Multi-band metasurface filtering method based on machine learning optimization

Abstract

The invention discloses a multi-band metasurface filtering method based on machine learning optimization, and the method comprises the steps: firstly constructing multi-band reconfigurable metasurface filtering hardware of a multi-layer silicon-based integrated architecture, and sequentially arranging a bottom dielectric layer, an isolation layer, a middle dielectric layer, a top dielectric layer and a metal coating layer from bottom to top; secondly, electromagnetic simulation data and real object actual measurement data are collected, and a multi-dimensional data set containing structure, frequency and performance parameters is constructed; building a multi-level machine learning optimization model containing performance prediction, parameter optimization and global optimization, and respectively realizing accurate mapping of parameters and performance, dynamic parameter adjustment and multi-band performance collaborative optimization; and finally, through model training optimization and multi-band performance optimization process execution, experimental verification and model iterative optimization are combined. According to the method, the bottlenecks of low efficiency, poor multi-band collaboration, large simulation and actual measurement deviation and the like of the traditional design are broken through, the filtering performance and the design efficiency are improved, and the multi-band signal processing requirement in a complex electromagnetic environment is met.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of metasurface electromagnetic regulation, wireless communication and machine learning, in particular to a multi-band metasurface filtering method based on machine learning optimization. BACKGROUND

[0002] In the fields of modern wireless communication, radar detection, terahertz imaging, etc., the electromagnetic environment is becoming increasingly complex, and single-band signal processing has been difficult to meet the application requirements of multi-task and high integration. For example, 5G / 6G communication needs to consider both Sub-6GHz wide coverage and millimeter wave high-speed transmission, and terahertz security needs to adapt to multiple feature bands of 0.3-1THz, which makes multi-band metasurface filters become core devices, and their performance and design efficiency directly determine the stability and functional density of the system. However, traditional technologies have significant bottlenecks in hardware, optimization, engineering landing, etc., as follows: I. Contradiction between hardware integration and reconfigurability Traditional multi-band filtering hardware often uses multi-resonant unit superposition or multi-layer independent structure scheme: the former easily causes electromagnetic coupling between units, and the isolation of high frequency bands (such as millimeter wave, terahertz) is usually lower than 20dB, which cannot resist strong interference; the latter makes the device thickness reach hundreds of microns, which is contrary to the requirements of "lightweight, CMOS compatible" of microelectronic systems. At the same time, existing reconfigurable technologies (such as diode regulation) can only realize single-band tuning, and adjusting the parameters of a certain frequency band often leads to the deterioration of the performance of other frequency bands.

[0003] II. Low design efficiency and dependence on experience The performance of the filter is highly nonlinearly coupled with the structural parameters (resonant unit size, dielectric layer thickness, etc.). Traditional parameter scanning + electromagnetic simulation trial-and-error method requires engineers to manually preset dozens of parameters, and a single simulation takes several hours, and it takes several weeks to traverse hundreds of parameters. Moreover, this method relies on experience and is difficult to traverse high-dimensional parameter space, and is prone to local optimization.

[0004] III. Lack of systematic solution for multi-objective optimization Multi-band optimization needs to balance the mutually restrictive targets of insertion loss, isolation, group delay, etc. The traditional fixed weight summation method relies on subjective experience to allocate weights and cannot dynamically adjust according to the scene (such as communication bandwidth or radar isolation). Moreover, it is difficult to handle the Pareto optimal solution problem, and often needs to sacrifice some indicators.

[0005] IV. Large deviation between simulation and measurement Simulation is based on ideal boundary conditions, while in actual processing, lithography errors, metal layer unevenness, packaging stress, etc. will cause a simulation-measurement gap.

[0006] In summary, traditional technologies are no longer sufficient to meet the demands of modern systems for high integration, high performance, and rapid iteration. New methods that integrate intelligent optimization and advanced hardware are urgently needed to break through these bottlenecks. Summary of the Invention

[0007] This invention proposes a multi-band reconfigurable metasurface filtering method based on machine learning optimization, which effectively overcomes the bottlenecks of traditional design such as low efficiency, poor multi-band coordination, and large deviation between simulation and actual measurement. It significantly improves the integration, performance stability, and design iteration efficiency of filtering devices, and adapts to the multi-band signal processing needs of complex electromagnetic environments such as 5G / 6G communication and terahertz imaging.

[0008] To address the aforementioned technical problems, this invention provides the following technical solution: a multi-band metasurface filtering method based on machine learning optimization, comprising the following steps: A multi-band reconfigurable metasurface filter hardware structure is constructed. The structure adopts a multi-layer silicon-based integrated architecture, with a bottom dielectric layer, an isolation layer, an intermediate dielectric layer, a top dielectric layer, and a metal cladding layer arranged sequentially from bottom to top. Electromagnetic simulation data and physical measurement data of metasurface filter structures are collected to construct a multi-dimensional dataset, which includes structural parameters, frequency parameters and performance parameters. Construct a multi-level machine learning optimization model, which includes a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model; The machine learning model is trained and optimized, the optimization process of multi-band metasurface filtering performance is executed, and experimental verification and model iterative optimization are carried out.

[0009] Furthermore, a multi-level machine learning optimization model is constructed, which includes a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model. The specific construction steps are as follows: Constructing a performance prediction sub-model: A deep learning network is used, with structural parameters and frequency parameters as input features and performance parameters as output targets. The nonlinear mapping between input and output is achieved through network structure design. The deep learning network includes a feature extraction layer and an output layer. The feature extraction layer is used to extract key features of structural and frequency parameters, and the output layer is used to output the prediction results of performance parameters. Constructing a parameter optimization sub-model: Based on reinforcement learning algorithm, a reward mechanism is constructed with multi-band filtering performance index as the optimization objective. The process of adjusting the parameters of the metasurface structure is transformed into an interaction process between the agent and the environment. Through iterative training, the agent learns the optimal parameter adjustment strategy to achieve dynamic optimization of filtering performance. Construct a global optimization sub-model: Introduce an evolutionary algorithm, using the output of the performance prediction sub-model as the fitness evaluation basis, and perform global optimization on multiple sets of candidate parameters output by the parameter optimization sub-model. Through selection, crossover, and mutation operations, select the optimal parameter combination that meets the comprehensive performance requirements of multiple frequency bands.

