Incremental multi-fidelity machine learning-assisted hybrid optimization method and system

Abstract

The present invention discloses a hybrid optimization method and system assisted by incremental multi-fidelity machine learning. The method mainly includes the steps of initial setup and initial sample acquisition, global low-fidelity proxy model #imgabs0# and residual model #imgabs1# training, global optimization, local proxy model training and optimization, low-fidelity full-wave simulation and updating of proxy model #imgabs2#, re-prediction and high-fidelity simulation. This method introduces multi-fidelity models and adaptive incremental learning in the process of training and updating proxy models, which can effectively reduce the computational complexity of sampling and training. At the same time, the hybrid optimization algorithm of global multi-objective and local single-objective is adopted in the optimization process, which can improve the efficiency of algorithm search. This method can be used in the fields of optimization design of multi-objective electromagnetic devices such as medium-sized antennas, arrays, filters, etc. with design parameters in 20-50 dimensions.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic device design and relates to an incremental multi-fidelity machine learning-assisted hybrid optimization method and system. Background Art

[0002] Over the past two decades, with the rapid development of artificial intelligence (AI), machine learning-assisted optimization (MLAO) methods for electromagnetic device design have received widespread attention and research in academia and industry. Using machine learning methods to establish low-cost surrogate models has greatly alleviated the computational burden of invoking full-wave simulation for evaluation in global optimization, providing a new paradigm for electromagnetic device design. Traditional MLAO methods typically study problems with relatively small design parameter sizes, typically under 20 dimensions. However, with the increasing complexity of electromagnetic device design, the dimensionality of design variables and the number of optimization objectives are also increasing. Medium-scale multi-objective optimization problems with design parameters between 20 and 50 dimensions are common in practical engineering, and traditional MLAO methods have certain limitations. The increase in the dimensionality of design parameters and the number of optimization objectives poses challenges to traditional MLAO methods in terms of sample acquisition, surrogate model training, and optimization. Summary of the Invention

[0003] Purpose of the invention: To address the above problems, the present invention proposes an incremental multi-fidelity machine learning-assisted hybrid optimization method and system, which can reduce the computational cost of sampling and training while significantly improving the optimization efficiency.

[0004] Technical Solution: To achieve the above-mentioned purpose, the present invention provides an incremental multi-fidelity machine learning-assisted hybrid optimization method, comprising the following steps:

[0005] (1) Define the design variables, optimization indicators, and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values;

[0006] (2) For each optimization objective, a low-fidelity proxy model is obtained by using the collaborative Kriging model training And the residual model

[0007] (3) Perform global optimization through multi-objective optimization algorithms to obtain multiple Pareto optimal solutions to multi-objective problems;

[0008] (4) Latin hypercube sampling is performed in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model in step (2). A local surrogate model is obtained based on the sample training in the neighborhood of each Pareto optimal solution. Then, a gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. The parameters are sorted according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each target.

[0009] (5) Select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations to perform low-fidelity full-wave simulation, and use adaptive incremental learning to update the agent model To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning;

[0010] (6) Using the proxy model In the prediction step (5), the optimal parameter combination of the preset number of groups is obtained, and the group of parameter combinations with the best response is selected to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, the loop is exited, otherwise the data set is updated and the process returns to step (2) to continue the optimization.

[0011] It is further preferred that a multi-starting point approach is selected when training parameters of the collaborative Kriging model in step (2).

[0012] Further preferably, the fitness function of the local optimization in step (4) is set to:

[0013]

[0014] in

[0015]

[0016] y LO,i,m (x LO,i ) is the parameter combination x LO,i The predicted value of the mth target, w m is the weight of the mth target, y g,m is the target value of the mth target.

[0017] Further preferably, the local proxy model in step (4) is a radial basis function model.

[0018] Further preferably, in step (5), retraining is performed when a preset number of iterations is reached or the simulation value, prediction value and prediction standard deviation of the newly added samples meet the set conditions.

[0019] Further optimization, the simulation value y of the newly added sample L,m (xLO,i ), predicted value and the predicted standard deviation satisfy When , retrain, β is the preset empirical constant.

