A deep learning-based inverse design method for microwave absorption metasurfaces
By employing a deep learning-based inverse design method, and utilizing convolutional neural networks and genetic algorithms to optimize the design of microwave absorbing metasurfaces, the problem of low efficiency in traditional design was solved, achieving an efficient and automated design process and discovering high-performance structures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies for microwave absorbing metasurface design suffer from problems such as low design efficiency, reliance on human experience and manual trial and error, and difficulty in exploring high-dimensional design spaces.
A deep learning-based inverse design approach is adopted, which involves constructing a convolutional neural network (CNN) for forward prediction model training and combining it with a genetic algorithm (GA) for inverse optimization, thereby achieving rapid prediction and optimization of geometric or material parameters and electromagnetic properties.
It significantly improves design efficiency, shortens the design cycle, reduces reliance on electromagnetic simulation software, enhances design repeatability and consistency, discovers high-performance structures, and lowers the technical threshold.
Smart Images
Figure CN122174653A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of electromagnetic functional materials and metamaterial structure design technology, and in particular to an inverse design method for microwave absorbing metasurfaces based on deep learning. Background Technology
[0002] Microwave-absorbing metasurfaces represent the forefront of contemporary electromagnetic functional materials. As a novel metamaterial with intricate artificial structures, their core lies in achieving efficient absorption and flexible control of electromagnetic waves in specific frequency bands through precise design and periodic arrangement of unit structures at the subwavelength scale. These materials can effectively reduce the radar cross-section of targets in radar stealth technology, suppress unnecessary electromagnetic interference and radiation leakage in the field of electromagnetic compatibility, and contribute to building anti-interception and anti-detection communication environments in communication security. Therefore, they possess broad and crucial application value.
[0003] Traditional metasurface design generally adopts a cyclical model of "human experience-based pre-design - electromagnetic simulation verification - parameter trial and error adjustment": Designers first pre-design possible structural prototypes based on classical electromagnetic theory and past experience, such as common patch type, slot type or multi-layer composite unit; then they use professional electromagnetic simulation software such as CST and HFSS to perform full-wave simulation to evaluate its absorption spectrum, reflectivity and other performance indicators; if the results do not meet expectations, they need to rely on personal experience to manually adjust a few geometric parameters (such as structural side length, dielectric thickness, period size, etc.) and re-simulate and verify, and so on in a cycle. This approach has profound limitations: on the one hand, due to the complexity of the unit structure and the intricate electromagnetic interactions, a single full-wave simulation often takes a huge amount of time, ranging from tens of minutes to several hours, resulting in a complete design optimization cycle that may last for weeks or even months, leading to low R&D efficiency; on the other hand, manual adjustments can usually only traverse a very limited number of parameter combinations, essentially a local search in a low-dimensional space, making it difficult to systematically explore the overall high-dimensional design space, including material properties, geometric topology, and arrangement, and potentially overlooking non-traditional configurations with better performance; furthermore, the quality of the entire design process is highly dependent on the designer's professional knowledge and experience, and the lack of unified and standardized methods and processes among different designers makes it difficult to guarantee the reproducibility and universality of the design results.
[0004] Deep learning, as a crucial branch of machine learning, essentially constructs neural networks with multi-layered connections, simulating the human brain's inherent mechanism of abstracting and understanding information layer by layer. This technology can automatically learn and extract multi-layered feature representations directly from raw data, without relying on domain experts to manually design and extract features, thus achieving an "end-to-end" intelligent learning paradigm from raw input to final output. In engineering design and physical modeling, deep learning, through specific architectures such as convolutional neural networks and fully connected networks, can efficiently process highly structured data such as images and gridded parameter matrices, learning highly complex and non-linear mapping relationships between input variables and output responses.
[0005] The key technical challenge lies in how to introduce deep learning into the reverse design of microwave absorbing metasurfaces, enabling rapid prediction of everything from geometric or material parameters to electromagnetic properties such as absorption and reflection spectra. This would transform the traditional computational process, which relies on physical numerical simulations and takes hours, into near real-time forward inference, achieving a speed improvement of several orders of magnitude. Simultaneously, it would shift from the traditional model that relies on personal experience and manual trial and error to a modern model centered on data-driven approaches, model prediction, and intelligent search, thereby enhancing design efficiency. Summary of the Invention
[0006] Purpose of the Invention: To address the shortcomings of existing technologies, the purpose of this invention is to improve the design efficiency of microwave absorbing metasurfaces. A deep learning-based inverse design method for microwave absorbing metasurfaces is proposed. This method introduces deep learning into the inverse design of microwave absorbing metasurfaces, training a deep neural network using a large amount of "structural parameter-electromagnetic response" paired data. This allows for rapid prediction of everything from geometric or material parameters to electromagnetic properties such as absorption and reflection spectra, completing a performance prediction within seconds. This transforms the traditional computational process, which relies on physical numerical simulations and takes hours, into near real-time forward inference, enabling forward prediction and inverse design from structure to electromagnetic response parameters. This achieves a speed improvement of several orders of magnitude, significantly increasing the speed of metasurface design.
