Microwave device multi-physics field optimization method taking electromagnetism as center based on feature assistance and agent model

Abstract

The invention discloses a microwave device multi-physics field optimization method taking electromagnetism as a center based on a feature assistance and proxy model. The method comprises the steps of setting initial values of geometric design variables and multi-physics field design variables; the multi-physical field response with electromagnetism as the core responds at the solution point {xg, xm}, multiple pieces of parallel multi-physical field data are generated, and f represents the frequency; according to the multi-physics field data, constructing a feature-assisted multi-physics field agent model based on a neural network transfer function, and calculating a gradient optimization derivative of the feature-assisted multi-physics field agent model; and on the basis of the gradient optimization derivative and the optimization feature auxiliary multi-physics field agent model, obtaining an optimal solution of the variable. According to the method, the robustness and optimization design efficiency of a microwave device multi-physics field optimization algorithm taking electromagnetism as a core are improved.

Description

Technical Field

[0001] This invention relates to the field of microwave / RF circuit and system design technology, and in particular to a multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models. Background Technology

[0002] With the development of microwave technology and wireless communication, radio frequency (RF) circuits and systems are becoming increasingly miniaturized and integrated. The electro-thermal-mechanical multiphysics coupling effect in microwave devices is also becoming more pronounced. Therefore, multiphysics design for microwave devices is becoming an important trend in the development of modern RF circuits. However, existing multiphysics simulations are time-consuming and occupy a large amount of computational space. Directly optimizing these simulations leads to repeated, time-consuming multiphysics simulations, which significantly increases the optimization design time.

[0003] In recent years, neural networks have been widely used for parametric modeling and surrogate optimization of microwave / RF circuits. A well-trained neural network can serve as a surrogate model for multiphysics analysis of devices, providing the output response in just a few seconds. Therefore, it can replace time-consuming multiphysics simulations in the optimization process, improving efficiency. Among various surrogate modeling techniques, neural network transfer function surrogate modeling, as a type of knowledge-based neural network modeling, is widely applied to surrogate modeling of microwave circuits / RF systems. This technique utilizes a neural network to fit the relationship between input design parameters and system zeros and poles, and then calculates the electromagnetic response through the transfer function, greatly improving the model's accuracy and generalization ability.

[0004] However, relying solely on surrogate models for optimization design suffers from poor robustness. When the optimization metric deviates significantly from existing results, the error function of the surrogate optimization algorithm does not decrease substantially during each optimization iteration, leading to difficulties in optimization convergence.

[0005] With the development of microwave devices / circuits towards higher power and higher integration, and the increasingly significant multiphysics coupling effect, it is very important to carry out research on multiphysics optimization methods based on feature-assisted neural network transfer function surrogate models. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of low efficiency and poor robustness in existing multiphysics optimization methods by providing a multiphysics optimization method for microwave devices centered on electromagnetics, based on feature-assisted and surrogate models. This method improves the convergence and convergence speed of electromagnetic-centric multiphysics optimization by extracting feature information from the electromagnetic response to assist optimization. It derives the first derivative of the feature-assisted multiphysics surrogate model output with respect to the multiphysics design variables and utilizes a trust region algorithm to optimize the iteration step size, further enhancing the robustness and optimization efficiency of the electromagnetic-centric multiphysics optimization algorithm.

[0007] A multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models includes the following steps:

[0008] S1. Set geometric design variables and multiphysics design variables Initial value, initial trust radius and Among them, the geometric design variables The multiphysics design variables include the height of the pillars between the coupling windows of microwave devices and the height of the pillars in the cavity. This includes the voltage applied to the piezoelectric device;

[0009] S2. Within the defined trust region, the multiphysics response R0(x) with electromagnetic as its core. g x m f) at the solution point {x g x m The response at} is used to generate multiple parallel multiphysics data, where f represents the frequency;

[0010] S3. Based on the multiphysics data, construct a feature-assisted multiphysics proxy model based on the neural network transfer function, and calculate the gradient optimization derivative of the feature-assisted multiphysics proxy model;

[0011] S4. Based on the gradient optimization derivative, optimize the feature-assisted multiphysics proxy model, according to the variables. and Find the optimal solution

[0012] S5. Determine if the termination condition is met. If yes, stop the optimization process; otherwise, update the trust radius. and Update the weight factors of different objective functions, increase the number of iterations, and then proceed to step S2.

