Terahertz waveguide cavity filter design optimization method based on deep neural network

Abstract

The application provides a terahertz waveguide cavity filter design optimization method based on a deep neural network, comprising the following steps: 1) designing a target index; 2) calculating initial estimates of geometric parameters according to a low-pass prototype and a band-pass-low-pass mapping; 3) defining a fixed parameter vector X for simulation sampling and a deep neural network (DNN) according to the calculation initial value of step 2, and using a normalized variable for standard expression; 4) performing small-scale coupling calibration; 5) generating multi-fidelity samples; 6) performing automatic processing on the simulation samples obtained in step 5) to generate a multi-task label vector Y; 7) training a DNN model; 8) constructing a tentative test candidate set; 9) obtaining a high-precision verification dataset through DNN calculation; 10) performing high-precision verification, and if the verification is passed, the process is ended, and if the verification condition is not met, the process returns to step 3) to adjust parameters and recalculate. The application can reduce the number of high-cost full-wave simulations, improve the design speed and the ability to resist manufacturing errors.

Description

Technical Field

[0001] This invention relates to the field of automated design of microwave / terahertz radio frequency devices, and more particularly to a deep neural network-based method for optimizing the design of terahertz waveguide cavity filters that combines filter prototype theory with deep neural networks (DNN). Background Technology

[0002] Waveguide cavity filters are widely used in high-frequency communication, imaging, and radar systems due to their high Q, low insertion loss, and good out-of-band rejection. Traditional waveguide cavity filter design relies on calculating prototype coefficients using a low-pass prototype and obtaining the coupling coefficients and external coupling through a bandpass-low-pass mapping. The coupling coefficients are then mapped to geometric dimensions (cavity length, coupling window aperture, coupling slot width, etc.) using empirical formulas or engineering experience. This is followed by extensive full-wave electromagnetic simulations (such as HFSS and CST) for fine parameter scanning and manual tuning, requiring numerous simulation iterations.

[0003] In the terahertz band, cavity dimensions are extremely small, making them highly sensitive to manufacturing tolerances and surface roughness. Simultaneously, the computational load of a single full-wave simulation is enormous, resulting in long iterative design cycles and high costs. Furthermore, traditional empirical formulas lack sufficient prediction accuracy when complex coupling structures or surface treatment variations occur. Therefore, a design method is needed that can maintain the rationality of physical priors (prototype theory), while using data-driven approaches to compensate for complex non-ideals and significantly reduce the number of simulation calls. Summary of the Invention

[0004] The purpose of this invention is to provide a design optimization method for terahertz waveguide cavity filters based on deep neural networks, so as to reduce the number of costly full-wave simulations, improve design speed and resistance to manufacturing errors, especially for engineering implementation in the terahertz frequency band.