[0007] Technical solution: The microwave absorbing metasurface of the present invention is composed of microwave absorbing metasurface units, each of which includes a printed substrate. The top surface of the printed substrate is printed and cured with conductive ink forming a conductive pattern, and the bottom surface of the printed substrate has a metal base plate.
[0008] This invention relates to a deep learning-based inverse design method for microwave-absorbing metasurfaces, comprising the following steps:
[0009] Step 1), Metasurface Structure Parameterization and Data Acquisition: Each microwave absorbing metasurface unit is discretized in a plane into an m x n two-dimensional grid, corresponding to multiple small cells; among them, small cells printed with conductive ink material are assigned a first value, such as 1, and small cells without conductive ink material are assigned a second value, such as 0; the structure of the entire unit is thus uniquely represented by an m x n binary matrix; an m x n binary matrix is randomly generated by computer as an initial structure sample; for each structure sample, the corresponding three-dimensional physical model is constructed, simulation boundary conditions and excitations are set through the program interface to drive electromagnetic simulation software, and full-wave simulation calculation is performed. The S11 parameter is obtained by frequency sweeping within the target frequency band. The S11 parameter is the reflection coefficient that varies with frequency; the operation is repeated and all binary structure matrices and corresponding S11 parameter data are summarized to form a training dataset.
[0010] The conductive ink is composed of poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) (PEDOT:PSS), MXene, and multi-walled carbon nanotubes (MWCNT); the printing substrate is made of polyethylene terephthalate (PET); a metal base plate is set under the printing substrate, and the three are stacked in sequence to form a sandwich-type composite structure of "conductive pattern-printing substrate-total reflection metal back plate", in which the metal base plate is used to achieve total reflection of electromagnetic waves.
[0011] In the electromagnetic simulation phase, the sheet resistance, side length, and thickness of the conductive ink material were set. The relative permittivity, loss tangent, side length, and thickness of the printing substrate material were also set. The side length and thickness of the metal base plate were also set. The electromagnetic simulation frequency was from 2GHz to 18GHz. Within this range, 1001 points of the S11 parameters and their corresponding structure matrices were collected at intervals and saved as a set of data. Multiple simulations were performed, collecting multiple sets of data to serve as the training dataset for the forward prediction model.
[0012] Step 2), Data preprocessing: Normalize the binary structure matrix and the corresponding S11 parameters (electromagnetic response parameters) in the target frequency band, and perform data augmentation, that is, divide the dataset after the binary structure matrix is flipped horizontally or vertically into training set, validation set and test set according to a preset ratio.
[0013] Step 3) Construct a convolutional neural network (CNN) containing an encoder and decoder as a forward prediction model for training; the process is as follows:
[0014] 3.1) The encoder includes multiple cascaded convolutional modules, each containing a convolutional layer, an activation function layer, and a normalization layer; the decoder includes at least one fully connected layer, an activation function layer, and a regularization layer, and uses output layer mapping to obtain S11 parameters, with the output dimension of the output layer corresponding to the number of sampling points of the S11 parameters.
[0015] 3.2) Using the binary structure matrices in the training and validation sets as input, output the corresponding normalized S11 parameters; use mean squared error as the loss function;
[0016] 3.3) Backpropagation is performed using a network optimization algorithm to calculate the gradient and update the weights and bias parameters in the convolutional neural network. The forward prediction model is trained until the loss function converges, and a prediction mapping from metasurface structure to microwave absorption response is established.
[0017] 4) The inverse design objective is optimized and the fitness function is determined using a genetic algorithm. The process is as follows:
[0018] 4.1) Population initialization: Generate an initial population containing n individuals, each corresponding to a binary structure matrix;
[0019] 4.2) Calculate the predicted S11 parameter value of each individual in the population in the target frequency band using a positive prediction model, and assign a fitness value according to the preset absorption bandwidth and minimum reflection loss weighted objective function.
[0020] 4.3) The population is updated by selection, crossover, and mutation. Selection is based on fitness function value to retain superior individuals, crossover is to exchange coding segments of different individuals to fuse characteristics, and mutation is to flip some coding bits to maintain population diversity.