[0010] Furthermore, the training and optimization of the machine learning model specifically includes: Dataset preprocessing involves removing outliers, imputing missing values, and standardizing features in the collected raw data, which is then divided into training, validation, and test sets according to a preset ratio. The performance prediction sub-model is trained by taking the training set data as input, adjusting the network parameters through an optimization algorithm, and iteratively optimizing the model using the prediction error on the validation set as the indicator until the model converges. The parameter optimization sub-model training uses the performance prediction sub-model as an environment simulator, sets the initial state and optimization goal, accumulates experience through continuous interaction between the agent and the environment, and updates the policy network parameters. The global optimization sub-model is trained, the parameter population is initialized, the population evolution is driven by the iterative rules of the evolutionary algorithm, and the individual fitness is evaluated in real time by the performance prediction sub-model until the population converges to the optimal solution.

[0011] Furthermore, the optimization process for performing multi-band metasurface filtering performance is specifically as follows: Initialize parameters: Based on the multi-band filtering design requirements, set the initial parameters and performance target thresholds of the metasurface structure; Performance prediction involves inputting initial parameters into the trained performance prediction sub-model to obtain prediction results for multi-band filtering performance. Parameter optimization: If the predicted performance does not reach the target threshold, the parameter optimization sub-model is activated to dynamically adjust the structural parameters according to the performance deviation. The adjustment effect is evaluated in real time through the performance prediction sub-model until the single-band performance meets the target. Global optimization involves inputting multiple sets of optimal single-band parameters output by the parameter optimization sub-model into the global optimization sub-model to conduct collaborative optimization of multi-band performance and output the final parameters that meet the overall performance requirements.

[0012] Furthermore, the specific steps for implementing experimental verification and model iterative optimization are as follows: Sample processing: Based on the parameters output by global optimization, multi-band reconfigurable metasurface filter samples are processed using microelectronic technology. Performance testing: A test system was built to measure the multi-band filtering performance of the sample and collect the measured performance data. The model is iterated, and the deviation between the measured performance and the predicted performance is compared. If the deviation exceeds the preset range, the measured data is added to the dataset, and the model training and parameter optimization are carried out again to form a closed loop iteration until the filtering performance meets the design requirements.

[0013] Furthermore, in the dataset, the structural parameters cover the geometry of the open-circuit resonator, the impedance configuration of the ring resonator, the operating state parameters of the adjustable device, and the layout parameters of the feed structure; the frequency parameters cover the target operating frequency band, frequency band spacing, and bandwidth range; and the performance parameters cover insertion loss, port isolation, group delay, polarization conversion efficiency, and angle stability.

[0014] Furthermore, the electromagnetic simulation data is obtained through electromagnetic simulation software. During the simulation, boundary conditions, excitation source types, and solution parameters corresponding to the metasurface filter structure are set, and the filtering performance under different combinations of structural parameters is simulated and calculated. The physical measured data is obtained by building a microwave anechoic chamber test system and a terahertz test system. During the test, a vector network analyzer and a terahertz time-domain spectrometer are used to collect the performance indicators of the sample's S-parameters, group delay, and polarization conversion efficiency.

[0015] Furthermore, the deep learning network of the performance prediction sub-model adopts a convolutional neural network (CNN) or a hybrid model that integrates deep learning and physical knowledge. The feature extraction layer of the CNN contains multiple convolutional layers and pooling layers. It extracts the spatial features of structural parameters and frequency parameters through convolution operations and reduces the feature dimensionality through pooling operations. The hybrid model incorporates the physical equations of metasurface electromagnetic control on the basis of the deep learning network.

[0016] Furthermore, the reinforcement learning algorithm of the parameter optimization sub-model adopts a deep Q-network (DQN) or a dual-delay deep Q-network (DDQN). The parameter adjustment of the metasurface filter structure is used as the action space of the agent, the deviation between the filtering performance and the target threshold is used as the environmental state, and the degree to which the performance requirements are met is used as the reward value. The training stability of the model is improved through experience replay and target network update mechanism. The evolutionary algorithm of the global optimization sub-model adopts either a genetic algorithm or a particle swarm optimization algorithm. In the genetic algorithm, the combination of metasurface structure parameters is used as chromosomes, and the comprehensive evaluation result of multi-band filtering performance is used as the fitness function. The evolutionary iteration of the population is achieved through operations such as roulette wheel selection, single-point crossover, and random mutation. In the particle swarm optimization algorithm, the parameter combination is used as particles, and the fitness function value is used as the fitness of the particles. Global optimization is achieved through particle velocity update and position update. The optimization algorithm of the performance prediction sub-model adopts the Adam adaptive moment estimation algorithm or the stochastic gradient descent (SGD) algorithm, and uses the mean squared error (MSE) or mean absolute error (MAE) as the loss function. It minimizes the deviation between the predicted value and the true value through iterative training. During the training process of the parameter optimization sub-model, an ε-greedy strategy is adopted to balance exploration and utilization. In the initial stage, the parameter adjustment strategy is explored randomly with a relatively high probability. As the training iterations progress, the probability of utilizing existing experience is gradually increased.

[0017] Furthermore, the optimization objectives of the multi-band filtering performance include insertion loss, port isolation, relative bandwidth, group delay fluctuation, and angle stability for each frequency band. By setting performance weight coefficients for different frequency bands, priority control of multi-objective optimization is achieved. During the parameter adjustment process, a step-by-step adjustment strategy is adopted for the geometric parameters of the open-circuit resonator, the operating parameters of the adjustable device, and the impedance parameters of the ring resonator. First, the key parameters affecting the global performance are adjusted, and then the local performance parameters are optimized.