[0013] The output y of the feature-assisted multiphysics surrogate model includes the output y0 of the neural network transfer function model and the feature frequency y. fand feature height y h ,Right now:

[0014]

[0015] The optimization method for the feature-assisted multiphysics proxy model is expressed as follows:

[0016]

[0017] in, U represents the objective function combining the original objective function and the characteristic objective function, where U represents the original objective function for design optimization. f The objective function represents the characteristic frequency, and its forced characteristic frequency y f Satisfies the characteristic frequency specification; U h This represents the objective function for feature height y, which will be the feature height y. h Shift towards the passband canonical; α and β are weighting factors for different objective functions; k represents the number of optimization iterations, initialized to zero; It is the optimal multiphysics surrogate model solution obtained after the k-th iteration;

[0018]

[0019] In the optimization process, the judgment If the value is less than or equal to 0, optimize the neural network transfer function model output y0; otherwise, optimize the feature frequency y. f and feature height y h .

[0020] Wherein, the characteristic frequency y f The extraction formula includes:

[0021]

[0022] Among them, y f N represents the characteristic frequency. f The number of characteristic frequencies is represented by Im(·), which denotes the function that extracts the imaginary part from the complex value; V is an N f The selection matrix of ×N is defined as V = [v l,i ], w k Let z represent the weight vector of the neural network in the k-th iteration, and z be a vector composed of zeros obtained from the model, with dimension N. i Let i represent the i-th element in z.

[0023] Wherein, the feature height y h Extracted using the following formula:

[0024]

[0025] in, Indicates the feature height, y h This represents the set of feature heights that includes all feature heights.

[0026] The calculation of the gradient optimization derivative of the feature-assisted multiphysics surrogate model includes:

[0027] make and Represent the zeros, poles, and gain of the transfer function with respect to the geometric variable x. g The first derivative;

[0028]

[0029] set up and For the transfer function zeros, poles, and gain relative to multiple physical variables x m The first derivative;

[0030]

[0031] make Defined as the transfer function output y o The first derivatives of its zeros, poles, and gain:

[0032]

[0033] Where e represents an N×1 column vector, all of which have the value 1;

[0034]

[0035] make Indicates the output y of the transfer function o For multiphysics design variables x g and x m First derivative:

[0036]

[0037] Among them, let Defined as characteristic frequency y f Regarding x g and x m First derivative:

[0038]

[0039] in

[0040] make Defined as feature height y h Regarding x gand x m The first derivative;

[0041]

[0042] in

[0043]

[0044] Among them, the control index parameter r is set. s According to the control index parameter r s Update trust radius The calculation method is as follows:

[0045]

[0046] Where r h and r l These represent the adjustment parameters r. s The upper and lower limits, η e and η c These represent the expansion coefficient and contraction coefficient of the trust region radius, respectively.

[0047] Wherein, the control index parameter r s The formula derivation is as follows:

[0048]

[0049] R represents the multiphysics simulation response centered on electromagnetic fields and its extracted features corresponding to y.

[0050] Specifically, when the error of the design variables and / or the corresponding electromagnetic response reaches a preset threshold during continuous optimization iterations, the optimization process is considered terminated; the termination condition is stated as follows:

[0051]

[0052] If the above termination condition is not met, the optimization process will continue to the next iteration, i.e., k = k + 1; the optimization will be performed iteratively until any termination condition is met.

[0053] This invention combines a two-step training mechanism with a trust region optimization step size method, utilizing characteristic information in the electromagnetic response to assist in the optimization of multiphysics fields of microwave devices, such as the location of system zeros and poles and loss height. This significantly improves model accuracy and optimization efficiency, quickly achieving the optimization targets. It has obvious advantages in convergence and optimization efficiency, and greatly shortens the total optimization time. It can accurately predict the multiphysics response of microwave devices, providing an efficient and reliable method for the design of multiphysics fields of microwave devices. At the same time, it has a positive effect on sustainable development and environmental protection, reducing computational resource consumption and carbon emissions, and improving device performance to promote efficient resource utilization. Attached Figure Description

[0054] Figure 1 This is a flowchart of the feature-assisted surrogate model-based multiphysics optimization method for microwave devices centered on electromagnetics, as described in this application.