[0021] 4.4) When the fitness function value reaches the preset threshold or the maximum number of iterations, the individual with the highest fitness value is output as the optimal metasurface structure for reverse design.
[0022] In step 3), the encoder consists of three cascaded convolutional modules used to extract and compress features from the input structural parameters step by step. Each convolutional module includes, in sequence: a first convolutional layer, a first activation and normalization layer, a second convolutional layer, a second activation and normalization layer, and a pooling layer. Both the first and second convolutional layers use 2×2 convolutional kernels for feature extraction. Batch normalization is performed after each convolutional layer. Normalization is applied, followed by non-linear activation using the LeakyReLU activation function; the pooling layer is a max pooling layer, used to downsample the feature map and enhance the model's regularization capability; after three convolutional modules, a flattening layer is connected to convert the extracted two-dimensional feature map into a one-dimensional feature vector; the decoder includes a fully connected layer, followed by the LeakyReLU activation function and a Dropout layer; finally, the predicted electromagnetic response data is obtained by mapping through an output layer; the output layer contains 1001 neurons, and its output dimension corresponds one-to-one with the 1001 data points obtained by sampling the S11 parameter curve within the target frequency band.
[0023] In step 3), during the training of the positive prediction model, the loss function of the positive prediction model is:
[0024] (1)
[0025] Where n represents the number of samples, such as 1001; The S11 value for the i-th frequency point predicted by the CNN; Let S11 be the value of the i-th frequency point obtained through CST simulation.
[0026] In step 4), during the reverse design optimization, a genetic algorithm (GA) is used to dynamically optimize the reverse design objective and determine the fitness function. The process is as follows: 4.1) Population initialization: An initial population containing n metasurface structure codes is randomly generated, i.e., an initial population containing n individuals is generated, each individual corresponding to a binary structure matrix; 4.2) Electromagnetic response data calculation and fitness function assignment: The absorption performance of each individual in the population is quickly calculated using a forward prediction model, and a fitness value is assigned according to a preset bandwidth and minimum reflection loss weighted objective function; 4.3) Iterative evolution steps: The population is continuously updated through selection, crossover, and mutation operations. The selection operation retains superior individuals based on the fitness function value, the crossover operation exchanges the coding segments of different individuals to fuse characteristics, and the mutation operation randomly flips some coding bits to maintain population diversity; 4.4) Convergence output steps: When the fitness function value reaches a preset threshold or reaches the maximum number of iterations, the individual with the highest fitness function value is output as the optimal metasurface structure for reverse design.
[0027] In step 4), when using a genetic algorithm to optimize the inverse design objective and determine the fitness function, the genetic algorithm has two optimization modes. When the objective is to obtain the optimal result, the fitness function is a weighted linear combination of the electromagnetic performance indices corresponding to the metasurface structure:
[0028] (2)
[0029] Where EAB represents the effective absorption bandwidth of the metasurface structure in the target frequency band, defined as the proportion of the frequency range where the reflection loss S11 is less than a preset threshold (-10 dB), and a larger value is preferred; RL represents the minimum reflection loss value of the metasurface structure in the target frequency band, and a smaller value is preferred; F Let be a normalized function of RL, whose function value increases monotonically as RL decreases; α and β are EAB and F, respectively. The weighting coefficients satisfy α + β = 1.
[0030] When the goal is to obtain a preset, fixed electromagnetic response data, the fitness function is:
[0031] (3)
[0032] in This indicates that the prediction bandwidth of the neural network is effectively absorbed. This indicates the initial target effective absorption bandwidth. To provide a normalization function for RL predictions using neural networks, The normalization function for the initial target RL is set, where α and β are... and The weighting coefficients satisfy α + β = 1.
[0033] In step 4), the iterative evolution steps of the genetic algorithm include:
[0034] (1) Selection process: The tournament selection method is adopted. Each time, m individuals are randomly selected from the current population for fitness competition. The individual with the highest fitness is selected into the parent population. This process is repeated until a parent individual with the same size as the original population is selected.
[0035] (2) Crossover process: Individuals in the parent population are paired with a preset crossover probability and a two-point crossover strategy is adopted: two crossover points are randomly set on a one-dimensional binary chromosome sequence of length 100, and the gene coding segments of the two paired individuals are exchanged between the crossover points to generate offspring individuals.
[0036] (3) Mutation process: Select a portion of offspring individuals with a preset individual mutation probability and use a single-point bit flip mutation operation: For the selected individuals, randomly flip the binary values on their chromosome sequence with a preset gene mutation rate, that is, change the local cell value from '0' to '1' or from '1' to '0'.