[0018] The beneficial effects of the above-described technical solution of the present invention are as follows: 1. This invention adopts a five-layer silicon-based integrated architecture. Through precise division and collaborative design of functions at each layer, it solves the core contradiction of low integration and weak reconfigurability in traditional multi-band metasurface filters. The bottom dielectric layer provides stable mechanical support and waveguide transmission environment; the isolation layer achieves effective isolation between DC control and high-frequency signals; the middle dielectric layer lays the foundation for multi-band filtering through a resonant unit array; the top dielectric layer optimizes impedance matching to reduce losses; and the metal cladding integrates adjustable devices to achieve dynamic performance adjustment.

[0019] 2. The multi-level machine learning optimization model constructed in this invention revolutionizes the design optimization process. The performance prediction sub-model, through the fusion of deep learning and physical knowledge, accurately establishes the nonlinear mapping relationship between structural parameters and filtering performance, replacing the traditional time-consuming full-wave simulation and significantly shortening the performance evaluation time. The parameter optimization sub-model, with the help of reinforcement learning algorithms, enables the agent to autonomously learn the optimal parameter adjustment strategy, quickly achieving single-band performance targets. The global optimization sub-model uses evolutionary algorithms to globally optimize multiple sets of candidate parameters, and combines multi-objective fitness functions to efficiently select the optimal parameter combination, achieving synergistic improvement in the performance of each frequency band. The entire design process eliminates excessive reliance on engineer experience, not only significantly shortening the design cycle but also comprehensively considering multi-dimensional performance indicators such as insertion loss, port isolation, and polarization conversion efficiency.

[0020] 3. This invention effectively bridges the gap between simulation and actual measurement in traditional design by constructing a multi-dimensional dataset, model training and optimization, and experimental verification and iteration. At the data level, electromagnetic simulation data is integrated with actual measured data, making the basic data for model training closer to real-world application scenarios and improving the realism and reliability of performance predictions. In the optimization and implementation phase, a complete experimental verification and model iteration process is designed. After processing samples according to the optimized parameters, actual measurements are conducted using a professional testing system. The deviation between measured and predicted performance is compared and analyzed. If the deviation exceeds a reasonable range, the measured data is immediately added to the dataset, and the model is retrained to continuously optimize model accuracy. Attached Figure Description

[0021] Figure 1 This is a flowchart of the multi-band metasurface filtering method based on machine learning optimization of the present invention; Figure 2 This is a diagram of the multi-level machine learning optimization model architecture of the multi-band metasurface filtering method based on machine learning optimization of the present invention; Figure 3 This is a hardware architecture diagram of the reconfigurable metasurface filtering method based on machine learning optimization of the present invention. Detailed Implementation

[0022] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0023] Example 1

[0024] like Figure 1 As shown, an embodiment of the present invention provides a multi-band metasurface filtering method based on machine learning optimization, comprising the following steps: S1. Construct a multi-band reconfigurable metasurface filter hardware structure. The structure adopts a multi-layer silicon-based integrated architecture, with the following layers arranged from bottom to top: bottom dielectric layer, isolation layer, intermediate dielectric layer, top dielectric layer, and metal cladding. Figure 3 As shown; S2. Collect electromagnetic simulation data and physical measurement data of the metasurface filter structure, and construct a multi-dimensional dataset, which includes structural parameters, frequency parameters and performance parameters; S3. Construct a multi-level machine learning optimization model, including a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model, such as... Figure 2 As shown; S4. Train and optimize the machine learning model, execute the optimization process for multi-band metasurface filtering performance, and carry out experimental verification and model iterative optimization.

[0025] In this embodiment, step S1 constructs a multi-band reconfigurable metasurface filter hardware structure. The structure adopts a multi-layer silicon-based integrated architecture, with a bottom dielectric layer, an isolation layer, an intermediate dielectric layer, a top dielectric layer, and a metal cladding layer arranged sequentially from bottom to top. Specifically: 1. Bottom dielectric layer: Function: Serves as the mechanical support substrate for the entire structure and the transmission carrier of electromagnetic waves at the bottom layer.

[0026] Materials: High-resistivity silicon (HRSi) or fused silica are used. High-resistivity silicon is chosen because of its high dielectric constant (HRSi). It is preferred due to its ≈11.7), low RF loss, and good compatibility in CMOS processes.

[0027] Design: A metal ground plane can be designed at the bottom of this layer to form a waveguide-like transmission environment together with the top structure, suppressing electromagnetic leakage and improving energy transmission efficiency.

[0028] 2. Isolation layer: Function: To achieve electrical isolation between the DC bias / control circuit and the RF signal path, preventing the DC control signal from interfering with the high-frequency microwave / terahertz signal.

[0029] Structure: It is usually one or more layers of silicon dioxide (SiO2) insulating film, formed by thermal oxidation or chemical vapor deposition (CVD) processes.

[0030] Integration: Metal interconnects (such as copper or aluminum) can be embedded in this layer to provide bias voltages and control signals for reconfigurable devices on the top layer (such as varactor diodes, PIN diodes, or MEMS switches).

[0031] 3. Intermediate dielectric layer: Function: This is the key functional layer for achieving frequency selection and electromagnetic coupling.

[0032] Structure: This layer contains a pre-designed array of resonant units, such as open-loop resonators (SRR), elliptical rings, I-shaped or H-shaped structures, etc. The geometry of these units (such as length, width, and gap) directly determines the initial resonant frequency of the filter.

[0033] Integration: The resonant unit is connected to the bias line in the lower isolation layer through a via, thereby dynamically adjusting the equivalent electromagnetic parameters (such as capacitance or inductance) of the unit by changing the voltage applied to the tunable device, thus achieving frequency response reconstruction.