[0055] Figure 2 This is a schematic diagram of the structure of the feature-assisted multiphysics proxy model proposed in this application.

[0056] Figure 3 This is a structural diagram of the fourth-order tunable cavity filter of this application.

[0057] Figure 4 This is a schematic diagram of the starting point for optimizing the fourth-order tunable cavity filter in this application.

[0058] Figure 5 This is a diagram showing the result of the third iteration optimization of the fourth-order tunable cavity filter in this application.

[0059] Figure 6 This is the final optimized result of the fourth-order tunable cavity filter in this application. Detailed Implementation

[0060] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0061] To accelerate multiphysics optimization centered on electromagnetics, surrogate models are used, as multiphysics optimization is even more time-consuming than electromagnetic optimization, thus gradient descent is often chosen. However, gradient descent optimization is prone to getting trapped in local minima, especially when the starting point is far from the optimal solution. To address this issue, this application, for the first time, extracts features from a multiphysics surrogate model to assist multiphysics optimization. To extract more stable features, this application proposes using a neural network transfer function as the core surrogate for feature extraction. See Appendix. Figure 1 As shown in the exemplary embodiment of this application, the feature-assisted surrogate model-based multiphysics optimization method for microwave devices centered on electromagnetics includes:

[0062] S1. Set geometric design variables and multiphysics design variables Initial value, initial trust radius and Among them, the geometric design variables The multiphysics design variables include the height of the pillars between the coupling windows of microwave devices and the height of the pillars in the cavity. This includes the voltage applied to the piezoelectric device;

[0063] S2. Within the defined trust region, the multiphysics response R0(x) with electromagnetic as its core. g x m f) at the solution point {x g x m The response at} is used to generate multiphysics data using parallel DOE, where f represents the frequency;

[0064] S3. Based on the multiphysics data, construct a feature-assisted multiphysics proxy model based on the neural network transfer function (e.g., Figure 2 (As shown), calculate the gradient optimization derivative of the feature-assisted multiphysics proxy model;

[0065] S4. Based on the gradient optimization derivative, optimize the feature-assisted multiphysics proxy model, according to the variables. and Find the optimal solution

[0066] S5. Determine if the termination condition is met. If yes, stop the optimization process; otherwise, update the trust radius. and Update the weight factors of different objective functions, increase the number of iterations, and then proceed to step S2.

[0067] This application embodiment addresses the multiphysics optimization problem for microwave devices, initially focusing on the electromagnetic field as the core of the multiphysics optimization, let x... g Let x be the vector of geometric design variables for microwave devices. m R(x) is the multiphysics variable vector of the microwave device. g x m Let represent the output response (e.g., S-parameters) of a multiphysics simulation centered on electromagnetics. Then, the original electromagnetic-centered multiphysics optimization model for microwave devices can be expressed as:

[0068]

[0069] Where U represents the objective function related to the design specifications. and These represent the optimal values ​​of the geometric variables and multiphysics variables of the microwave device, respectively. The selection of these parameters ensures that the output response of the multiphysics simulation meets the design specifications.

[0070] In this embodiment of the application, the output y of the feature-assisted multiphysics proxy model includes the output y0 of the neural network transfer function model and the feature frequency y. f and feature height y h ,Right now:

[0071]

[0072] The optimization method for the feature-assisted multiphysics proxy model is expressed as follows:

[0073]

[0074] in, U represents the objective function combining the original objective function and the characteristic objective function, where U represents the original objective function for design optimization. f The objective function represents the characteristic frequency, and its forced characteristic frequency y f Satisfies the characteristic frequency specification; U h This represents the objective function for feature height y, which will be the feature height y. h Shift towards the passband canonical; α and β are weighting factors for different objective functions; k represents the number of optimization iterations, initialized to zero; It is the optimal multiphysics surrogate model solution obtained after the kth iteration; by introducing U f and U h The parameters of this multiphysics proxy optimization method can focus on correcting the passband response characteristics in the initial stage, thereby effectively increasing the possibility of escaping local minima.