[0005] The objective of this invention and the technical problem it solves are achieved through the following technical solution. The terahertz waveguide cavity filter design optimization method based on deep neural networks proposed in this invention includes the following steps: Step 1: Design target parameters, including target center frequency f0, angular frequency ω0, and lower limit of target bandwidth f. l With upper limit frequency f h Absolute bandwidth (BW), normalized bandwidth (FBW), and passband ripple (A) p ; Step 2: Based on the target indicators in Step 1, calculate the minimum cavity order n and the normalized prototype coefficient g required according to the low-pass prototype and band-pass-low-pass mapping. i And calculate the bandpass coupling coefficient k according to the narrowband approximation. i,i+1 To obtain initial estimates of the resonant cavity length l, coupling window height h, and thickness t; Step 3: Parameterize and define the input vector X for training / optimization: Based on the initial values ​​calculated in step 2, a fixed parameter vector X is defined for the simulation sampling and deep neural network (DNN), and expressed using normalized variables as the standard. Assuming that the filter port coupling is fixed and the waveguide cross-section is fixed, the parameter vector is defined as follows: The length of each resonant cavity Coupling window height The configuration file specifies the numerical range limits for each dimension, which will be used in steps 4 and 5. Step 4: Perform small-scale coupling calibration, specifically including: Step 4.1 Select the normalized mesh of the coupled subspace and construct... The set L and The set H; Step 4.2 By performing multinomial regression on the dataset, a description of the variable relationships is obtained, and the coupled surrogate model F is acquired. sur , ; Step 5: Generate multiple-fidelity samples by generating N samples in the parameter domain using Latin hypercube sampling. LF For each low-fidelity sample, a low-fidelity simulation is run to obtain the low-fidelity S-parameters and label data Y. LF Record simulation settings and mesh parameters; Step 6: Analyze the N obtained in Step 5. LF Each simulated sample undergoes automated processing to generate a multi-task label vector Y. ; Step 7: Use the dataset Training a multi-task regression model Activation function The output layer is a linear multi-task output; the training loss is a combination of weighted mean squared error and L2 regularization. Where w is the task weight, λ is the L2 regularization coefficient, and training stops when the validation loss no longer decreases within U consecutive executions; upon completion of training, the multi-task regression model is saved, and its multi-task output is defined as Save the model after training is complete; Step 8: Construct X using the parameters calculated in Step 2. (01) A candidate set of number M is generated using heuristic sampling centered at X. For each X in the set, a prediction is given by a trained DNN. Calculate relative to design target The normalized differences are sorted according to the following scoring function: Where α is a fixed weight corresponding to different parameters, and X in the candidate set is sorted in ascending order by J(X) and the first P are retained to enter step 9; Step 9: The candidates retained in Step 8 For each parameter, a local mesh is constructed, and n local points are taken for each parameter. g The relative range of the grid is set to ±r; the local range J(X) is increased by batch calculation through DNN, the optimal point of each local grid is taken, and all local optimal points are merged. The top K points according to J(X) are used for high-precision verification. Step 10: Analyze the K candidate sets output in Step 9. High-precision simulation was performed in HFSS, and the real labels were extracted based on step 6. And calculate the candidate target deviation vector. With prediction error vector If M is satisfied pass If all candidates simultaneously meet the following conditions, the verification is deemed successful: If the verification passes, the solution is considered successful, and the design optimization ends. If the calculation fails the verification, the current configuration is recorded, and the process returns to step 3 to adjust parameter n and recalculate.

[0006] The objectives of this invention and the technical problems it addresses can be further achieved by the following technical measures.

[0007] The aforementioned terahertz waveguide cavity filter design optimization method based on deep neural networks includes the following steps in step 2: Step 2.1 Calculate the relevant target parameters: Where Ω is the normalized frequency in the low-pass region, used for table lookup or with prototype coefficients g. i The mapping formula is meaningful when ω>0, and when applied to a specific stopband point f s At that time, through Calculate the normalized frequency value of the stopband point after mapping. Substitute this into the prototype design formula; the mapping will map the frequencies at both ends of the bandpass to the corresponding Ω in the low-pass domain, requiring the selection of an appropriate f. s (Stopband point) makes Ω s ≥1; Step 2.2 Substitute the relevant parameters into the Chebyshev prototype formula to calculate the lowest order n of the prototype: ; Find the corresponding prototype coefficient g i(Low-pass table or numerical table), and calculate the initial coupling value k according to the narrowband mapping. i,i+1 : ; Step 2.3 Calculate the relevant resonant cavity dimensions. Since a standard rectangular waveguide is used, the corresponding rectangular waveguide side lengths a and b are fixed values. Calculate the cutoff frequency. waveguide wavelength ,in Therefore, the cavity size can be estimated to be approximately: ; Step 2.4 Calculate the relevant coupling window height h and thickness t. The coupling window thickness has a relatively small impact on the filter performance and is usually taken as about 1 / 8 of the resonant cavity length, as follows: .

[0008] The aforementioned design optimization method for terahertz waveguide cavity filters based on deep neural networks, step 4.1 involves constructing... The set L and The set H includes: for each pair A two-cavity coupled unit model is established, with matching waveguides connected to both ends. Low-fidelity simulation is used to simulate the coupled cavity structures corresponding to sets L and H. S-parameters are calculated for each structure and the resonant frequencies of symmetric / antisymmetric modes are extracted. The simulation settings are recorded for subsequent fidelity consistency checks.