[0020] Based on the same inventive concept, the present invention provides an incremental multi-fidelity machine learning-assisted hybrid optimization system, comprising:

[0021] The initial setting and initial sample acquisition module is used to define the design variables, optimization indicators and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values;

[0022] The global proxy model training module is used to train a low-fidelity proxy model for each optimization objective using the co-kriging model. And the residual model

[0023] The global optimization module is used to perform global optimization through a multi-objective optimization algorithm to obtain multiple Pareto optimal solutions to multi-objective problems;

[0024] The local surrogate model training and optimization module is used to perform Latin hypercube sampling in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model. The local surrogate model is trained based on the samples in the neighborhood of each Pareto optimal solution. Then, a gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. These are ranked according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each objective.

[0025] Low-fidelity simulation and proxy models The update module is used to select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations for low-fidelity full-wave simulation, and update the agent model using adaptive incremental learning To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning;

[0026] and reforecasting and high-fidelity simulation modules for leveraging surrogate models Predict the optimal parameter combination of the preset number of groups, and select the parameter combination with the best response to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, it ends, otherwise the data set is updated and re-trained through the global agent model training module, global optimization module, local agent model training and optimization module and low-fidelity simulation and agent model The update module continues to be optimized.

[0027] The present invention also provides a computer system comprising a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein the computer program / instruction, when executed by the processor, implements the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method.

[0028] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method.

[0029] The present invention also provides a computer program product comprising a computer program / instruction, which, when executed by a processor, implements the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method.

[0030] Beneficial effects: Compared with the existing technology, the present invention has the following beneficial effects: (1) A reliable multi-fidelity model is used for sampling, which reduces the sampling time; (2) During the training process, the proxy model is updated by adaptive incremental learning. Incremental learning can utilize the hyperparameter knowledge of the old model, reducing the training time; (3) During the optimization process, a hybrid optimization algorithm combining global multi-objective optimization with local single-objective optimization is used to improve the optimization convergence speed, thereby reducing the number of full-wave simulations and the time of full-wave simulations. Local optimization introduces additional computational cost. Training the local proxy model with data generated by the global proxy model reduces the computational time of local optimization to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is an overall flow chart of the method of an embodiment of the present invention.

[0032] Figure 2 is a detailed flow chart of the algorithm of an embodiment of the present invention;

[0033] Figure 3 It is a schematic diagram of the antenna structure used to verify the algorithm proposed in the present invention;

[0034] Figure 4 It is an iterative curve graph of different optimization algorithms;

[0035] Figure 5It is the antenna response simulation curve before and after optimization. DETAILED DESCRIPTION

[0036] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] like Figure 1 and Figure 2 As shown, an embodiment of the present invention discloses an incremental multi-fidelity machine learning-assisted hybrid optimization method, comprising the following steps:

[0038] (1) Initial setting and initial sample acquisition: Define the design variables, optimization indicators and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values.

[0039] (2) Global Low-Fidelity Proxy Model With the residual model Training: For each optimization objective, a low-fidelity proxy model is trained using the co-kriging model. And the residual model

[0040] (3) Global optimization: Global optimization is performed through a multi-objective optimization algorithm to obtain multiple Pareto optimal solutions to multi-objective problems.

[0041] (4) Local surrogate model training and optimization: Latin hypercube sampling is performed in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model in step (2). The local surrogate model is trained based on the samples in the neighborhood of each Pareto optimal solution. Then, the gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. The parameters are sorted according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each target.

[0042] (5) Low-fidelity full-wave simulation and updating of proxy models Select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations to perform low-fidelity full-wave simulation, and use adaptive incremental learning to update the agent model To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning.

[0043] (6) Re-forecasting and high-fidelity simulation: using surrogate models In the prediction step (5), the optimal parameter combination of the preset number of groups is obtained, and the group of parameter combinations with the best response is selected to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, the loop is exited, otherwise the data set is updated and the process returns to step (2) to continue the optimization.

[0044] The present invention introduces a multi-fidelity model and adaptive incremental learning during the training and updating of proxy models, effectively reducing the computational complexity of sampling and training. Furthermore, the optimization process utilizes a hybrid optimization algorithm that combines global multi-objective and local single-objective optimization, improving algorithm search efficiency. This method can be applied to the optimization design of multi-objective electromagnetic devices, such as medium-sized antennas, arrays, and filters, with design parameters ranging from 20 to 50 dimensions.

[0045] The advantages of the present invention are illustrated below with an example of a real antenna structure. Figure 3 As shown in FIG, a structural diagram of a substrate integrated waveguide slot antenna array is given, and the design parameters and their value ranges are shown in Table 1.