[0075]

[0076] In this embodiment of the application, during the optimization process, it is determined that... If the value is less than or equal to 0, then optimize the neural network transfer function model output y. o Otherwise, optimize the feature frequency y f and feature height y h .

[0077] in, Figure 2 The structure of the feature-assisted multiphysics surrogate model is shown. Let f be the frequency, k represent the number of proposed optimization iterations, and y o The output of the transfer function of a multiphysics neural network. It approximates the multiphysics simulation response. The multiphysics response R0(x) g x mf) is obtained through multiphysics simulation based on the input frequency and design variables. Tr =|y o -R o | represents the error calculated during the two-step neuro-TF surrogate model training process, used to train the neural network.

[0078] In the proposed multiphysics neural network transfer function model, the pole / zero scheme of the transfer function is preferred to facilitate feature extraction.

[0079] The output of the multiphysics neural network transfer function model is expressed as:

[0080]

[0081] Where j represents the imaginary sign; N represents the order of the transfer function; w represents the weight parameters of the neural network; g represents the transfer function gain; and z represents the transfer function gain. i and p i These represent the zeros and poles of the transfer function, respectively.

[0082] In this embodiment, to establish the neural network transfer function model, vector fitting technology is first employed. Pole-zero extraction is performed on the design parameter samples. From the multiphysics responses (such as S-parameters) of all samples, the pole / zero data of the transfer function are extracted using a vector fitting algorithm. Then, a two-step training algorithm is used to train the neuro-TF multiphysics neural network transfer function model, performing a two-step neural network transfer function surrogate model training. First, let y f and y h Let y represent the characteristic frequency and characteristic height, respectively. The characteristic frequency y is extracted from the multiphysics neural network transfer function model. f and feature height y h It is used to assist in the design and optimization of multiphysics neural network transfer function models.

[0083] After constructing the multiphysics neural network transfer function model, feature frequencies and feature heights will be extracted. Let N... f To represent the number of characteristic frequencies, N is chosen from all zeros of the transfer function with positive imaginary parts. f The zeros of the transfer function make the absolute value of its real part relatively small; then based on the selected N... f The characteristic frequency is calculated from the imaginary part of the zeros of the transfer function. Wherein, the characteristic frequency y... f The extraction formula includes:

[0084]

[0085]

[0086] Among them, yf N represents the characteristic frequency. f The number of characteristic frequencies is represented by Im(·), which denotes the function that extracts the imaginary part from the complex value; V is an N f The selection matrix of ×N is defined as V = [v l,i ], w k Let z represent the weight vector of the neural network in the k-th iteration, and z be a vector composed of zeros obtained from the model, with dimension N. i Let i represent the i-th element in z.

[0087] After identifying the feature frequencies, the feature height y needs to be extracted. h Feature height y h The S-parameter response, defined as the response between two consecutive characteristic frequencies in the mid-frequency region, is proposed. The proposed characteristic height y... h The definition ensures that the number of feature heights remains constant, which is necessary during optimization, especially when the characteristic frequencies of the filter response cannot be explicitly identified. The first feature height... It is extracted based on the transfer function response of the characteristic frequency, and the characteristic height y h Extracted using the following formula:

[0088]

[0089] in, Indicates the feature height, y h This represents the set of feature heights that includes all feature heights.

[0090] In this embodiment of the application, after extracting the feature frequency and feature height, the overall feature-assisted multiphysics proxy model output y is defined as follows:

[0091]

[0092] In this embodiment of the application, calculating the gradient optimization derivative of the feature-assisted multiphysics surrogate model includes calculating the first derivative of the proposed feature-assisted multiphysics surrogate model output with respect to the multiphysics design variables, including:

[0093] make and Represent the zeros, poles, and gain of the transfer function with respect to the geometric variable x. g The first derivative;

[0094]

[0095] set up and For the transfer function zeros, poles, and gain relative to multiple physical variables x m The first derivative;

[0096]

[0097] make Defined as the transfer function output y o The first derivatives of its zeros, poles, and gain:

[0098]

[0099] Where e represents an N×1 column vector, all of which have the value 1;

[0100]

[0101] make Indicates the output y of the transfer function o For multiphysics design variables x g and x m First derivative:

[0102]

[0103] Among them, let Defined as characteristic frequency y f Regarding x g and x m First derivative:

[0104]

[0105] in

[0106] make Defined as feature height y h Regarding x g and x m The first derivative;

[0107]

[0108] in

[0109]

[0110] In this embodiment of the application, after deriving the derivative of the feature-assisted multiphysics surrogate model, gradient-based optimization can be performed, such as using the trust region algorithm to perform gradient-based optimization and obtain the optimal solution of the variable.

