Composite function metasurface reverse design method based on transfer learning

Abstract

The invention provides a reverse design method of a composite function metasurface based on transfer learning, relates to the field of metamaterial design and optimization, and solves the problem of low efficiency of a traditional design method of a metasurface with a complex structure. Comprising the following steps: generating a data set containing various metasurface structure parameters and corresponding spectral responses; building a deep prediction neural network taking the unit structure parameters as input and the spectral response as output; the trained network is combined with a genetic particle swarm optimization algorithm, metasurface phase distribution, transmissivity and other requirements determined in advance are used as objective functions, and optimal parameters are searched through multiple iterations; and migrating universal features learned on the large-scale data set by the source domain network model through a parameter fine tuning method, applying the universal features to a new small data set target domain, repeating the previous process until all parameters are determined, and completing the design. According to the method, the complex metasurface design efficiency can be improved, the neural network performance is ensured, meanwhile, the requirement of the deep learning method for the data collective quantity is reduced, the robustness of the model is improved, and a low-cost practical scheme is provided for metasurface inverse design.

Description

Technical Field

[0001] The present invention relates to the field of optical metamaterials, and in particular to a method for reverse design of composite functional metasurfaces based on transfer learning. Background Art

[0002] Metasurfaces are two-dimensional planar devices composed of subwavelength nanostructures. They offer significant advantages in being ultrathin, lightweight, and highly integrated, and related research has seen rapid development in recent years. By precisely controlling the phase, amplitude, and polarization of light waves, metasurfaces can achieve functions at the nanoscale that are difficult for traditional optical devices to accomplish, such as multifunctional imaging, holographic displays, and polarization control. Furthermore, metasurfaces offer strong design flexibility and excellent manufacturing compatibility, allowing for large-scale production using existing nanofabrication technologies. These metasurfaces offer novel solutions for the miniaturization, multifunctionality, and high performance of next-generation optical devices, significantly promoting the innovation and development of optical technology.

[0003] Designing metasurfaces through phase control is a core method for achieving various functionalities. Its basic principle is to adjust the geometric shape, size and arrangement of subwavelength nanostructures to introduce a specific phase distribution in space, thereby achieving precise manipulation of light waves. Currently, commonly used design methods include phase modulation based on resonant units, propagation phase control, and geometric phase control. As the functional complexity of metasurfaces increases, the unit structure needs to simultaneously meet multi-dimensional optical properties such as phase, amplitude, and polarization during the design process, while taking into account the constraints in the manufacturing process. The parameter space is huge and mutually coupled. This not only increases the difficulty of design and makes it difficult to efficiently determine the optimal solution through traditional methods, but also restricts the performance optimization and further development of metasurface functions. It is urgent to introduce more advanced computational methods and optimization algorithms to break through the existing bottlenecks.

[0004] Current metasurface design methods can be mainly divided into three categories: traditional design methods, optimization algorithm design methods, and deep learning design methods. Traditional design methods usually determine the basic parameter range based on analytical models or semi-analytical models, and rely on the designer's experience and physical intuition to make simulation adjustments. They are suitable for metasurfaces with simple functions, but they are difficult to efficiently handle multi-parameter coupling problems when the functions are complex. The optimization algorithm design method uses a global search strategy to find the optimal solution in the multi-parameter space, which significantly improves the design efficiency, but still has limitations such as large computational complexity and slow convergence speed. The deep learning design method constructs a neural network model and uses a large amount of data training to achieve the mapping from target function to structural parameters. It has the advantages of fast speed and strong generalization ability, and provides a new paradigm for the efficient design of metasurfaces. However, it still needs to solve problems such as difficulty in data acquisition and insufficient model interpretability.

[0005] Combining optimization algorithms with deep learning for metasurface design can fully leverage the advantages of both, accelerating the design process while handling more complex functional requirements and constraints, providing new solutions for the efficient design and high-performance implementation of metasurfaces. Summary of the Invention

[0006] In response to the defects or shortcomings in the existing technology, the present invention provides a reverse design method for composite functional metasurfaces based on transfer learning. By combining the forward prediction neural network and the genetic particle swarm optimization algorithm, the structural parameters can be determined quickly and accurately, which helps to improve the efficiency and actual performance of metasurface design.