[0046]

[0047] The following describes a specific implementation method based on a multi-objective optimization task. Based on the above antenna structure, the incremental multi-fidelity machine learning-assisted hybrid optimization method of the present invention includes the following steps:

[0048] (1) Initial setting and initial sample acquisition: First, the design variables, optimization indicators, and optimization space [a, b] of the problem need to be defined. D , where a and b are the upper and lower bounds of the variables, and D is the dimension of the design parameters. Figure 3 Taking the antenna in as an example, the design parameters are 22 listed in Table 1, that is, D = 22, and the design indicators include |S in the 76GHz~81GHz band. 11 | Less than -10dB, SLL of 6 frequency points with a frequency interval of 1GHz from 76GHz to 81GHz is less than -20dB, a total of 7 indicators. Latin Hypercube Sampling (LHS) is used to obtain N L Low-fidelity initial samples, in this case N L =D, denoted as X L , and the response value Y is obtained by using the low-fidelity full-wave simulation model L =U L (X L ). Then from X L Select N H Samples X H And perform high fidelity full wave simulation, in this case N H =4, the response value of the high-fidelity model is YH =U H (X H Both high- and low-fidelity responses were simulated using ANSYS. The high-fidelity full-wave simulation used a discrete model frequency sweep, with a maximum adaptive number of 30, a convergence criterion ΔS of 0.01, and a frequency interval of 0.1 GHz. The low-fidelity full-wave simulation used a maximum adaptive number of 10, a convergence criterion ΔS of 0.02, and a frequency interval of 1 GHz. Simulation times for the high- and low-fidelity models were 14 and 4 minutes, respectively.

[0049] (2) Low-fidelity proxy models With the residual model Training: For each target, a low-fidelity proxy model is trained using the co-kriging model for each design target. And the residual model The input and output parameters of the low-fidelity model are X L and low-fidelity response Y L ; The input and output parameters of the residual model are X H and Y R , where Y R =Y H -ρY L ρ is a hyperparameter that needs to be estimated when training the surrogate model. To reduce the possibility of the gradient algorithm falling into a local optimum, a multi-starting point approach is selected when training the parameters, and the number of starting points is set to 3.

[0050] (3) Global optimization: Global optimization is performed through a multi-objective optimization algorithm to obtain the Pareto frontier X of the multi-objective problem. GO ={x GO,i |i=1,…,N GO}, where N GO The multi-objective optimization algorithm in this embodiment uses the non-dominated sorting genetic algorithm II (NSGA-II). In some embodiments, a multi-objective evolutionary algorithm, a non-dominated sorting genetic algorithm III, etc. may also be used.

[0051] (4) Local proxy model training and optimization: When training a global proxy model, a training target often needs to model multiple frequency points or angle points to obtain better training results, and the local optimization process needs to be performed on each solution on the Pareto front, which will increase the prediction cost. The local proxy model is trained near each Pareto optimal solution obtained in step (3) to reduce the prediction cost of local optimization. The training of the local model will bring additional computational overhead. In order to alleviate this problem, Latin hypercube sampling is first performed in the neighborhood of each Pareto optimal solution to obtain sample points, denoted as The response value of each sample is obtained by predicting the global surrogate model in step (2) rather than by full-wave simulation. The response value predicted by the global surrogate model is recorded as and Used to train the radial basis function model. After obtaining the local proxy model of each target, the gradient-based single-objective optimization algorithm is used for local optimization, and the fitness function is set as:

[0052]

[0053] in

[0054]

[0055] y LO,i,m (xL O,i ) is the parameter combination x LO,i The predicted value of the mth target, w m is the weight of the mth objective. The optimization process is repeated N times GO times, get N GO A local optimal parameter combination, denoted as X LO , and calculate the function value of formula (1) to N GO To avoid the situation where there are too many Pareto optimal solutions and the local optimization time is too long, N GO If N GO >N s , then from x GO Randomly select N s Perform local optimization on N solutions. s Set to 100.

[0056] (5) Low-fidelity full-wave simulation and updating of proxy models First, from X LO Select I LO The optimal parameter combination is used to perform low-fidelity full-wave simulation. Considering the computational cost, I LO=3. Then the agent model is updated using adaptive incremental learning In order to reduce the computational complexity of training, in this embodiment, the simulation value y of each 10 iterations or newly added samples is L,m (x LO,i ), predicted value and the predicted standard deviation satisfy:

[0057]

[0058] The hyperparameters of the low-fidelity proxy model are updated using retraining. Otherwise, the proxy model is updated using incremental learning. β is a preset empirical constant, which is set to 3 in this embodiment.