[0111] In this embodiment of the application, the control index parameter r is set. s According to the control index parameter r s Update trust radius The calculation method is as follows:

[0112]

[0113] Where r h and r l These represent the adjustment parameters r. s The upper and lower limits, for example, r h =0.8 and r l =0.1; η e and η c Let η represent the expansion coefficient and contraction coefficient of the trust region radius, respectively. e =1.3 and η c =0.7.

[0114] Wherein, the control index parameter r s The formula derivation is as follows:

[0115]

[0116] R represents the multiphysics simulation response centered on electromagnetic fields and its extracted features corresponding to y.

[0117] Specifically, when the error of the design variables and / or the corresponding electromagnetic response reaches a preset threshold during continuous optimization iterations, the optimization process is considered terminated; the termination condition is stated as follows:

[0118]

[0119] If the above termination condition is not met, the optimization process will continue to the next iteration, i.e., k = k + 1; the optimization will be performed iteratively until any termination condition is met.

[0120] The following example of optimizing a fourth-order tunable cavity filter verifies the feasibility of the optimization algorithm proposed in this application.

[0121] like Figure 3 As shown, h1, h2, and h3 are defined as the column heights between the coupling windows of a fourth-order tunable cavity filter; h c1 ,h c2 V1 and V2 are defined as the height of the pillar in the resonant cavity of the fourth-order tunable cavity filter. V1 and V2 are defined as the voltages applied to the piezoelectric device of the fourth-order tunable cavity filter. Under the action of voltage, the device will deform, thereby changing the shape of the resonant cavity and affecting the final electromagnetic response.

[0122] Wherein, the design variable x is defined as [h1h2h3h... c1 h c2 V1V2]T.

[0123] In this example, the design index is specified as |S 11|≤-20dB, 10.75GHz-11.05GHz, characteristic frequency index U f 10.75GHz≤y f ≤11.05GHz, characteristic height index is U h For y f ≤-20dB.

[0124] The starting point in this example is x. 0 =[3.2 3.84 3.66 3.02 2.72 0 0] T [mm mm mm mm mm VV], its electromagnetic response is far from the design specifications, such as Figure 4 As shown, its electromagnetic response was calculated using COMSOL Multiphysicis. In each optimization iteration, 81 sets of design parameters for training were generated using the DOE orthogonal sampling method, and then 81 sets of training data were obtained using parallel computing. Although the current electromagnetic response is far from the design specifications, the error function reflected by the characteristic frequencies is outside the specifications. Therefore, the optimization algorithm using feature-assisted methods can further improve the convergence and convergence speed of the algorithm.

[0125] Next, initialize the trust region radius δ 0 =[0.1 0.1 0.1 0.1 0.1 100100] T [mm mm mm mm mm mmV V] represents the model range or optimization range of this iteration.

[0126] In this example, the number of valid zeros N of the transfer function k =6, Number of characteristic frequencies N f =4. Figure 5 The results show the optimization after three iterations.

[0127] It can be seen that in the first few iterations, the focus was on optimizing feature frequency and feature height. After three iterations, the final optimized design metrics can be quickly approached.

[0128] Subsequently, since all characteristic frequencies fall within the passband, U f If the value is ≤0, the algorithm automatically disables feature frequency optimization and focuses on global error function optimization. For example... Figure 6 As shown, after one more iteration, the optimization for this example is complete. Table 1 shows the results of each optimization iteration, and the final solution is:

[0129] x 4 =[3.38625 4.08947 3.63204 3.29116 3.00399 266.71162 147.14372] T[mmmm mm mm mm VV]. Table 2 shows the optimization time for this example using this optimization algorithm.

[0130] Table 1 Results of each optimization iteration

[0131]

[0132] Table 2 Optimization Time

[0133]

[0134] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0135] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the claims be included within the invention.