[0037] In step (1), the metasurface unit structure is digitally parameterized and characterized. Each unit is discretized into a two-dimensional grid of m rows × n columns, where each grid unit is assigned a first value or a second value depending on whether conductive material is printed on it. The structure of the entire unit is represented by an m × n binary matrix. Multiple binary matrices are generated as structural samples by the program. For each structural sample, electromagnetic response data in the target frequency band is obtained by electromagnetic simulation.
[0038] Working principle: The forward prediction model used in this invention is a convolutional neural network (CNN) containing an encoder and a decoder; wherein, the encoder consists of multiple cascaded convolutional modules, each of which contains a convolutional layer, an activation function layer (LeakyReLU), and a normalization layer (Batch Normalization); the decoder includes at least one fully connected layer, an activation function layer, and a regularization layer; the final output layer contains multiple neurons, and its output dimension corresponds to the number of sampling points of the electromagnetic response parameters.
[0039] In the reverse design process of this invention, the first step is to construct a dataset: a structural parameter space for the microwave absorbing metasurface unit is defined, and multiple sets of structural parameter combinations are sampled and generated within this space; electromagnetic simulations are performed on each set of structural parameters to obtain their corresponding electromagnetic response parameter curves, forming a mapping dataset between structural parameters and electromagnetic responses; secondly, data preprocessing and partitioning are performed: the electromagnetic response data is normalized and data augmentation is performed, and then the dataset is divided into training, validation, and test sets; during the training of the forward prediction model, a convolutional neural network (CNN) is constructed as the forward prediction model; the structural parameters from the training and validation sets are used as input to... The normalized electromagnetic response data is used as the output target to train the forward prediction model until its loss function converges, thereby establishing a high-precision and fast prediction mapping from the metasurface structure to its microwave absorption response. During the reverse design optimization, a genetic algorithm optimizer is constructed, and a fitness function is determined, which takes the target absorption bandwidth and minimum reflection loss as the core optimization objectives. The trained forward prediction model is embedded in the genetic algorithm (GA) as a fast evaluator of individual fitness. Through the iterative evolution of the genetic algorithm, the parameters of the metasurface structure that make the fitness function value optimal are automatically searched and output, thus completing the reverse design from the target performance to the physical structure.
[0040] Beneficial effects: Compared with the prior art, the present invention has the following advantages:
[0041] 1) This invention's deep learning-based inverse design method for microwave-absorbing metasurfaces achieves high-precision and rapid prediction of the microwave absorption response from the metasurface structure by constructing a convolutional neural network (CNN) forward prediction model. This replaces the traditional time-consuming electromagnetic simulation calculations, reducing the time for a single performance evaluation from minutes to milliseconds, thus improving design efficiency. This integrated "prediction-optimization" framework breaks through the limitations of traditional empirical design patterns and significantly reduces R&D time costs.
[0042] 2) This invention creatively embeds a trained CNN model into a genetic algorithm (GA) optimizer, forming an intelligent reverse design system. During optimization, two modes are employed: one is searching for the globally optimal performance, and the other is matching a preset target performance, providing flexible design strategy selection. Through iterative evolution of the genetic algorithm, a vast design space (e.g., a 10×10 grid) is created. It automatically searches for the optimal solution among possible structures, overcoming the curse of dimensionality problem faced by traditional methods, and can discover high-performance structures that are difficult to conceive through human experience.
[0043] 3) The reverse design method of this invention significantly lowers the technical threshold for microwave absorbing metasurface design. Users do not need a deep understanding of electromagnetic theory or extensive design experience; they only need to set performance parameters such as the target absorption bandwidth and minimum reflection loss, and the system can automatically output the optimal structural design scheme that meets the requirements. This intelligent design process not only improves the repeatability and consistency of the design but also reduces reliance on expensive electromagnetic simulation software, thereby lowering R&D costs and the demand for specialized technical personnel.
[0044] 4) The widespread application of this invention will strongly promote the transformation of electromagnetic functional material design from experience-driven to data-driven, and facilitate technological progress and product iteration in fields such as microwave absorption and stealth materials. This framework has good scalability and can be adapted to the design of other types of electromagnetic functional materials, providing a general technical solution for intelligent material design, and has significant industrial application value and socio-economic benefits.