[0034] 4. Top Dielectric Layer: Function: Protects the underlying delicate structure and provides a suitable impedance matching environment to optimize the radiation and reception efficiency of electromagnetic waves.

[0035] Materials: Use low-loss polymer films such as polyimide or benzocyclobutene (BCB), or continue to use silica.

[0036] Design: Its thickness has been optimized to reduce impedance mismatch between the feed structure and free space, thereby reducing insertion loss.

[0037] 5. Metallic coating: Function: It forms the outermost layer of the metasurface, and its patterned design directly interacts with electromagnetic waves to complete functions such as filtering and polarization conversion. It also serves as the integration layer for reconfigurable devices.

[0038] Structure and materials: Metals with good conductivity, such as gold (Au) or aluminum (Al), are used to form specific metal patterns (such as the aforementioned resonant unit) through micro-machining processes such as photolithography and etching.

[0039] Where dynamic tuning is required, tunable semiconductor devices, such as varactor diodes (for continuous frequency tuning) or PIN switching diodes (for discrete state switching), are integrated. These devices are integrated with the underlying monolithic resonant unit.

[0040] Feeding: The top layer also integrates a feeding network, such as a coplanar waveguide (CPW) or microstrip line, to efficiently couple radio frequency signals to the metasurface resonant region.

[0041] In this embodiment, step S2 involves collecting electromagnetic simulation data and physical measurement data of the metasurface filter structure. The electromagnetic simulation data is obtained using electromagnetic simulation software. During the simulation, boundary conditions, excitation source types, and solution parameters corresponding to the metasurface filter structure are set, and the filtering performance under different combinations of structural parameters is simulated and calculated. The physical measurement data is obtained by building a microwave anechoic chamber testing system and a terahertz testing system. During the testing, a vector network analyzer and a terahertz time-domain spectrometer are used to collect the performance indicators of the sample, including S-parameters, group delay, and polarization conversion efficiency. The core objective of this step is to construct a large-scale, high-fidelity, multi-dimensional dataset, which will serve as the basis for training and validating machine learning models. The data sources include high-precision electromagnetic simulation data and reliable physical measurement data, which complement and validate each other.

[0042] I. Electromagnetic Simulation Data Acquisition The simulation platform employs industry-recognized full-wave electromagnetic simulation software, such as CST Studio Suite, ANSYS HFSS, or Lumerical FDTD (for the optical / terahertz band). These software programs can accurately solve Maxwell's equations and simulate the electromagnetic response of metasurfaces.

[0043] Then, parametric modeling is performed, and a parametric model of the multilayer structure from step S1 is established in the simulation software. All adjustable structural parameters (such as SRR side length, ring spacing, opening size, dielectric layer thickness, etc.) are set as variables.

[0044] Next, perform simulation settings, including: 1. Boundary conditions: Based on the periodic characteristics of the metasurface, set master-slave boundary conditions on the element boundaries to simulate an infinite array; set open or radiative boundary conditions in the normal direction to simulate free space. 2. Excitation source type: Set plane wave excitation (for simulating far-field response) or waveguide port excitation (for simulating near-field feed coupling) according to the operating frequency band and port type. 3. Solver and parameters: Select a frequency domain solver or a time domain solver. Set the precise solution frequency range (covering all target frequency bands), mesh generation accuracy (ensuring convergence), and frequency sweep method.

[0045] Finally, simulation data is generated automatically. Automated scripts are written using software APIs (such as CSTVBA, HFSSScript) or combined programming languages ​​(such as Python). The scripts automatically traverse the pre-designed parameter space (using methods such as Latin hypercube sampling, full factorial sampling, or random sampling) and perform simulation calculations for each combination of structural parameters. The performance results of each simulation are automatically extracted and saved, mainly including: S-parameters (S11, S21): reflecting insertion loss and return loss; Group Delay: calculated from the phase derivative of the S-parameters, reflecting dispersion characteristics; Surface Current Distribution: used to assist in analyzing the resonance mechanism; Far-field Radiation Pattern (if applicable): used to analyze angular stability.

[0046] II. Data Collection from Actual Measurements Physical testing is a crucial step in verifying the accuracy of simulation models and obtaining real-world data, which is then used for final verification and model iteration.

[0047] First, the test environment is set up. For microwave bands (e.g., X, Ku, K bands): the test system is built in a microwave anechoic chamber to shield against environmental electromagnetic interference and simulate a free-space environment. For terahertz bands: a terahertz time-domain spectroscopy (TDS) system is built, or a vector network analyzer (VNA) is used in conjunction with a terahertz spread spectrum module. Core test equipment includes: Vector Network Analyzer (VNA): Used for accurate measurement of the S-parameters (amplitude and phase) of a test substrate (DUT). Rigorous calibration (such as SOLT calibration) is required before testing to eliminate systematic errors.

[0048] Terahertz time-domain spectroscopy (TDS) system: used in the terahertz band, it can directly measure the change of electric field intensity of electromagnetic pulses over time, and obtain the spectrum information (amplitude and phase) after Fourier transform, thereby deriving S-parameters and group delay.

[0049] Probe station / antenna system: used to precisely feed signals into metasurface chips or receive their radiated signals.

[0050] Next, the testing process and data acquisition are performed, including structural parameters, frequency parameters, and performance parameters. Structural parameters cover the geometry of the open-circuit resonator, the impedance configuration of the ring resonator, the operating parameters of the adjustable devices, and the layout parameters of the feed structure. Frequency parameters cover the target operating frequency band, band spacing, and bandwidth range. Performance parameters cover insertion loss, port isolation, group delay, polarization conversion efficiency, and angular stability. The group delay is calculated directly by the VNA or obtained through numerical differentiation of the S21 phase. Polarization conversion efficiency is calculated by measuring the components of the incident wave and the reflected / transmitted wave in different polarization directions. Angular stability is achieved by rotating the sample stage to change the incident angle of the electromagnetic wave.