[0009] In the aforementioned terahertz waveguide cavity filter design optimization method based on deep neural networks, the low-fidelity samples in step 5 are the main data source for DNN training; at the same time, a small portion of medium / high-fidelity samples are reserved for verification and transfer learning.

[0010] The aforementioned terahertz waveguide cavity filter design optimization method based on deep neural networks includes the following specific operations in step 6: applying cubic spline interpolation to S(f) for each sample and smoothing it as needed to reduce the impact of simulation noise on extremum extraction; locating the measured passband center f0 using the peak method or the symmetric second-order moment method. (meas) f is determined by the -3 dB point or a specified threshold. l ,f h And calculate BW (meas) and FBW (meas) In the passband center Calculate insertion loss and return loss: Stopband point f s Stopband attenuation: Combining the results, we get: .

[0011] In the aforementioned design optimization method for terahertz waveguide cavity filters based on deep neural networks, step 7 involves developing a DNN model. During training, the input parameters are X(j) and the coupled surrogate value. The output is The optimizer used is Adam, with parameters β1, β2, ε, initial learning rate η, batch size Batchsize, and maximum number of epochs MaxEpoch.

[0012] In the aforementioned design optimization method for terahertz waveguide cavity filters based on deep neural networks, step 7 involves developing a DNN model. During training, the network is set to a fully connected network with an input layer, 512 nodes, 256 nodes, 128 nodes, and an output layer. The activation function of each hidden layer is ReLU, and the output layer is linearly activated.

[0013] Compared with existing technologies, this invention has significant advantages and beneficial effects. Through the above technical solution, this invention achieves considerable technological advancement and practicality, and has broad industrial application value, possessing at least the following advantages: 1. Combining physical prototyping methods with data-driven models can compensate for the effects of complex coupling and manufacturing non-ideals while preserving theoretical priors; 2. By using DNN batch prediction and proxy optimization, the number of calls to high-precision full-wave simulation can be reduced from thousands to dozens, thereby significantly shortening the design cycle; 3. By incorporating a manufacturing error model into the training set and performing online fine-tuning, the robustness of the design to manufacturing tolerances and the consistency of batch production can be improved; 4. The method of the present invention has good scalability and can be adapted to various terahertz frequency bands (such as 100 GHz, 340 GHz) or rectangular waveguide resonant cavity structures of different sizes through transfer learning. Attached Figure Description

[0014] Figure 1 is a schematic diagram of the overall process of the terahertz waveguide cavity filter design optimization method based on deep neural networks of the present invention; Figure 2 is a schematic diagram of the parameterization annotation of a single cavity of a waveguide cavity filter in the design optimization method of terahertz waveguide cavity filter based on deep neural network of the present invention.

[0015] [Explanation of Key Component Symbols] 1-Narrow rectangular waveguide; 2-Coupled window; 3-Resonant cavity; 4-Coupled window thickness; 5-Coupled window height; 6-Wide side of rectangular waveguide. Detailed Implementation

[0016] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description, in conjunction with the accompanying drawings and preferred embodiments, explains the specific implementation, features, and effects of the terahertz waveguide cavity filter design optimization method based on deep neural networks proposed in this invention.

[0017] Please see Figure 1 This is a flowchart illustrating the terahertz waveguide cavity filter design optimization method based on deep neural networks of the present invention. The design optimization method includes the following steps: Step 1: Design target indicators, including target center frequency f0 (Hz) and angular frequency. The lower limit of the target bandwidth f l With upper limit frequency f h Calculate the absolute bandwidth (Hz), normalized bandwidth , Passband ripples A p (dB).