[0045] 5) The reverse design method of this invention transforms the traditional model that relies on personal experience and manual trial and error into a modern model centered on data-driven, model prediction and intelligent search. This not only significantly improves design efficiency but also broadens the boundaries of performance optimization. It provides crucial speed support and decision-making foundation for subsequent intelligent automatic design based on optimization algorithms such as genetic algorithms and Bayesian optimization, making it possible to explore a vast high-dimensional parameter space efficiently and automatically. This opens up a new path for the research and development of next-generation high-performance, customizable microwave absorbing materials. Attached Figure Description
[0046] Figure 1 This is a schematic diagram of the structure of the microwave-absorbing metasurface in an embodiment of the present invention;
[0047] Figure 2 This is a flowchart of data collection in an embodiment of the present invention;
[0048] Figure 3 This is a flowchart of the forward prediction process used in this invention;
[0049] Figure 4 This is a flowchart of the reverse prediction process in this invention;
[0050] Figure 5 This is a schematic diagram of the forward neural network structure of the present invention;
[0051] Figure 6 The loss function curve for positive prediction training in this invention;
[0052] Figure 7 This is a diagram showing the prediction results of the reverse prediction method of this invention. Detailed Implementation
[0053] Example:
[0054] This invention presents a deep learning-based inverse design method for microwave-absorbing metasurfaces, establishing forward prediction and inverse design models from structure to electromagnetic response parameters, thereby improving the speed of microwave-absorbing metasurface design. In the following embodiments, the metal substrate is a copper sheet substrate 3.
[0055] Example 1
[0056] The inverse design method for microwave absorbing metasurfaces based on deep learning in this invention is as follows:
[0057] Step 1) Metasurface Structure Parameterization and Data Acquisition: The top surface of each absorbing metasurface unit is discretized into a 10x10 two-dimensional grid, corresponding to 100 small cells; among them, the small cells printed with conductive ink 1 are assigned the value "1", and the unprinted small cells are assigned the value "0"; the top surface pattern of the entire metasurface unit is thus uniquely mapped to a 10x10 binary structure matrix. The specific content of this binary structure matrix is the two-dimensional spatial distribution information composed of the values 0 and 1, which represents the arrangement pattern of the conductive ink; the binary structure matrix is automatically and randomly generated by a computer program (Python) as the initial structure sample; for each structure sample, the corresponding three-dimensional physical model is automatically constructed by the electromagnetic simulation software (CST StudioSuite 2024) through the program interface. In electromagnetic simulation, the modeling process is as follows: a copper sheet substrate with a side length of 30mm×30mm and a thickness of 0mm is created sequentially, as well as a printed substrate material with a side length of 30mm×30mm, a thickness of 4mm, a relative permittivity of 3.3, and a loss tangent of 0.015. Finally, based on the row and column coordinates of the values "1" in the binary structure matrix, a corresponding conductive ink patch model with a side length of 3mm×3mm, a thickness of 0mm, and a sheet resistance of 20Ω / sq is automatically generated at the corresponding spatial position on the upper layer of the printed substrate. Subsequently, simulation boundary conditions and excitations were set: the boundary conditions in the X and Y directions of the model were set as periodic unit cells to simulate an infinitely periodic metasurface array; the positive Z-axis was set as an expanded open boundary; a Floquet port was set as the excitation in the positive Z-axis direction, with the incident angle set as perpendicular (θ=0°, φ=0°), and two electromagnetic wave modes were considered; the frequency domain solver of the electromagnetic simulation software was called to perform full-wave simulation calculations, and frequency sweeping was performed within the target frequency band of 2GHz to 18GHz. After the calculation was completed, the S11 parameter data was extracted and exported: due to the presence of a copper sheet substrate with total internal reflection, the transmittance S21 is 0, and the amplitude of this S11 parameter data (i.e., the reflection coefficient varying with frequency within the 2GHz-18GHz frequency band) can be directly used to calculate and verify the broadband absorptivity of the metasurface corresponding to the binary structure matrix. Specifically, within the 2GHz~18GHz frequency range, 1001 data points from the S11 parameters and their corresponding binary structure matrices are collected at even intervals and saved as a set of data. The above automated generation, modeling, solving, and data export operations are iterated multiple times, for a total of 5000 simulations, collecting 5000 sets of data to form a training dataset for subsequent convolutional neural network (CNN) reverse engineering, such as... Figure 2 As shown.
[0058] The conductive ink 1 is composed of poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) (PEDOT:PSS), MXene, and multi-walled carbon nanotubes (MWCNTs). The printing substrate 2 is made of polyethylene terephthalate (PET). A copper sheet 3 is placed below the printing substrate 2. Using screen printing, the conductive ink 1 is printed onto the top surface of the printing substrate 2 according to a preset pattern, and then placed in an oven for drying and curing, thereby forming the conductive pattern on the substrate. Subsequently, a microwave low-loss epoxy resin adhesive is uniformly coated onto the bottom surface of the printing substrate, and the smooth copper sheet 3 is then attached and pressed onto the bottom surface of the printing substrate. Through the above assembly steps, layers are stacked sequentially from top to bottom to form the conductive ink 1. Figure 1 The sandwich-type composite structure shown is 'conductive pattern-printed substrate-total reflection metal backplate'. The bottom layer of the total reflection metal backplate (i.e., the copper sheet base plate 3) is used to completely block the transmission of incident electromagnetic waves to achieve total reflection of electromagnetic waves.