[0007] The technical solutions of the present invention are as follows:

[0008] A method for reverse design of a composite functional metasurface based on transfer learning, characterized by comprising the following steps:

[0009] S1. Determine the basic structure of the metasurface and the corresponding structural parameters, as well as the spectral response corresponding to each set of parameters, and collect and process the data;

[0010] S2. Build a forward spectral prediction neural network model, including a residual structure and fully connected layers, to learn the relationship between structural parameters and the physical relationship of spectral response;

[0011] S3. Migrate the parameters of the neural network model trained for the current metasurface structure and complete rapid training on other datasets through fine-tuning;

[0012] S4. Calculate the target phase distribution of the metasurface, combine the trained neural network as a transient simulator with the genetic particle swarm optimization algorithm, and use the optimization algorithm to search for the basic structural parameters of the metasurface that meet the requirements in a large range of parameter space. Arrange the basic structures as needed to finally obtain a composite functional metasurface.

[0013] In step S1, the metasurface unit structure includes the length and width of a rectangular cell or the radius of a circular cell, the height of the nanocolumns, and the cell period. The spectral response includes the changes in the phase delay and transmittance of the outgoing light after linearly polarized light in different directions enters the cell as the wavelength of the incident light changes.

[0014] The process collected a total of five data sets, with the wavelength of the incident light maintained between 700nm and 900nm. Among them, there were 25,500 sets of rectangular nanorod cell parameters and corresponding phase distributions when linear polarization in the x direction was incident, 2,500 sets each of rectangular nanorod cell parameters and corresponding phase distributions when linear polarization in the y direction was incident, rectangular nanorod cell parameters and corresponding transmittance distributions when linear polarization in the x and y directions was incident, and circular nanorod cell parameters and corresponding phase distributions.

[0015] In step S2, the forward prediction neural network model includes an input layer, five fully connected layers, and an output layer, where each fully connected layer is followed by a normalization layer and an activation function. The first four fully connected layers form two residual structures, and the last fully connected layer is used to process the output dimension. The loss function of the network is the mean square error, and the accuracy is defined by the cosine similarity.

[0016] In step S3, the forward prediction neural network trained in step S2 is used as a pre-trained model, the first four fully connected layers in the pre-trained model are frozen, the network weights of the frozen part are all loaded into the new task, and the unfrozen layers of the model are trained using the dataset of the new task.

[0017] The data structure of the new task is consistent with that of the source task, and the data features have certain similarities. The amount of the data set used for the new task is one tenth of that of the source task.

[0018] In step S4, the metasurface phase distribution is determined by the performance of the target device. The genetic particle swarm algorithm uses binary coding to encode the metasurface structural parameters. The update phases of the particle swarm algorithm and the genetic algorithm are combined. The optimization objective function is set according to the target phase distribution. The constraints include the range of structural parameters and the range of transmittance and phase distribution corresponding to the structure. In the process of calculating the fitness, the five trained forward prediction neural networks are used to realize the transformation of structural parameters to phase distribution and transmittance.

[0019] The technical effects of the present invention are as follows: (1) The forward residual spectrum prediction neural network proposed in the present invention can quickly and accurately predict the phase distribution of incident light wavelengths in the range of 700nm to 900nm based on given structural parameters, with a prediction error of about 0.02. (2) The transfer learning method proposed in the present invention is used in forward prediction neural networks with the same data structure and similar data distribution, and can achieve accuracy and loss values ​​close to those of the source task with 1 / 10 of the data set, greatly improving the generalization ability of the network model and improving design efficiency. (3) The present invention combines the trained forward prediction neural network with the genetic particle swarm optimization algorithm to achieve target parameter selection under multiple constraints, providing a practical idea for the design of composite functional metasurfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] To facilitate understanding of the technical solutions of the present invention, the following briefly describes the drawings involved in the embodiments or prior art. It should be noted that the drawings listed below are only examples of specific embodiments of the present invention, and those skilled in the art can also deduce other relevant drawings based on the provided drawings without inventive effort.

[0021] Figure 1This is a schematic diagram of the composite functional metasurface of the present invention, integrating collimation and polarization functions. Cells are typically composed of individual nanopillars of varying structures and sizes, used to control polarization. Arranging cells with different phase distributions as needed allows for operations such as light collimation and beam splitting based on polarization control. This implementation demonstrates the integration of linear polarization and collimation functions.

[0022] Figure 2 Schematic diagram of the forward residual spectrum prediction neural network structure of the present invention.

[0023] Figure 3 Schematic diagram of the transfer learning training method of the present invention.