[0059] (6) Re-prediction and high-fidelity simulation: First, use the proxy model The I obtained in the prediction step (5) LO A set of parameter combinations is generated, and then the best response parameter combination is selected for high-fidelity full-wave simulation. If the simulation results meet the design specifications, the loop is exited; otherwise, the data set is updated and the optimization continues in step (2).

[0060] The optimization effect of the present invention is illustrated below by comparative experiments:

[0061] Figure 4Table 2 and Table 2 give the comparison results of the incremental variable-fidelity machine learning-assisted hybrid optimization (IVF-MLAHO, denoted as Algorithm 1) method, the variable-fidelity machine learning-assisted hybrid optimization (VF-MLAHO, denoted as Algorithm 2) method, the incremental variable-fidelity machine learning-assisted multiobjective optimization (IVF-MLAMO, denoted as Algorithm 3) method, the incremental variable-fidelity machine learning-assisted weight sum optimization (IVF-MLAWSO, denoted as Algorithm 4) method and the single-fidelity machine learning-assisted weight sum optimization (SF-MLAWSO, denoted as Algorithm 5) method.

[0062]

[0063] Each algorithm was run independently for 5 times. In the five optimizations, the proposed IVF-MLAHO algorithm met the design target at an average of 25.6 iterations. The VF-MLAHO algorithm did not fully meet the design target in the second and fourth optimizations. The unsatisfied target in the second optimization was |S 11 |, the final optimization value is |S 11 |=-9.89dB; the indicator that was not met in the fourth optimization was the sidelobe level at 80GHz. The final optimization value was -19.45dB, which is very close to the optimization target. Compared with the VF-MLAHO algorithm, the IVF-MLAHO algorithm saved 79.6% of the training time. The other three algorithms only achieved the design target once or not in the five optimizations. A set of results before and after the IVF-MLAHO algorithm optimization are shown as follows: Figure 5 As shown, before optimization |S 11| Less than -10dB at 76.3GHz~77GHz and 77.4~78.9GHz, after optimization|S 11 The worst value across the entire frequency band is -11.19 dB, meeting the design target. Before optimization, the sidelobe levels at 80 GHz and 81 GHz were -18.78 dB and -15.44 dB, respectively. After optimization, the SLLs at all six frequency points between 76 and 81 GHz are less than -20 dB.

[0064] Based on the same inventive concept, an embodiment of the present invention discloses an incremental multi-fidelity machine learning-assisted hybrid optimization system, comprising:

[0065] The initial setting and initial sample acquisition module is used to define the design variables, optimization indicators and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values;

[0066] The global proxy model training module is used to train a low-fidelity proxy model for each optimization objective using the co-kriging model. And the residual model

[0067] The global optimization module is used to perform global optimization through a multi-objective optimization algorithm to obtain multiple Pareto optimal solutions to multi-objective problems;

[0068] The local surrogate model training and optimization module is used to perform Latin hypercube sampling in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model. The local surrogate model is trained based on the samples in the neighborhood of each Pareto optimal solution. Then, a gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. These are ranked according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each objective.

[0069] Low-fidelity simulation and proxy models The update module is used to select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations for low-fidelity full-wave simulation, and update the agent model using adaptive incremental learning To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning;

[0070] and reforecasting and high-fidelity simulation modules for leveraging surrogate models Predict the optimal parameter combination of the preset number of groups, and select the parameter combination with the best response to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, it ends, otherwise the data set is updated and re-trained through the global agent model training module, global optimization module, local agent model training and optimization module and low-fidelity simulation and agent model The update module continues to be optimized.

[0071] An embodiment of the present invention also discloses a computer system, including a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor. When the computer program / instruction is executed by the processor, the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method are implemented.

[0072] An embodiment of the present invention also discloses a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method.

[0073] An embodiment of the present invention also discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method.

[0074] The program / instruction code for implementing the inventive method can be written in any combination of one or more programming languages. These programs / instruction codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device so that the program / instruction code, when executed by the processor or controller, causes the steps of the inventive method to be implemented. The program / instruction code can be executed entirely on the machine, partially on the machine, partially on the machine as an independent software package and partially on a remote machine, or completely on a remote machine or server. The parts not described in detail in the present invention are all known technologies of those skilled in the art.