[0059] Step 2) Data Preprocessing: The binary structure matrix obtained in Step 1) and its corresponding electromagnetic response parameter data are matched and converted in format. Specifically, the electromagnetic response parameters are the S11 reflection coefficients of the metasurface in the 2GHz to 18GHz frequency band. First, the electromagnetic response parameter data is linearized (normalized): Since the original S11 parameter data are negative values on a logarithmic scale (dB), in order to adapt to the input and output range of the neural network and accelerate model convergence, the following formula is used to calculate the data at each frequency point, converting the logarithmic S11 data into linear amplitude values in the [0,1] interval, which serve as the model's label data:
[0060]
[0061] Secondly, data augmentation is performed on the input binary structure matrix: with a 50% probability, the binary structure matrix is mirrored 90° along either the horizontal or vertical direction. Since metasurface units typically possess physical symmetry at periodic boundaries, this spatial geometric transformation can significantly expand the structural diversity of the effective training samples without altering the physical absorption characteristics. Subsequently, the processed dataset is divided into an 80% training set, a 10% validation set, and a 10% test set according to a predetermined ratio, for use by the deep learning model for training.
[0062] Step 3) Train the positive prediction model:
[0063] Step 3.1) Constructing the forward prediction network structure: Construct a convolutional neural network (CNN) containing an encoder and a decoder as the forward prediction model for training. The encoder consists of three cascaded convolutional modules, with the specific structure as follows: Figure 5 As shown, the module is used to extract and compress features step by step from the input structural parameters: The first convolutional module contains two consecutive convolutional layers, both using a 2×2 kernel, with a stride of 1 and padding of 1. After each convolutional operation, batch normalization and LeakyReLU(0.1) non-linear activation with a slope of 0.1 are performed sequentially, followed by a max pooling layer (MaxPool2d(2)) with a kernel size of 2 for feature dimensionality reduction. The second convolutional module contains two consecutive convolutional layers, using a 2×2 kernel, with a stride of 1 and padding of 1, and is also combined with batch normalization and LeakyReLU(0.1) activation. After extracting deeper features, this module outputs a feature map with a dimension of 6×6×64; then it is downsampled again by a max pooling layer with a kernel size of 2. The third convolutional module contains two consecutive convolutional layers with a kernel size of 2×2, a stride of 1, and padding of 1, along with batch normalization and LeakyReLU(0.1) activation. To ensure the scale of the final feature map, an adaptive average pooling layer (AdaptiveAvgPool2d) is applied at the end, resulting in a strictly output deep feature map with dimensions of 3×3×256. A flatten layer is then connected after the three convolutional modules to convert the extracted two-dimensional feature map into a one-dimensional feature vector. The decoder includes a fully connected layer, followed by a LeakyReLU(0.1) activation function and a Dropout(0.5) layer. Finally, the predicted electromagnetic response data is mapped through an output layer containing 1001 neurons, whose output dimension corresponds one-to-one with the 1001 data points obtained by uniformly sampling the S11 parameter curve within the target frequency band.
[0064] Step 3.2) Forward Propagation and Loss Function Calculation: The training set data divided in Step 2) is input in batches into the forward prediction model. Through forward propagation via the encoder and decoder, the corresponding predicted electromagnetic response data is output. In the training of the forward prediction model, the mean squared error (MSE) is used as the loss function to quantify the error between the network's predicted values and the true label values. The formula for calculating the loss function MSE of the forward prediction model is:
[0065]
[0066] Where n represents the number of samples, which is 1001 here; The S11 value for the i-th frequency point predicted by the CNN; Let S11 be the value of the i-th frequency point obtained through CST simulation.
[0067] Step 3.3) Backpropagation and Model Iteration Convergence: Based on the loss function (MSE) value calculated in Step 3.2), backpropagation is performed using a network optimization algorithm to calculate the gradient and continuously update the weights and bias parameters in the convolutional neural network. The forward and backward propagation processes are iterated multiple times; in this embodiment, convergence is achieved through 100 iterations (Epochs). The loss function curve for training the forward prediction model is shown below. Figure 6 As shown, as training progresses, the loss value of the training set eventually converges to around 0.003, and the loss value of the test set converges to around 0.006. Both remain at a low level and the difference is small, indicating that the positive prediction model has not suffered from severe overfitting and has good generalization ability, thus proving that the training of the positive prediction model is complete.
