adjusting the network parameters, a trained optimal network is saved, and the decoder is taken out as an independent generation model. The 36-dimensional hyperparameters conforming to the Gaussian distribution are used as the input of the decoder, and the randomness of the hyperparameters is used to generate fiber structures similar to the data set but different.

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