[0075] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. An incremental multi-fidelity machine learning-assisted hybrid optimization method, characterized in that The following steps are involved: (1) Define the design variables, optimization indicators, and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values; (2) For each optimization objective, a low-fidelity proxy model is obtained by using the collaborative Kriging model training And the residual model (3) Perform global optimization through multi-objective optimization algorithms to obtain multiple Pareto optimal solutions to multi-objective problems; (4) Latin hypercube sampling is performed in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model in step (2). A local surrogate model is obtained based on the sample training in the neighborhood of each Pareto optimal solution. Then, a gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. The parameters are sorted according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each target. (5) Select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations to perform low-fidelity full-wave simulation, and use adaptive incremental learning to update the agent model To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning; (6) Using the proxy model In the prediction step (5), the optimal parameter combination of the preset number of groups is obtained, and the group of parameter combinations with the best response is selected to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, the loop is exited, otherwise the data set is updated and the process returns to step (2) to continue the optimization.

2. The incremental multi-fidelity machine learning-assisted hybrid optimization method according to claim 1, characterized in that: In step (2), multiple starting points are selected when training parameters of the co-Kriging model.

3. The incremental multi-fidelity machine learning-assisted hybrid optimization method according to claim 1, characterized in that: The fitness function of local optimization in step (4) is set as: in y LO,i,m (x LO,i ) is the parameter combination x LO,i The predicted value of the mth target, w m is the weight of the mth target, y g,m is the target value of the mth target.

4. The incremental multi-fidelity machine learning-assisted hybrid optimization method according to claim 1, characterized in that: The local proxy model in step (4) is a radial basis function model.

5. The incremental multi-fidelity machine learning-assisted hybrid optimization method according to claim 1, characterized in that: In step (5), retraining is performed when the preset number of iterations is reached or the simulation value, prediction value and prediction standard deviation of the newly added samples meet the set conditions.

6. The incremental multi-fidelity machine learning-assisted hybrid optimization method according to claim 5, characterized in that: In the simulation value y of the newly added sample L,m (x LO,i ), predicted value and the predicted standard deviation satisfy When , retrain, β is the preset empirical constant.

7. An incremental multi-fidelity machine learning-assisted hybrid optimization system, characterized in that include: The initial setting and initial sample acquisition module is used to define the design variables, optimization indicators and optimization space of the optimization problem, use Latin hypercube sampling to obtain low-fidelity initial samples and perform low-fidelity full-wave simulation to obtain response values, and select samples from the low-fidelity initial samples to perform high-fidelity full-wave simulation to obtain response values; Global low-fidelity proxy model With the residual model The training module is used to train the low-fidelity proxy model using the co-kriging model for each optimization objective. And the residual model The global optimization module is used to perform global optimization through a multi-objective optimization algorithm to obtain multiple Pareto optimal solutions to multi-objective problems; The local surrogate model training and optimization module is used to perform Latin hypercube sampling in the neighborhood of each Pareto optimal solution. The response value of the sample is predicted by the global surrogate model. The local surrogate model is trained based on the samples in the neighborhood of each Pareto optimal solution. Then, a gradient-based single-objective optimization algorithm is used for local optimization to obtain multiple sets of locally optimal parameter combinations. These are ranked according to the fitness function value. The fitness function value of the local optimization is the weighted sum of the predicted values ​​of each objective. Low-fidelity simulation and proxy models The update module is used to select the optimal parameter combination of a preset number of groups from the sorted multiple groups of local optimal parameter combinations for low-fidelity full-wave simulation, and update the agent model using adaptive incremental learning To reduce the computational complexity of training; when the preset conditions are met, the hyperparameters of the low-fidelity proxy model are updated by retraining; otherwise, the proxy model is updated by incremental learning; and reforecasting and high-fidelity simulation modules for leveraging surrogate models Predict the optimal parameter combination of the preset number of groups, and select the parameter combination with the best response to perform high-fidelity full-wave simulation; if the simulation result meets the design indicators, it ends, otherwise the data set is updated and re-trained through the global agent model training module, global optimization module, local agent model training and optimization module and low-fidelity simulation and agent model The update module continues to be optimized.

8. A computer system comprising a memory, a processor, and a computer program / instruction stored in the memory and executable on the processor, wherein: When the computer program / instructions are executed by a processor, the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method according to any one of claims 1 to 6 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the incremental multi-fidelity machine learning-assisted hybrid optimization method according to any one of claims 1 to 6 are implemented.

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