[0068] Step 4) Reverse Design Optimization: To obtain a binary structure matrix with globally optimal absorption performance, guided by the inverse design objective, a genetic algorithm (GA) is used to dynamically optimize and iterate the structure encoding representing the physical arrangement of the metasurface. The specific process is as follows: Figure 4 As shown, it includes:
[0069] Step 4.1) Population initialization: Randomly generate an initial population containing n individuals, where each individual corresponds to a 10×10 binary structure matrix. In this embodiment, the population size n is set to 100.
[0070] Step 4.2) Electromagnetic response data calculation and fitness assignment: Input the 10×10 binary structure matrix of each individual in the population into the forward prediction CNN model trained in Step 3) to quickly calculate the predicted values of 1001 S11 parameters for that individual in the target frequency band; then, extract the effective absorption bandwidth and minimum reflection loss based on the extracted S11 parameter prediction values, and combine this with the inverse design objective of obtaining the globally optimal broadband absorption result. At this time, the fitness function is a weighted linear combination of the electromagnetic response data corresponding to the metasurface structure:
[0071]
[0072] Wherein, EAB represents the effective absorption bandwidth ratio, calculated as the ratio of the number of frequency points in the S11 prediction value that are less than a preset threshold (-10dB) to the total number of sampling points (1001); RL represents the minimum reflection loss value of the metasurface structure in the target frequency band, which should be as small as possible; F The normalization function for RL is defined in this embodiment as F(-RL) = This maps the data to the interval [0, 1]; α and β are EAB and F. In this embodiment, the weighting coefficients are set to α=0.8 and β=0.2.
[0073] Step 4.3) Perform iterative evolution: Based on the calculated fitness values, the population is continuously updated through selection, crossover, and mutation operations. The specific process is as follows:
[0074] In the selection phase, a tournament selection method is adopted. Each time, three individuals are randomly selected from the current population to compete for fitness. The individual with the highest fitness is selected into the parent population. This process is repeated until a parent individual with the same size as the original population is selected, thereby preserving the structural matrix with excellent wave absorption potential.
[0075] In the crossover process, individuals in the parent population are paired with a 50% crossover probability, and a two-point crossover strategy is adopted: two crossover points are randomly set on a one-dimensional binary chromosome sequence of length 100, and the gene coding segments between the two individuals are exchanged to generate offspring individuals that combine the excellent physical arrangement characteristics of both.
[0076] In the mutation phase, a subset of offspring individuals are selected with a 20% mutation probability, and a single-point bit-flipping mutation operation is used: for the selected individuals, the binary values on their chromosome sequence are randomly flipped with a 5% gene mutation rate (i.e., local small cells are changed from '0' to '1' or from '1' to '0', which physically corresponds to the random erasure or addition of conductive ink small blocks) in order to maintain the structural diversity of the population and escape local optima.
[0077] Step 4.4) Convergence Output: Repeat steps 4.2) and 4.3). In this embodiment, the goal is to obtain the globally optimal broadband absorption result, and the maximum number of iterations is set to 200. The optimization process terminates when the iteration reaches 200 iterations (the fitness change results during the iteration process are as follows). Figure 7 As shown in the figure, the individual with the highest fitness in the current population is output; the 10×10 binary structure matrix corresponding to this individual is the optimal metasurface physical structure output by reverse design, which can be directly used to guide the screen printing preparation of conductive ink.