[0051] III. Construction of Multidimensional Datasets Finally, simulation and experimental data are integrated to construct a structured dataset. Simulation data is aligned and compared with experimental data of corresponding parameter combinations to verify the accuracy of the simulation model and calculate simulation and experimental errors. Some high-confidence experimental data can be merged with simulation data for model training to enhance the model's generalization ability. The dataset is a structured table (such as a CSV or HDF5 file), with each row representing a sample and containing the following dimensions: input features (X) and output label (Y). A version control mechanism is then established to label the dataset, ensuring the reproducibility of the experiments.

[0052] After the dataset is constructed, step S3 constructs a multi-level machine learning optimization model, which includes a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model. The specific construction steps are as follows: Step S31: Constructing a performance prediction sub-model: A deep learning network is used, with structural and frequency parameters as input features and performance parameters as the output target. The network structure is designed to achieve a non-linear mapping between input and output. The deep learning network includes a feature extraction layer and an output layer. The feature extraction layer extracts key features of the structural and frequency parameters, and the output layer outputs the predicted performance parameters. Specifically, the deep learning network for the performance prediction sub-model uses a Convolutional Neural Network (CNN) or a hybrid model integrating deep learning and physical knowledge. The feature extraction layer of the CNN contains multiple convolutional and pooling layers. Convolutional operations extract spatial features of the structural and frequency parameters, and pooling operations reduce the feature dimensionality. The hybrid model incorporates the physical equations of metasurface electromagnetic control into the deep learning network. Step S32: Constructing a parameter optimization sub-model: Based on reinforcement learning algorithms, a reward mechanism is constructed with multi-band filtering performance indicators as the optimization objective. The process of adjusting the parameters of the metasurface structure is transformed into an interaction process between the agent and the environment. Through iterative training, the agent learns the optimal parameter adjustment strategy to achieve dynamic optimization of filtering performance. The reinforcement learning algorithm of the parameter optimization sub-model adopts a deep Q-network (DQN) or a dual-delay deep Q-network (DDQN). The parameter adjustment amount of the metasurface filtering structure is used as the action space of the agent, the deviation between the filtering performance and the target threshold is used as the environment state, and the degree to which the performance requirements are met is used as the reward value. The training stability of the model is improved through experience replay and target network update mechanisms.

[0053] Step S33: Construct a global optimization sub-model: Introduce an evolutionary algorithm, using the output of the performance prediction sub-model as the fitness evaluation basis, to globally optimize multiple sets of candidate parameters output by the parameter optimization sub-model. Through selection, crossover, and mutation operations, the optimal parameter combination that meets the comprehensive performance requirements of multiple frequency bands is selected. The evolutionary algorithm of the global optimization sub-model adopts either a genetic algorithm or a particle swarm optimization algorithm. In the genetic algorithm, the combination of metasurface structure parameters is used as chromosomes, and the comprehensive evaluation result of multi-frequency band filtering performance is used as the fitness function. Evolutionary iteration of the population is achieved through operations such as roulette wheel selection, single-point crossover, and random mutation. In the particle swarm optimization algorithm, the parameter combination is used as a particle, and the fitness function value is used as the particle's fitness. Global optimization is achieved through particle velocity and position updates.

[0054] In this embodiment, step S4 involves training and optimizing the machine learning model, specifically as follows: Step S41: Dataset preprocessing. The collected raw data is subjected to outlier removal, missing value imputation, and feature standardization. The data is then divided into training set, validation set, and test set according to a preset ratio. Step S42: Training the performance prediction sub-model. Using the training set data as input, the network parameters are adjusted through an optimization algorithm. The prediction error of the validation set is used as the indicator for iterative optimization until the model converges. The optimization algorithm of the performance prediction sub-model adopts the adaptive moment estimation Adam or stochastic gradient descent SGD algorithm, and uses the mean squared error MSE or mean absolute error MAE as the loss function. The deviation between the predicted value and the true value is minimized through iterative training. Step S43: Training the parameter optimization sub-model. Using the performance prediction sub-model as an environment simulator, set the initial state and optimization goal. Accumulate experience through continuous interaction between the agent and the environment, and update the policy network parameters. During the training of the parameter optimization sub-model, an ε-greedy strategy is adopted to balance exploration and utilization. In the initial stage, the parameter adjustment strategy is explored randomly with a relatively high probability. As the training iterations progress, the probability of utilizing existing experience is gradually increased. Step S44: Global optimization sub-model training, initialize parameter population, drive population evolution with the iterative rules of evolutionary algorithm, combine performance prediction sub-model to evaluate individual fitness in real time, until the population converges to the optimal solution.

[0055] In this embodiment, step S4 executes the optimization process for the multi-band metasurface filter performance. The optimization objectives for the multi-band filter performance include insertion loss, port isolation, relative bandwidth, group delay fluctuation, and angle stability for each frequency band. By setting performance weight coefficients for different frequency bands, priority control of multi-objective optimization is achieved. During parameter adjustment, a step-by-step adjustment strategy is adopted for the geometric parameters of the open-circuit resonator, the operating parameters of the adjustable devices, and the impedance parameters of the ring resonator. First, the key parameters affecting the overall performance are adjusted, and then the local performance parameters are optimized. The specific implementation method is as follows: S45. Initialize parameters: Based on the multi-band filtering design requirements, set the initial parameters and performance target thresholds of the metasurface structure. S46. Performance prediction: Input the initial parameters into the trained performance prediction sub-model to obtain the prediction results of multi-band filtering performance. S47. Parameter optimization: If the predicted performance does not reach the target threshold, start the parameter optimization sub-model, dynamically adjust the structural parameters according to the performance deviation, and evaluate the adjustment effect in real time through the performance prediction sub-model until the single-band performance meets the standard. S48. Global optimization: Input the multiple sets of single-band optimal parameters output by the parameter optimization sub-model into the global optimization sub-model to carry out collaborative optimization of multi-band performance and output the final parameters that meet the comprehensive performance requirements.