[0018] Step 2: Based on the target metrics from Step 1, calculate the minimum cavity order n and the normalized prototype coefficient g required using the low-pass prototype (e.g., Chebyshev or Butterworth) and the bandpass-low-pass mapping. i And calculate the bandpass coupling coefficient K according to the narrowband approximation. i,i+1 This is done to obtain initial estimates of the geometric parameters. The specific steps are as follows: Step 2.1 Calculate the relevant target parameters: Where Ω is the normalized frequency in the low-pass region, used for table lookup or with prototype coefficients g. i The mapping formula is meaningful when ω>0, but when applied to a specific stopband point f... s At that time, through Calculate the normalized frequency value of the stopband point after mapping. Then, substitute this into the prototype design formula. The mapping will map the frequencies at both ends of the bandpass to the corresponding Ω in the low-pass domain, requiring the selection of a suitable f. s (Stopband point) makes Ω s ≥1; Step 2.2 Substitute the relevant parameters into the Chebyshev prototype formula to calculate the lowest order n of the prototype: Find the corresponding prototype coefficient g i (Low-pass table or numerical table), and calculate the initial coupling value k according to the narrowband mapping. i,i+1 : Step 2.3 Calculate the relevant resonant cavity dimensions. Since a standard rectangular waveguide is used, its corresponding side lengths a and b are fixed values. Calculate the cutoff frequency. waveguide wavelength ,in Therefore, the resonant cavity length l can be approximated as follows: Step 2.4 Calculate the relevant coupling window height h and thickness t. The coupling window thickness has a relatively small impact on the filter performance and is usually taken as about 1 / 8 of the resonant cavity length, as follows: Step 3: Parameterize and define the input vector X for training / optimization: Based on the initial values ​​calculated in step 2, a fixed parameter vector X is defined for the simulation sampling and deep neural network (DNN), and expressed using normalized variables. If the port coupling and waveguide cross-section are fixed, the parameter vector is defined as follows: The length of each resonant cavity Coupling window height The configuration file specifies the numerical range limits (lower / upper limits) for each dimension for use in steps 4 and 5. Step 4: Perform small-scale coupling calibration. The specific steps are as follows: Step 4.1 Select the normalized mesh of the coupled subspace and construct... The set L and The set H is used to establish a two-cavity coupled unit model, with matched waveguides connected to both ends. The coupled cavity structures corresponding to sets L and H are simulated, and the S-parameter results and parameter settings are saved. Step 4.2: By performing multinomial regression on the dataset of the above parameters, a description of the variable relationships is obtained, and the coupled surrogate model F is acquired. sur : Step 5: Generation of multi-fidelity samples. The specific steps are as follows: Generate N samples using Latin hypercube sampling in the parameter domain. LF For each low-fidelity sample, a low-fidelity simulation is run to obtain the low-fidelity S-parameters and label data Y. LF Record simulation settings and mesh parameters. Obtain N. LF A low-fidelity sample.

[0019] Step 6: Analyze the N obtained in Step 5. LF Each simulated sample undergoes automated processing to generate a multi-task label vector Y. Specifically, this involves performing cubic spline interpolation and necessary smoothing on S(f) to determine the passband center. (Using the peak method or the symmetric second-moment method), f is determined through the -3 dB point or a specified threshold. l ,f h And calculate BW （meas） and FBW （meas） In the passband center Calculate insertion loss and return loss: Stopband point f s Stopband attenuation: Combining the results, we get: Step 7: Use the dataset Training a multi-task regression model Activation function The output layer is a linear multi-task output; the optimizer is Adam, with parameters β1, β2, ε, initial learning rate η, batch size Batchsize, and maximum number of epochs MaxEpoch. The training loss is a combination of weighted mean squared error and L2 regularization. Where w is the task weight and λ is the L2 regularization coefficient. Training stops when the validation loss no longer decreases within U consecutive executions. Upon completion of training, the multi-task regression model is saved, and its multi-task output is defined as... ; Step 8: Construct X using the parameters calculated in Step 2. (01) A candidate set of number M is generated using heuristic sampling centered at X. For each X in the set, a prediction is given by a trained DNN. Calculate relative to design target The normalized differences are sorted according to the following scoring function: Where α is a fixed weight corresponding to different parameters. Sort X in the candidate set in ascending order by J(X) and retain the first P candidates to proceed to step 9; Step 9: The candidates retained in Step 8 For each parameter, a local mesh is constructed, and n local points are taken for each parameter. g The relative range of the grid is set to ±r. The local range J(X) is increased through batch computation using a DNN. The optimal point of each local grid is taken, and all local optimal points are merged. The top K local optimal points are selected according to J(X) for high-precision verification. Step 10: Analyze the K candidate sets output in Step 9. High-precision simulation was performed in HFSS, and the real labels were extracted based on step 6. And calculate the candidate target deviation vector. With prediction error vector If M is satisfied pass If all candidates simultaneously meet the following conditions, the verification is deemed successful: If the calculation fails the verification, record the current configuration and return to step 3 to adjust the parameters and recalculate.