Claims
1. A deep learning-based inverse design method for microwave absorbing metasurfaces, characterized in that: The microwave absorbing metasurface is composed of microwave absorbing metasurface units, each of which includes a printed substrate. The top surface of the printed substrate is printed and cured with conductive ink that forms a conductive pattern, and the bottom surface of the printed substrate has a metal base plate. The inverse design method includes the following steps: 1) Discretize the top surface of the microwave absorbing metasurface unit into a two-dimensional grid with m rows × n columns and multiple corresponding cells; assign a first value to cells printed with conductive ink and a second value to cells without conductive ink, generating an m × n binary structure matrix as the initial structure sample; construct a three-dimensional physical model of the microwave absorbing metasurface unit using electromagnetic simulation software, set simulation boundary conditions and excitation, perform full-wave simulation calculation, and obtain the S11 parameters by frequency sweep within the target frequency band, where the S11 parameters are the reflection coefficients that vary with frequency; repeat the operation and summarize the S11 parameters and the corresponding binary structure matrix to form a training dataset; 2) Normalize the binary structure matrix and the corresponding S11 parameters in the target frequency band, and divide the dataset after horizontally or vertically flipping the binary structure matrix into training set, validation set and test set. 3) Construct a convolutional neural network containing an encoder and decoder as a forward prediction model for training. The process is as follows: 3.1) The encoder used includes multiple cascaded convolutional modules, each containing a convolutional layer, an activation function layer, and a normalization layer; the decoder includes at least one fully connected layer, an activation function layer, and a regularization layer, and uses an output layer mapping to obtain S11 parameters, wherein the output dimension of the output layer corresponds to the number of sampling points of the S11 parameters. 3.2) Using the binary structure matrices in the training and validation sets as input, output the corresponding normalized S11 parameters; use mean squared error as the loss function; 3.3) Backpropagation is performed using a network optimization algorithm to calculate the gradient and update the weights and bias parameters in the convolutional neural network. The forward prediction model is trained until the loss function converges, and a prediction mapping from metasurface structure to microwave absorption response is established. 4) The genetic algorithm is used to optimize the inverse design objective and determine the fitness function. The process is as follows: 4.1) Population initialization: Generate an initial population containing n individuals, each individual corresponding to a binary structure matrix; 4.2) Calculate the predicted S11 parameter value of each individual in the population in the target frequency band using the positive prediction model, and assign a fitness function value according to the preset absorption bandwidth and minimum reflection loss weighted objective function. 4.3) The population is updated by selection, crossover, and mutation. Selection is based on fitness function value to retain superior individuals, crossover is to exchange coding segments of different individuals to fuse characteristics, and mutation is to flip some coding bits to maintain population diversity. 4.4) When the fitness value reaches a preset threshold or the maximum number of iterations, the individual with the highest fitness value is output as the optimal metasurface structure for reverse design.
2. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 4), when using a genetic algorithm to optimize the inverse design objective, the fitness function is as follows when the objective is to obtain the optimal result: ; Where EAB is the effective absorption bandwidth of the metasurface structure in the target frequency band; RL is the minimum reflection loss value of the metasurface structure in the target frequency band; F Let be the normalization function of RL; α and β are EAB and F, respectively. The weighting coefficients are given, and α + β = 1.
3. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 4), when using a genetic algorithm to optimize the inverse design objective, if the objective is to obtain a preset fixed electromagnetic response data, the fitness function is: ； in, This indicates that the prediction bandwidth of the neural network is effectively absorbed. This indicates the initial target effective absorption bandwidth. To provide a normalization function for RL predictions using neural networks, The normalization function for the initial target RL is α. The weighting coefficient, β is The weighting coefficients are given, and α + β = 1.
4. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 1), the process of constructing the three-dimensional physical model of the microwave absorbing metasurface unit is as follows: establish the metal substrate model and the printed substrate model, and generate the conductive ink patch model at the corresponding position on the upper layer of the printed substrate according to the row and column coordinates of the first value in the binary structure matrix.
5. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 1), the process of setting boundary conditions and excitation is as follows: set the boundary conditions in the X and Y directions of the three-dimensional physical model as periodic element boundaries; set the positive Z-axis direction as an open boundary; set the Floquet port as an excitation in the positive Z-axis direction and set the incident angle as vertical incidence.
6. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 1), the S11 parameter is the reflection coefficient that varies with frequency to verify the broadband absorptivity of the microwave absorbing metasurface corresponding to the binary structure matrix; the operation is repeated and the S11 parameter and the corresponding binary structure matrix are summarized to form a training dataset.
7. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 2), when normalizing the binary structure matrix and the corresponding S11 parameters in the target frequency band, the logarithmic-scaled S11 data is transformed into linear amplitude values in the interval [0,1]. As label data for three-dimensional physical models, .
8. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 3), the loss function of the positive prediction model is: Where n represents the number of samples; The S11 value is the value of the i-th frequency point in the positive prediction. Let S11 be the value of the i-th frequency point obtained through CST simulation.
9. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: In step 3.1), the encoder includes three cascaded convolutional modules and a flattening layer. The convolutional modules include a first convolutional layer, a first activation and normalization layer, a second convolutional layer, a second activation and normalization layer, and a pooling layer. The pooling layer downsamples the feature map. The flattening layer converts the extracted two-dimensional feature map into a one-dimensional feature vector.
10. The inverse design method for microwave absorbing metasurfaces based on deep learning according to claim 1, characterized in that: The conductive ink is composed of poly(3,4-ethylenedioxythiophene-polystyrene sulfonate), MXene, and multi-walled carbon nanotubes; the printing substrate is polyethylene terephthalate.