[0056] In this embodiment, experimental verification and iterative model optimization are carried out, and the specific steps are as follows: S49. Sample processing: Based on the parameters output by global optimization, multi-band reconfigurable metasurface filter samples are processed using microelectronic technology. S410, Performance Testing: Build a test system to measure the multi-band filtering performance of the sample and collect the measured performance data. S411. Model iteration: Compare the deviation between the measured performance and the predicted performance. If the deviation exceeds the preset range, supplement the dataset with the measured data, retrain the model and optimize the parameters, forming a closed-loop iteration until the filtering performance meets the design requirements.

[0057] Example 2

[0058] This embodiment aims to design a dual-band reconfigurable metasurface filter in both the Ka band (26-40GHz) and the terahertz low-frequency band (0.3-0.5THz). It fully presents the application process of a multi-band metasurface filtering method based on machine learning optimization and verifies the effectiveness of the method in complex electromagnetic environments.

[0059] The hardware structure for a multi-band reconfigurable metasurface filter is constructed using a five-layer silicon-based integrated architecture. The design parameters and functions of each layer are shown in the table below.

[0060] II. Construction of Multidimensional Datasets (I) Electromagnetic simulation data acquisition 1. Simulation platform and parameter settings: CST Studio Suite 2023 was used, the frequency domain solver was selected, the boundary conditions were set to "master-slave boundary (periodic array) + open boundary (free space)", the excitation source was plane wave (far field response) and waveguide port (near field feed), the frequency range covered 26-40GHz (Ka band) and 0.3-0.5THz (terahertz band), and the mesh generation accuracy was λ / 20 (λ is the center wavelength of the corresponding frequency band).

[0061] 2. Parametric Simulation and Data Extraction: Using a Python script to call CSTAPI, Latin hypercube sampling was employed to traverse the parameter space (SRR side length 15-25μm, varactor diode bias voltage 0-5V, PIN diode switching state (0 / 1), etc., totaling 12 variables), generating 2000 sets of structural parameter combinations. Simulation was performed on each set of parameters, automatically extracting performance parameters: insertion loss (IL), port isolation (ISO), group delay (GD), polarization conversion efficiency (PTE), and angular stability (θ=0°-60°).

[0062] (II) Collection of physical measurement data 1. Test system setup: Ka band: Microwave anechoic chamber environment, vector network analyzer, equipped with a Ka band standard gain antenna (gain 15dBi), test distance 3m.

[0063] Terahertz band: Terahertz time-domain spectroscopy system, sampling rate 10GS / s, dynamic range 60dB.

[0064] 2. Sample Preparation and Testing: Fifty sets of typical simulation parameters were selected, and samples were fabricated using microelectronic processes (photolithography, sputtering, etching). Actual measurements were performed on each sample. Insertion loss and port isolation: Measure the S-parameters (S11, S21) using a vector network analyzer, and calculate IL = -10lg|S21|² and ISO = -10lg|S12|².

[0065] Polarization conversion efficiency: The ratio of cross-polarization to co-polarization components is measured by rotating the polarization direction of the transmit / receive antenna (0°-90°).

[0066] Angular stability: Rotate the sample stage (0°-60°) and record the change in IL at different incident angles.

[0067] (III) Dataset Preprocessing Preprocessing was performed on 2000 sets of simulation data and 50 sets of measured data: 1. Outlier removal: The 3σ criterion was used to remove outlier samples with IL>3dB (Ka band) / 5dB (terahertz band), a total of 82 groups were removed.

[0068] 2. Missing value imputation: For missing samples in some group delay data, the K-nearest neighbor (KNN) algorithm is used to impute them, with the K value set to 5.

[0069] 3. Feature standardization: Structural parameters (such as SRR side length) and frequency parameters (such as frequency band spacing) are standardized using Z-score (mean is 0, standard deviation is 1).

[0070] 4. Dataset partitioning: The dataset was divided into a training set (1378 sets), a validation set (394 sets), and a test set (196 sets) in a ratio of 7:2:1, with the actual test data evenly distributed across the three sets.

[0071] III. Construction of Multi-level Machine Learning Optimization Models (a) Performance Prediction Sub-model Model structure: The model adopts a hybrid model of "CNN + physical knowledge fusion". The input layer is 12-dimensional features (structural parameters + frequency parameters). The feature extraction layer contains 3 convolutional blocks (each convolutional block: convolutional layer (3×3 kernel, 16 filters) + ReLU activation + max pooling (2×2)). The metasurface electromagnetic control physical equation (such as the Lorentz harmonic oscillator model) is incorporated as a constraint layer. The output layer is 5-dimensional performance parameters (IL, ISO, GD, PTE, angular stability).

[0072] Training parameters: The optimization algorithm is Adam, the learning rate is 0.001, the batch size is 32, the loss function is mean squared error (MSE), the number of iterations is 200, and the prediction error on the validation set converges to MSE < 0.01.

[0073] (II) Parameter Optimization Sub-model Algorithm selection: Dual-Delay Deep Q-Network (DDQN) to model the metasurface parameter tuning process as a Markov Decision Process (MDP): State space (S): The deviation between the current performance parameters and the target threshold (e.g., ΔIL = target IL - current IL).

[0074] Operation space (A): Structural parameter adjustment amount (such as SRR side length ±0.5μm, varactor diode bias ±0.1V).

[0075] Reward function (R): R = 10 - (ΔIL + ΔISO + 0.5 × ΔGD) (an additional reward of 20 is given if performance targets are met).

[0076] Training strategy: adopt ε-greedy strategy (initial ε=0.9, decay by 0.1 every 100 rounds, final ε=0.1), experience replay buffer size 10000, target network update cycle 10 rounds, train until the agent achieves a performance target of >90% in a single frequency band.