[0020] The present invention will be further illustrated below using a typical design process for a 220GHz filter as an example.

[0021] Step I: Develop relevant performance indicators based on the design objectives, as follows: The center frequency f0 = 220 GHz, and the lower and upper limits of the target bandwidth are f0 and f1, respectively. l =215GHz, f h =225GHz, absolute bandwidth BW=10GHz, normalized bandwidth FBW≈0.045, passband ripple A p =0.1dB, at the stopband point f s The requirement is to suppress the stopband A. s ≥40 dB.

[0022] Step II: Conduct prototype design and initial coupling estimation based on the design objectives.

[0023] The 220GHz filter employs a rectangular standard waveguide, with waveguide dimensions conforming to the WR-4.3 standard. The narrow side 1 of the rectangular waveguide has a dimension of a = 1.092 mm, and the wide side 6 has a dimension of b = 0.546 mm. The wavelength is 1.363 mm, and the waveguide wavelength is 1.744 mm. The stopband point is set at f. s =235GHz, thus obtaining the normalized frequency Ω s =2.904. (The last part, "A", appears to be a typo and can be left as is.) p =0.1dB, A s =40 dB, substituted into the Chebyshev prototype and calculated using the bandpass-lowpass mapping, the minimum order n≈4.156, taking the integer order n=5. The low-pass prototype coefficients are: g0=1, g1=1.7058, g2=1.2296, g3=2.5408, g4=1.2296, g5=1.7058, g6=1. Substituting these parameters into... The corresponding initial coupling value k is calculated. i,i+1 The corresponding coupling window height 5 and coupling window thickness 4 are calculated based on the initial coupling value. These values ​​are used as preliminary estimates of geometric parameters for setting the center and value range of subsequent parameterized sampling.

[0024] Step III: Calculate the order n=5 according to Step II. If a suitable result cannot be obtained, adjust the value of n and define the normalization parameter vector. Set the upper and lower limits of the parameters, respectively. , .

[0025] Step IV: Small-scale coupling calibration, the specific steps are as follows: Step IV.1 Generates a normalized mesh set on the coupling subspace, containing the set of resonant cavity lengths L and the set of coupling window heights H. For each pair... Construct a two-cavity coupled unit model: with matched waveguides at both ends, use low-fidelity simulation (coarse mesh, fast mode analysis) to calculate S-parameters for each structure and extract the resonant frequencies of symmetric / antisymmetric modes, and record simulation settings (mesh parameters, convergence criteria) for subsequent fidelity consistency checks.

[0026] Step IV.2 uses multinomial regression to fit the coupled data to obtain the coupled surrogate model. This agent is used to approximate the coupling coefficients during the main training set construction phase, reducing the number of costly simulations for large-scale samples.

[0027] Step V: Generate N within the configuration domain by employing Latin hypercube sampling. LF =3000 low-fidelity samples. Run low-fidelity electromagnetic simulations on each sample to obtain S 21 (f) and S 11 (f) Simulation settings and grid information were recorded. These low-fidelity samples served as the primary data source for DNN training; a small subset of medium / high-fidelity samples were reserved for validation and transfer learning.