[0024] Figure 4 This is a flow chart of the forward prediction neural network combined with the genetic particle swarm optimization algorithm of the present invention. First, the nanocolumns are encoded. Since the period and height of each cell in the hypersurface need to remain consistent, only the length L and width W of the rectangular nanocolumns and the radius R of the circular nanocolumns need to be encoded. The binary encoding method is used to encode the two parameters of the nanocolumns. Each three-digit parameter is composed of nine "0" or "1" codes, and an individual particle contains 18 bits of code. Initialize a population containing N particles, each particle represents a potential solution, and randomly generates its initial position X0 and speed V0. Then, the parameters corresponding to each particle are input into the trained neural network to obtain the predicted spectral response value. Calculate the difference Abs between the predicted value and the target value, and on this basis, bring it into the objective function to obtain the fitness value Fitness, update the individual optimal solution Pbest and the global optimal solution Gbest, and adjust the particle speed V according to the rules of the particle swarm algorithm. i and position X i In the iteration part, the operation of the genetic algorithm is introduced, including selecting particles with higher fitness values ​​as parents, performing crossover operations to generate new particles, and performing mutation operations on some particles to increase population diversity. If the fitness value Fitness decreases, the position X0 and speed V0 of the new particle group are reinitialized and the above steps are repeated; if the fitness value Fitness does not decrease, the speed V is updated for the old particle group. i and position X i , and repeat the subsequent cycles until the termination condition is met, it is considered to have reached the optimal fitness value Fitness, and the individual parameters that meet the requirements are output.

[0025] Figure 5 It is the loss value and accuracy rate during the forward prediction neural network training process of the present invention.

[0026] Figure 6 These are the loss values ​​and accuracy rates obtained by quickly training each small data set during the transfer learning process of the present invention.

[0027] Figure 7 The figure is the calculation result of the embodiment of the present invention in the simulation software. DETAILED DESCRIPTION

[0028] In order to more clearly illustrate the objectives, technical means and advantages of the present invention, the following will be described in detail with reference to specific embodiments and related drawings. It should be emphasized that the embodiments and their explanations listed herein are only used to illustrate the principles of the present invention and are not intended to limit the scope of the present invention.

[0029] Figure 1 Schematic diagram of the composite functional metasurface of the present invention. Figure 2 It is a schematic diagram of the forward residual spectrum prediction neural network structure of the present invention. Figure 3 Schematic diagram of the transfer learning training method of the present invention. Figure 4 This is a flow chart of the forward prediction neural network combined with genetic particle swarm optimization algorithm of the present invention. Figure 5 yes Figure 2 Loss and accuracy during the forward prediction neural network training process. Figure 6 yes Figure 3 The loss value and accuracy obtained by quickly training each small data set during the transfer learning process. Figure 7 yes Figure 4 The calculation results of the embodiment of the algorithm in the simulation software.

[0030] refer to Figures 1 to 7 As shown, a composite functional metasurface inverse design method based on transfer learning mainly includes the following steps:

[0031] S1. Determine the basic structure of the metasurface and the corresponding structural parameters, as well as the spectral response corresponding to each set of parameters, and collect and process the data;

[0032] S2. Build a forward spectral prediction neural network model, including a residual structure and fully connected layers, to learn the relationship between structural parameters and the physical relationship of spectral response;

[0033] S3. Migrate the parameters of the neural network model trained for the current metasurface structure and complete rapid training on other datasets through fine-tuning;

[0034] S4. Calculate the target phase distribution of the metasurface, combine the trained neural network as a transient simulator with the genetic particle swarm optimization algorithm, and use the optimization algorithm to search for the basic structural parameters of the metasurface that meet the requirements in a large range of parameter space. Arrange the basic structures as needed to finally obtain a composite functional metasurface.

[0035] The present invention provides a method for reverse design of composite functional metasurfaces based on transfer learning. This method improves the efficiency and actual performance of metasurface design through several key innovations. First, the present invention introduces a forward prediction residual neural network as an instantaneous simulator to replace traditional simulation software. Combined with the optimization algorithm, it greatly reduces the transformation time from parameters to spectral response in each iteration, improves the optimization efficiency and reduces the running memory. Secondly, the present invention provides a fast and efficient neural network training paradigm, which can realize the spectral prediction model of different structural units with a small amount of data on the basis of the existing network, and can achieve a training effect close to that of the source data set.