[0136] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A multiphysics optimization method for microwave devices centered on electromagnetics, based on feature-assisted and surrogate models, characterized in that: Includes the following steps: S1. Set geometric design variables and multiphysics design variables Initial value, initial trust radius and Among them, the geometric design variables The multiphysics design variables include the height of the pillars between the coupling windows of microwave devices and the height of the pillars in the cavity. This includes the voltage applied to the piezoelectric device; S2. Within the defined trust region, the multiphysics response R0(x) with electromagnetic as its core. g x m f) at the solution point {x g x m The response at} is used to generate multiple parallel multiphysics data, where f represents the frequency; S3. Based on the multiphysics data, construct a feature-assisted multiphysics proxy model based on the neural network transfer function, and calculate the gradient optimization derivative of the feature-assisted multiphysics proxy model; S4. Based on the gradient optimization derivative, optimize the feature-assisted multiphysics proxy model, according to the variables. and Find the optimal solution S5. Determine if the termination condition is met. If yes, stop the optimization process; otherwise, update the trust radius. and Update the weight factors of different objective functions, increase the number of iterations, and then proceed to step S2.

2. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 1, characterized in that, The output y of the feature-assisted multiphysics proxy model includes the output y0 of the neural network transfer function model and the feature frequency y. f and feature height y h ,Right now:

3. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 2, characterized in that, The optimization method for the feature-assisted multiphysics proxy model is expressed as follows: in, U represents the objective function combining the original objective function and the characteristic objective function, where U represents the original objective function for design optimization. f The objective function represents the characteristic frequency, and its forced characteristic frequency y f Satisfies the characteristic frequency specification; U h This represents the objective function for feature height y, which will be the feature height y. h Shift towards the passband canonical; α and β are weighting factors for different objective functions; k represents the number of optimization iterations, initialized to zero; It is the optimal multiphysics surrogate model solution obtained after the k-th iteration; In the optimization process, the judgment is... If the value is less than or equal to 0, optimize the neural network transfer function model output y0; otherwise, optimize the feature frequency y. f and feature height y h .

4. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 3, characterized in that, The characteristic frequency y f The extraction formula includes: Among them, y f N represents the characteristic frequency. f The number of characteristic frequencies is represented by Im(·), which denotes the function that extracts the imaginary part from the complex value; V is an N f The selection matrix of ×N is defined as V = [v l,i ], w k Let z represent the weight vector of the neural network in the k-th iteration, and z be a vector composed of zeros obtained from the model, with dimension N. i Let i represent the i-th element in z.

5. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 4, characterized in that, The feature height y h Extracted using the following formula: in, Indicates the feature height, y h This represents the set of feature heights that includes all feature heights.

6. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 5, characterized in that, The calculation of the gradient optimization derivative of the feature-assisted multiphysics surrogate model includes: make and Represent the zeros, poles, and gain of the transfer function with respect to the geometric variable x. g The first derivative; set up and For the transfer function zeros, poles, and gain relative to multiple physical variables x m The first derivative; make Defined as the transfer function output y o The first derivatives of its zeros, poles, and gain: Where e represents an N×1 column vector, all of which have the value 1; make Indicates the output y of the transfer function o For multiphysics design variables x g and x m First derivative:

7. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 6, characterized in that, make Defined as characteristic frequency y f Regarding x g and x m First derivative: in make Defined as feature height y h Regarding x g and x m The first derivative; in 8. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 7, characterized in that, Set the control index parameter r s According to the control index parameter r s Update trust radius The calculation method is as follows: Where r h and r l These represent the adjustment parameters r. s The upper and lower limits, η e and η c These represent the expansion coefficient and contraction coefficient of the trust region radius, respectively.

9. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 8, characterized in that, The control index parameter r s The formula derivation is as follows: R represents the multiphysics simulation response centered on electromagnetic fields and its extracted features corresponding to y.

10. The multiphysics optimization method for electromagnetic-centric microwave devices based on feature-assisted and surrogate models according to claim 1, characterized in that, When the error of the design variables and / or the corresponding electromagnetic response reaches a preset threshold during continuous optimization iterations, the optimization process is considered to terminate; the termination condition is stated as follows: If the above termination condition is not met, the optimization process will continue to the next iteration, i.e., k = k + 1; the optimization will be performed iteratively until any termination condition is met.

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