[0077] (III) Global Optimization Sub-model Algorithm selection: Genetic Algorithm (GA), population size 50, number of iterations 50: Chromosome encoding: 12-dimensional real number encoding (corresponding to 12 structural parameters).

[0078] Fitness function: F = 0.3 × IL score + 0.2 × ISO score + 0.2 × GD score + 0.2 × PTE score + 0.1 × Angular stability score (each index score is calculated as “target value / measured value”, with a maximum score of 100).

[0079] Genetic operations: roulette wheel selection (selection probability is positively correlated with fitness), single-point crossover (crossover probability 0.8), random mutation (mutation probability 0.05).

[0080] Model training and multi-band optimization process execution (I) Model Training Process Performance prediction sub-model training: Using the input features of the training set as input, the output layer predicts performance parameters. The number of convolutional kernels and the constraint weights of the physical equation are adjusted through the validation set MSE. Finally, the prediction error of the test set IL is <0.1dB.

[0081] Training of parameter optimization sub-model: Using the performance prediction sub-model as an environment simulator, the agent initially adjusts the parameters randomly, and updates the policy network by interacting with the environment (input parameters → predict performance → calculate reward). After training for 5000 rounds, the number of iterations required to achieve the single-band (Ka band) IL target (<1.5dB) is reduced from 50 rounds to 15 rounds.

[0082] Global optimization sub-model training: Initialize 50 sets of parameter populations, generate a new population through genetic operations in each generation, call the performance prediction sub-model to evaluate fitness, and the population converges to the optimal solution (fitness > 90 points) in the 35th generation.

[0083] (II) Multi-band optimization process Parameter initialization: Set target performance thresholds: Ka band (IL<1.5dB, ISO>25dB, GD fluctuation<0.5ns); Terahertz band (IL<3dB, ISO>20dB, PTE>85%); Initial parameters are intermediate values ​​after simulation optimization (SRR side length 20μm, varactor diode bias voltage 2.5V, etc.).

[0084] Performance prediction: Input the initial parameters into the performance prediction sub-model and output the prediction results: Ka band IL=2.2dB (not up to standard), Terahertz band IL=3.8dB (not up to standard).

[0085] Parameter optimization: Start the DDQN sub-model. For the Ka band: adjust the SRR side length to 21μm, the varactor diode bias to 3.2V, and the predicted IL drops to 1.4dB (meets the target). For the terahertz band: adjust the SRR side length to 52μm, keep the PIN diode in the on state, and the predicted IL drops to 2.8dB (meets the target).

[0086] Global optimization: The two sets of single-band optimal parameters are input into the GA sub-model. The dual-band performance is weighed through the fitness function, and the final optimized parameters are output: Ka band SRR side length 20.8μm, bias voltage 3.1V; Terahertz band SRR side length 51.5μm, PIN diode conduction, and the predicted dual-band comprehensive fitness score is 92.

[0087] Experimental verification and model iteration (a) Sample processing and performance testing 1. Sample processing: Based on the global optimization parameters, three filter samples were processed using photolithography (resolution 0.5μm), gold sputtering (200nm), and silicon dioxide deposition.

[0088] 2. Actual performance: Ka band: IL=1.45dB (predicted 1.4dB), ISO=26dB (predicted 25.5dB), GD fluctuation=0.48ns (predicted 0.5ns).

[0089] Terahertz band: IL=2.9dB (predicted 2.8dB), ISO=21dB (predicted 20.5dB), PTE=86% (predicted 85%).

[0090] Angular stability: When θ=60°, the change in IL is <0.3dB (predicted <0.25dB).

[0091] (ii) Model Iterative Optimization Bias analysis: The deviation between the measured and predicted values ​​is <0.15dB (IL), which does not exceed the preset deviation range (<0.2dB). However, 50 sets of measured data were added to the dataset, forming a new dataset of 2050 sets.

[0092] Iterative training: The performance prediction sub-model was retrained, and the MSE on the test set was reduced to 0.008. Based on the new model, the parameter optimization and global optimization process were repeated. The final measured performance of the sample was: IL=1.42dB in the Ka band and IL=2.85dB in the terahertz band, which fully met the design requirements.

[0093] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-band metasurface filtering method based on machine learning optimization, characterized in that, Includes the following steps: A multi-band reconfigurable metasurface filter hardware structure is constructed. The structure adopts a multi-layer silicon-based integrated architecture, with a bottom dielectric layer, an isolation layer, an intermediate dielectric layer, a top dielectric layer, and a metal cladding layer arranged sequentially from bottom to top. Electromagnetic simulation data and physical measurement data of metasurface filter structures are collected to construct a multi-dimensional dataset, which includes structural parameters, frequency parameters and performance parameters. Construct a multi-level machine learning optimization model, which includes a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model; The machine learning model is trained and optimized, the optimization process of multi-band metasurface filtering performance is executed, and experimental verification and model iterative optimization are carried out.

2. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, A multi-level machine learning optimization model is constructed, which includes a performance prediction sub-model, a parameter optimization sub-model, and a global optimization sub-model. The specific construction steps are as follows: Constructing a performance prediction sub-model: A deep learning network is used, with structural parameters and frequency parameters as input features and performance parameters as output targets. The nonlinear mapping between input and output is achieved through network structure design. The deep learning network includes a feature extraction layer and an output layer. The feature extraction layer is used to extract key features of structural and frequency parameters, and the output layer is used to output the prediction results of performance parameters. Constructing a parameter optimization sub-model: Based on reinforcement learning algorithm, a reward mechanism is constructed with multi-band filtering performance index as the optimization objective. The process of adjusting the parameters of the metasurface structure is transformed into an interaction process between the agent and the environment. Through iterative training, the agent learns the optimal parameter adjustment strategy to achieve dynamic optimization of filtering performance. Construct a global optimization sub-model: Introduce an evolutionary algorithm, using the output of the performance prediction sub-model as the fitness evaluation basis, and perform global optimization on multiple sets of candidate parameters output by the parameter optimization sub-model. Through selection, crossover, and mutation operations, select the optimal parameter combination that meets the comprehensive performance requirements of multiple frequency bands.

3. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The training and optimization of the machine learning model specifically includes: Dataset preprocessing involves removing outliers, imputing missing values, and standardizing features in the collected raw data, which is then divided into training, validation, and test sets according to a preset ratio. The performance prediction sub-model is trained by taking the training set data as input, adjusting the network parameters through an optimization algorithm, and iteratively optimizing the model using the prediction error on the validation set as the indicator until the model converges. The parameter optimization sub-model training uses the performance prediction sub-model as an environment simulator, sets the initial state and optimization goal, accumulates experience through continuous interaction between the agent and the environment, and updates the policy network parameters. The global optimization sub-model is trained, the parameter population is initialized, the population evolution is driven by the iterative rules of the evolutionary algorithm, and the individual fitness is evaluated in real time by the performance prediction sub-model until the population converges to the optimal solution.

4. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The optimization process for multi-band metasurface filtering performance is as follows: Initialize parameters: Based on the multi-band filtering design requirements, set the initial parameters and performance target thresholds of the metasurface structure; Performance prediction involves inputting initial parameters into the trained performance prediction sub-model to obtain prediction results for multi-band filtering performance. Parameter optimization: If the predicted performance does not reach the target threshold, the parameter optimization sub-model is activated to dynamically adjust the structural parameters according to the performance deviation. The adjustment effect is evaluated in real time through the performance prediction sub-model until the single-band performance meets the target. Global optimization involves inputting multiple sets of optimal single-band parameters output by the parameter optimization sub-model into the global optimization sub-model to conduct collaborative optimization of multi-band performance and output the final parameters that meet the overall performance requirements.

5. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The specific steps for implementing experimental verification and model iterative optimization are as follows: Sample processing: Based on the parameters output by global optimization, multi-band reconfigurable metasurface filter samples are processed using microelectronic technology. Performance testing: A test system was built to measure the multi-band filtering performance of the sample and collect the measured performance data. The model is iterated, and the deviation between the measured performance and the predicted performance is compared. If the deviation exceeds the preset range, the measured data is added to the dataset, and the model training and parameter optimization are carried out again to form a closed loop iteration until the filtering performance meets the design requirements.

6. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, In the dataset, the structural parameters cover the geometry of the open-loop resonator, the impedance configuration of the ring resonator, the operating parameters of the adjustable devices, and the layout parameters of the feed structure. The frequency parameters cover the target operating frequency band, frequency band spacing, and bandwidth range; the performance parameters cover insertion loss, port isolation, group delay, polarization conversion efficiency, and angle stability.

7. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The electromagnetic simulation data is obtained through electromagnetic simulation software. During the simulation, boundary conditions, excitation source types, and solution parameters corresponding to the metasurface filter structure are set, and the filtering performance under different combinations of structural parameters is simulated and calculated. The physical test data is obtained by building a microwave anechoic chamber test system and a terahertz test system. During the test, a vector network analyzer and a terahertz time-domain spectrometer are used to collect the performance indicators of the sample's S-parameters, group delay, and polarization conversion efficiency.

8. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The deep learning network of the performance prediction sub-model adopts a convolutional neural network (CNN) or a hybrid model that integrates deep learning and physical knowledge. The feature extraction layer of the convolutional neural network contains multiple convolutional layers and pooling layers. It extracts spatial features of structural parameters and frequency parameters through convolutional operations and reduces feature dimensionality through pooling operations. The hybrid model incorporates physical equations for the electromagnetic control of metasurfaces into a deep learning network.

9. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The reinforcement learning algorithm of the parameter optimization sub-model adopts Deep Q Network (DQN) or Dual Delay Deep Q Network (DDQN). The parameter adjustment of the metasurface filter structure is used as the action space of the agent, the deviation between the filtering performance and the target threshold is used as the environment state, and the degree to which the performance requirements are met is used as the reward value. The training stability of the model is improved through experience replay and target network update mechanism. The evolutionary algorithm of the global optimization sub-model adopts either a genetic algorithm or a particle swarm optimization algorithm. In the genetic algorithm, the combination of metasurface structure parameters is used as chromosomes, and the comprehensive evaluation result of multi-band filtering performance is used as the fitness function. The evolutionary iteration of the population is achieved through operations such as roulette wheel selection, single-point crossover, and random mutation. In the particle swarm optimization algorithm, the parameter combination is used as particles, and the fitness function value is used as the fitness of the particles. Global optimization is achieved through particle velocity update and position update. The optimization algorithm of the performance prediction sub-model adopts the adaptive moment estimation Adam or stochastic gradient descent SGD algorithm, with mean squared error (MSE) or mean absolute error (MAE) as the loss function, and minimizes the deviation between the predicted value and the true value through iterative training; during the training process of the parameter optimization sub-model, an ε-greedy strategy is adopted to balance exploration and utilization. In the initial stage, the parameter adjustment strategy is randomly explored, and the probability of utilizing existing experience is gradually increased with training iterations.

10. The multi-band metasurface filtering method based on machine learning optimization according to claim 1, characterized in that, The optimization objectives of the multi-band filtering performance include insertion loss, port isolation, relative bandwidth, group delay fluctuation, and angle stability for each frequency band. By setting performance weight coefficients for different frequency bands, priority control of multi-objective optimization is achieved. During the parameter adjustment process, a step-by-step adjustment strategy is adopted for the geometric parameters of the open-loop resonator, the operating parameters of the adjustable device, and the impedance parameters of the ring resonator. First, the key parameters affecting the global performance are adjusted, and then the local performance parameters are optimized.

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