[0036] The specific embodiments of the present invention are further described below:

[0037] In the data of the metasurface design described in step S1, the spectral response of each set of data is 100-dimensional, including the changes of the phase delay and transmittance of the outgoing light after the linearly polarized light in different directions enters the cell with the wavelength of the incident light. The wavelength of the incident light is kept between 700nm and 900nm. The labels corresponding to the data are the four parameters of the 4-dimensional corresponding unit structure, such as Figure 2 75% of the data is used as the training set and 25% is used as the test set.

[0038] In the forward prediction residual neural network described in step S2, the parameters are transferred in the fully connected layer using the following formula:

[0039] F(x)=σ(w*x)+b

[0040] Where F(x) is the output vector, x is the input vector, σ is the activation function, w is the weight matrix, and b is the bias matrix. The activation function is the linear rectification function ReLU, and its mathematical expression is:

[0041] S(z)=max(0,z)

[0042] The parameter transfer method of the residual block part in the structure is:

[0043] H(x)=F(x)+x

[0044] Where x is the input data, F(x) is the result of the nonlinear mapping of the input data through the fully connected layer, and H(x) is the output. When backpropagation is used to update parameters, the gradient propagation formula is:

[0045]

[0046] During the training process, the mean square error is used as the loss function, and its expression is:

[0047]

[0048] Where R represents the true label value and R' represents the predicted value output by the network. The cosine similarity is used to evaluate the accuracy, and its expression is:

[0049]

[0050] After the network is trained for 500 epochs, Figure 5 As shown, the loss values ​​of the training set and test set dropped to 0.0217 and 0.0264, and the accuracy increased to 0.9641 and 0.9607.

[0051] In the transfer learning described in step S3, the source domain is the parameters of the rectangular nanocolumn cell and the corresponding phase distribution when the linear polarization in the x direction is incident. The corresponding source task neural network is the network trained with 25,500 sets of data in step S2. The target domain is the parameters of the rectangular nanocolumn cell and the corresponding phase distribution when the linear polarization in the y direction is incident, the parameters of the rectangular nanocolumn cell and the corresponding transmittance distribution when the linear polarization in the x and y directions is incident, and the parameters of the circular nanocolumn cell and the corresponding phase distribution. The corresponding target task neural networks are trained using 2,500 sets of data respectively through fine-tuning. During the training process, the parameters in the source neural network are first transferred to the target neural network, and then the parameters of the first four fully connected layers are frozen. Only the target data set is used to train the last fully connected layer and the output layer. The training results are as follows. Figure 6 As shown in the figure, to prevent overfitting, the early stopping method is used. It is stipulated that the training process should be stopped when the loss value does not decrease for 20 consecutive rounds. Therefore, some networks are only trained for about 400 rounds. The loss values ​​of the four networks are all below 0.093, and the accuracy rates are all above 0.964.

[0052] In the genetic particle swarm optimization algorithm described in step S4, different optimization objective functions and constraints are set for different nanopillar structures. The rectangular nanopillar is represented as:

[0053] Min||Phase prex (L,W)-Phase prey (L,W)|-180|

[0054] st|Phase pre -Phase obj |≤15°

[0055] Transmit pre >0.8

[0056] L∈[90,300],W∈[90,300]

[0057] That is, we hope to ensure the phase distribution when the polarized light in the x and y directions is incident. prex and Phase preyWhen the difference is close to π, the phase distribution pre The value of the target phase obj The phase difference is less than 15°, and the transmittance is pre More than 80%. Circular nanopillars are represented by:

[0058] Min|Phase pre (R)-Phase obj |

[0059] stR∈[45,150]

[0060] That is, the desired phase distribution Phase pre The value of the target phase obj As close as possible. These requirements are determined by the performance of the designed metasurface. In this example, they are used to ensure that the cells can convert incident light into linearly polarized light. The constraints on length, width, and radius are determined by machining accuracy and period.

[0061] During the algorithm optimization process, Figure 4 As shown in the figure, the maximum number of iterations is set to 100, the number of particle swarms N = 200, the initial positions are randomly distributed in the definition domain of the constraint condition on the size, the initial velocities are randomly distributed in [-1, 1], the inertia weight during the iteration process is 0.8, the genetic mutation probability is 0.1, and the crossover probability is 0.6.

[0062] The method optimizes the metasurface parameters according to the collimated target phase, and the target phase is obtained according to the following formula:

[0063]

[0064] Select wavelength λ = 795nm, focal length f = 76um, and the cell phase modulation can be obtained. Relationship with radius r.