[0028] Step VI: Apply cubic spline interpolation to S(f) for each sample and smooth it as needed to reduce the impact of simulation noise on extreme value extraction. Locate the measured passband center f0 using the peak method. (mesa) The passband boundary f is identified by a preset threshold. l (meas) and f h (meas) Calculate the corresponding BW （meas） and FBW （meas） , at f0 (mesa) Calculate the corresponding insertion loss. and return loss At the stopband point f s Calculate stopband attenuation This forms a multi-task label vector. ; Step VII, through N LF A dataset constructed from 10 samples Set parameters for DNN model Training. The input parameters are X(j) and the coupled proxy value. The output is The network is configured as a fully connected network with an input layer, 512 nodes, 256 nodes, 128 nodes, and an output layer. Each hidden layer uses ReLU activation, and the output layer uses linear activation. The loss function is... The weighting coefficients are set to w = [0.40, 0.30, 0.15, 0.10, 0.05], and the L2 regularization coefficient λ = 1 × 10⁻⁶. -4 The Adam optimizer uses parameters β1=0.9. β²=0.999, ε=10 -8 The initial learning rate η = 10 -3 Batch size = 64, maximum epochs = 500. Save the model after training is complete. Step VIII, using the initial value X from step II. 0 M=5000 candidates are generated using heuristic sampling around the center. For each candidate, a trained DNN is used to... Make predictions and set the target vector. The weighting coefficient is set as: α f =0.4, α bw =0.4, α il =0.15, α rl =0.15, sort the candidates in ascending order of J(X) and keep the first P=200 to proceed to step IX; Step IX: Construct a local mesh for each retained candidate, taking n values ​​for each parameter within a relative range of ±r=5%. g =9 local points, and use DNN to batch calculate the score J(X) on the local grid. Take the best point for each local grid and summarize all local best points. Select the top K=20 according to J(X) as high-precision verification input.

[0029] Step X: Perform high-precision simulation (fine mesh, strict convergence) on the K candidates obtained in Step IX in HFSS to extract the true label Y. (real) And calculate the target deviation vector. With prediction error vector If M is satisfied pass If all three candidates simultaneously meet the conditions, the verification is considered successful. The conditions are as follows: If the verification is successful, the final design scheme of the 220GHz waveguide cavity filter can be determined; otherwise, the current configuration is recorded and step III is rolled back to adjust parameter n and recalculate.

[0030] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A design optimization method for terahertz waveguide cavity filters based on deep neural networks, characterized in that, Includes the following steps: Step 1: Design target parameters, including target center frequency f0, angular frequency ω0, and lower limit of target bandwidth f. l With upper limit frequency f h Absolute bandwidth (BW), normalized bandwidth (FBW), and passband ripple (A) p ; Step 2: Based on the target indicators in Step 1, calculate the minimum cavity order n and the normalized prototype coefficient g required according to the low-pass prototype and band-pass-low-pass mapping. i And calculate the bandpass coupling coefficient k according to the narrowband approximation. i,i+1 To obtain initial estimates of the resonant cavity length l, coupling window height h, and thickness t; Step 3: Parameterize and define the input vector X for training / optimization: Based on the initial values ​​calculated in step 2, a fixed parameter vector X is defined for simulation sampling and DNN, and expressed using normalized variables as the standard. Assuming the filter port coupling is fixed and the waveguide cross-section is fixed, the parameter vector is defined as follows: The length of each resonant cavity Coupling window height ; Specify the numerical range constraints for each dimension in the configuration file; Step 4: Perform small-scale coupling calibration, specifically including: Step 4.1 Select the normalized mesh of the coupled subspace and construct... set L and The set H; Step 4.2 By performing multinomial regression on the dataset, a description of the variable relationships is obtained, and the coupled surrogate model F is acquired. sur : ; Step 5: Generate multiple-fidelity samples by generating N samples in the parameter domain using Latin hypercube sampling. LF For each low-fidelity sample, a low-fidelity simulation is run to obtain the low-fidelity S-parameters and label data Y. LF Record simulation settings and mesh parameters; Step 6: Analyze the N obtained in Step 5. LF Each simulated sample undergoes automated processing to generate a multi-task label vector Y. ; Step 7: Use the dataset Training a multi-task regression model Activation function The output layer is a linear multi-task output; the training loss is a combination of weighted mean squared error and L2 regularization. Where w is the task weight, λ is the L2 regularization coefficient, and training stops when the validation loss no longer decreases within U consecutive executions; upon completion of training, the multi-task regression model is saved, and its multi-task output is defined as Save the model after training is complete; Step 8: Construct X using the parameters calculated in Step 2. （01） A candidate set of number M is generated using heuristic sampling centered at X. For each X in the set, a prediction is given by a trained DNN. Calculate relative to design target The normalized differences are sorted according to the following scoring function: Where α is a fixed weight corresponding to different parameters, and X in the candidate set is sorted in ascending order by J(X) and the first P are retained; Step 9: The candidates retained in Step 8 For each parameter, a local mesh is constructed, and n local points are taken for each parameter. g The relative range of the grid is set to ±r; the local range J(X) is increased by batch calculation through DNN, the optimal point of each local grid is taken, and all local optimal points are merged. The top K points according to J(X) are used for high-precision verification. Step 10: Analyze the K candidate sets output in Step 9. High-precision simulation was performed in HFSS, and the real labels were extracted based on step 6. And calculate the candidate target deviation vector. With prediction error vector If M is satisfied pass If all candidates simultaneously meet the following conditions, the verification is deemed successful: If the verification passes, the solution is considered successful, and the design optimization ends; if the calculation fails the verification, the current configuration is recorded, and the process returns to step 3 to adjust parameter n and recalculate.

2. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 1, characterized in that, Step 2 includes the following steps: Step 2.1 Calculate the relevant target parameters: Where Ω is the normalized frequency in the low-pass region, used for table lookup or with prototype coefficients g. i The mapping formula is meaningful when ω>0, and when applied to a specific stopband point f s At that time, through Calculate the normalized frequency value of the stopband point after mapping. Substitute this into the prototype design formula; the mapping will map the frequencies at both ends of the bandpass to the corresponding Ω in the low-pass domain, requiring the selection of an appropriate f. s Make Ω s ≥1; Step 2.2 Substitute the relevant parameters into the Chebyshev prototype formula to calculate the lowest order n of the prototype: ； Find the corresponding prototype coefficient g i And calculate the initial coupling value k according to the narrowband mapping. i,i+1 : ； Step 2.3 Calculate the relevant resonant cavity dimensions. Since a standard rectangular waveguide is used, the corresponding rectangular waveguide side lengths a and b are fixed values. Calculate the cutoff frequency. waveguide wavelength ,in The resonant cavity length l is approximately: ; Step 2.4 Calculate the relevant coupling window height h and thickness t. The coupling window thickness has a relatively small impact on the filter performance, and is taken as 1 / 8 of the resonant cavity length, as follows: .

3. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 1, characterized in that, Step 4.1 Construction set L and The set H includes: for each pair A two-cavity coupled unit model is established, with matching waveguides connected to both ends. Low-fidelity simulation is used to simulate the coupled cavity structures corresponding to sets L and H. S-parameters are calculated for each structure and the resonant frequencies of symmetric / antisymmetric modes are extracted. The simulation settings are recorded for subsequent fidelity consistency checks.

4. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 1, characterized in that, The low-fidelity samples in step 5 are the main data source for DNN training; at the same time, a small number of medium / high-fidelity samples are reserved for validation and transfer learning.

5. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 1, characterized in that, Step 6 includes the following specific operations: applying cubic spline interpolation to S(f) for each sample and smoothing it as needed to reduce the impact of simulation noise on extreme value extraction; locating the measured passband center f0 using the peak method or the symmetric second-moment method. (meas) f is determined by the -3 dB point or a specified threshold. l ,f h And calculate BW (meas) and FBW (meas) In the passband center Calculate insertion loss and return loss: Stopband point f s Stopband attenuation: Combining the results, we get: .

6. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 1, characterized in that, In step 7, the DNN model is performed. During training, the input parameters are X(j) and the coupled surrogate value. The output is The optimizer used is Adam, with parameters β1, β2, ε, initial learning rate η, batch size Batchsize, and maximum number of epochs MaxEpoch.

7. The terahertz waveguide cavity filter design optimization method based on deep neural networks according to claim 6, characterized in that, In step 7, the DNN model is performed. During training, the network is set to a fully connected network with an input layer, 512 nodes, 256 nodes, 128 nodes, and an output layer. The activation function of each hidden layer is ReLU, and the output layer is linearly activated.

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