[0065] The simulation results of the parameters after the algorithm optimization are as follows Figure 7 As shown, the xz-plane focusing effect is significant. Based on the normalized z-axis electric field distribution, the focal point is located at 77.13 μm from the metasurface, close to the theoretical design value of 76 μm. At the same time, the xy-plane spot at the focal point is small and bright, and the corresponding polarization ellipse approximates linear polarization, showing performance close to expectations.

[0066] The parts not elaborated in detail in this specification are all conventional technologies well known to those skilled in the art. It should be noted that the above description is intended to provide technical personnel in the relevant fields with an understanding of the present invention, but should not be regarded as limiting the scope of protection of the present invention. Any equivalent replacement, optimization adjustment or simplified implementation of the above content without departing from the core idea of ​​the present invention shall fall within the scope of the claims of the present invention.

Claims

1. A method for reverse design of composite functional metasurfaces based on transfer learning, characterized in that: The following steps are involved: S1. Determine the basic structure of the metasurface and the corresponding structural parameters, as well as the spectral response corresponding to each set of parameters, and collect and process the data; S2. Build a forward spectral prediction neural network model, including a residual structure and fully connected layers, to learn the relationship between structural parameters and the physical relationship of spectral response; S3. Migrate the parameters of the neural network model trained for the current metasurface structure and complete rapid training on other datasets through fine-tuning; S4. Calculate the target phase distribution of the metasurface, combine the trained neural network as a transient simulator with the genetic particle swarm optimization algorithm, and use the optimization algorithm to search for the basic structural parameters of the metasurface that meet the requirements in a large range of parameter space. Arrange the basic structures as needed to finally obtain a composite functional metasurface.

2. The method for reverse design of composite functional metasurfaces based on transfer learning according to claim 1, characterized in that: In step S1: The metasurface unit structure includes the length and width of a rectangular cell or the radius of a circular cell, the height of the nanocolumns, and the cell period. The spectral response includes the changes in the phase delay and transmittance of the outgoing light after linearly polarized light in different directions enters the cell as the wavelength of the incident light changes.

3. The method for inverse design of a composite functional metasurface based on transfer learning according to claim 1 or 2, characterized in that: A total of five data sets were collected, and the wavelength of the incident light was kept between 700nm and 900nm. Among them, there were 25,500 sets of rectangular nanorod cell parameters and the corresponding phase distribution when linear polarization in the x direction was incident, 2,500 sets of rectangular nanorod cell parameters and the corresponding phase distribution when linear polarization in the y direction was incident, 2,500 sets of rectangular nanorod cell parameters and the corresponding phase distribution when linear polarization in the x and y directions was incident, and 2,500 sets of circular nanorod cell parameters and the corresponding phase distribution.

4. The method for reverse design of composite functional metasurfaces based on transfer learning according to claim 1, characterized in that: In step S2: The forward prediction neural network model includes an input layer, five fully connected layers, and an output layer. Each fully connected layer is followed by a normalization layer and an activation function. The first four fully connected layers form two residual structures, and the last fully connected layer is used to process the output dimension. The loss function of the network is the mean square error, and the accuracy is defined by cosine similarity.

5. The method for reverse design of composite functional metasurfaces based on transfer learning according to claim 1, characterized in that: In step S3: Use the forward prediction neural network trained in step S2 as the pre-trained model, freeze the first four fully connected layers in the pre-trained model, load all the frozen network weights into the new task, and use the dataset of the new task to train the unfrozen layers of the model.

6. The method for reverse design of a composite functional metasurface based on transfer learning according to claim 1 or 5, characterized in that: The data structure of the new task is consistent with that of the source task, and the data features have certain similarities. The amount of the data set used for the new task is one tenth of that of the source task.

7. The method for reverse design of composite functional metasurfaces based on transfer learning according to claim 1, characterized in that: In step S4: The metasurface phase distribution is determined by the performance of the target device. The genetic particle swarm algorithm uses binary coding to encode the metasurface structural parameters. The update phases of the particle swarm algorithm and the genetic algorithm are combined. The optimization objective function is set according to the target phase distribution. The constraints include the range of structural parameters, as well as the transmittance and phase distribution ranges corresponding to the structure. In the process of calculating the fitness, five trained forward prediction neural networks are used to realize the transformation of structural parameters into phase distribution and transmittance.

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