A machine learning approach to the new classical annular viscous torque

Abstract

The present invention provides a machine learning method for a neoclassical toroidal viscous torque, which relates to the technical field of controlled nuclear fusion. The present invention obtains the computational efficiency evaluation coefficient of each module to screen out modules that have computational bottlenecks and require alternative models, obtains alternative models through training, discriminates and optimizes the alternative models based on the reliability coefficients, replaces submodules with computational bottlenecks with alternative models, forms a neoclassical toroidal viscous torque model that couples physics and neural networks, obtains the computational evaluation efficiency coefficient of the alternative model, and obtains the coupling reliability coefficient, judges and optimizes the neoclassical toroidal viscous torque model that couples physics and neural networks. The present invention improves computational efficiency, breaks through the time cost bottleneck of traditional methods, is flexible enough to adapt to the input requirements of different physical parameters, and provides accurate and fast support for experimental discharge control and scheme design.

Description

Technical Field

[0001] The present invention relates to the technical field of controlled nuclear fusion, and in particular to a machine learning method for neoclassical annular viscous torque. Background Art

[0002] A tokamak device uses magnetic confinement to confine plasma and achieves controlled nuclear fusion by continuously heating the plasma. The ideal tokamak magnetic field configuration is toroidally symmetric. However, under real experimental conditions, due to factors such as coil magnetic field disturbances, the tokamak magnetic field often exhibits toroidal asymmetry. This toroidal asymmetry generates an additional toroidal torque through the neoclassical toroidal viscosity effect. This additional toroidal torque, known as the NTV torque, affects the toroidal rotation of the plasma, thereby affecting tokamak plasma instabilities and device performance.

[0003] Therefore, NTV torque analysis is essential for achieving controlled nuclear fusion. Accurate and rapid NTV torque simulation analysis helps enhance understanding of experimental phenomena and improves prediction and control capabilities for future experiments. Currently, the traditional neoclassical toroidal viscous torque physics calculation process (NTV-PHY) solves NTV torque numerically. However, this numerical method is extremely time-consuming to perform NTV torque analysis.

[0004] Chinese invention patent application number CN117371299A discloses a machine learning method for calculating the neoclassical toroidal viscous torque of a tokamak. This method extracts input and output data from a conventional tokamak neoclassical toroidal viscous torque calculation program, constructs a dataset for model training, and designs and trains a deep neural network model capable of predicting the tokamak's neoclassical toroidal viscous torque based on the dataset. This technical solution demonstrates the computational efficiency of the AI ​​method, but its fully end-to-end implementation of neoclassical toroidal viscous torque calculation lacks physical completeness and interpretability.

[0005] In the Chinese invention patent with application number CN119046590A, the implementation method of the AI ​​agent model of the linearized drift dynamic equation is disclosed. It is still an end-to-end implementation method for the linearized drift dynamic equation, and has not been connected with other physical processes of the neoclassical annular viscous torque. It is impossible to develop a complete calculation process for the neoclassical annular viscous torque, and lacks physical completeness and practical operability.

[0006] According to the above applications and existing technologies, the existing methods for calculating the neoclassical toroidal viscous torque of tokamaks have computational efficiency issues in NTV torque simulation when establishing equations based on physical principles, and black box unexplainable issues in NTV torque simulation when using machine learning methods. These contradictions restrict the development of physical research and the optimization of device performance.

[0007] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0008] The purpose of the present invention is to provide a new classical annular viscous torque machine learning method to solve the problems raised in the above background technology.

[0009] To achieve the above object, the present invention provides the following technical solutions:

[0010] A new classical annular viscous torque machine learning method, the specific steps include:

[0011] Step 1: Divide the traditional neoclassical hoop viscous torque physical model process into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. Obtain the runtime and computational efficiency evaluation coefficient of each submodule, set the computational efficiency evaluation coefficient threshold, and identify the module with computational bottlenecks.

[0012] Step 2: Using the input of the submodule with a computational bottleneck as the training set and the output as the label, a fully connected neural network is trained to obtain a surrogate model. A reliability coefficient is constructed based on the input and output of the surrogate model. The corresponding submodule with a computational bottleneck is replaced with the surrogate model to form a new classical hoop viscous torque model that couples physics and neural networks.

[0013] Step 3: Obtain the computational efficiency evaluation coefficient of the surrogate model in the new classical annular viscous torque model of coupled physics and neural networks, set the reliability threshold and model evaluation threshold, and judge the optimization status of the surrogate model by combining the reliability coefficient, the computational efficiency evaluation coefficient of the surrogate model, the reliability threshold, and the model evaluation threshold;

[0014] Step 4: Input the training set into the traditional neoclassical annular viscous torque physical model to obtain the true torque, and input the training set into the neoclassical annular viscous torque model of coupled physics and neural network to obtain the simulated prediction value. Construct the coupling reliability coefficient based on the true torque and the simulated prediction value, set the coupling reliability threshold, and combine the coupling reliability coefficient, the computational efficiency coefficient of the alternative model, the coupling reliability threshold, and the model evaluation threshold to determine the correct neoclassical annular viscous torque model of coupled physics and neural network.

[0015] Furthermore, the traditional neoclassical annular viscous torque physical model is divided into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. These submodules are numbered and the running time of each submodule is obtained. The computational efficiency evaluation coefficient of each submodule is evaluated using the module running time. The computational efficiency evaluation coefficient is based on the following formula:

[0016] ;

[0017] in, For the The computational efficiency evaluation coefficient of each submodule, For the The running time of each submodule, is the total running time of the traditional neoclassical hoop viscous torque physical model, , Retrieve variable for module number, , ;

[0018] Set the calculation efficiency evaluation coefficient threshold. When the computational efficiency evaluation coefficient of a submodule exceeds the computational efficiency evaluation coefficient threshold, it means that the There are computational bottlenecks in each submodule, and model replacement is required.

[0019] Furthermore, the submodule with a computational bottleneck is obtained and calibrated as a model replacement module. The input and output of the submodule with a computational bottleneck are obtained. The input of the submodule with a computational bottleneck is used as a training set, and the output of the submodule with a computational bottleneck is used as a label. The training is input into a fully connected neural network to obtain a replacement model. The reliability coefficient is obtained based on the input and output of the replacement model. The formula is as follows:

[0020] ;

[0021] in, is the reliability coefficient, is the number of training set samples, For the replacement model The output corresponding to the samples is is the mean of the output of the model replacement module, For the The labels of samples, Retrieve variables for sample numbers, , ;

[0022] The sub-modules with computational bottlenecks in the traditional neoclassical toroidal viscous torque physical model are removed and replaced with corresponding alternative models to form a neoclassical toroidal viscous torque model that couples physics and neural networks.

[0023] Furthermore, the computational efficiency evaluation coefficient of the alternative model in the new classical annular viscous torque model of coupled physics and neural networks is obtained. The logic is:

[0024] When obtaining the runtime of each submodule in step 1, each submodule has a corresponding input. This input is then fed back into the surrogate model, which then obtains an output based on the input. The time consumed by the surrogate model is the runtime of the surrogate model. The total runtime of the neoclassical circumferential viscous torque model that couples physics and neural networks is obtained by adding the runtime of the surrogate model to the runtime of the submodule without computational bottlenecks.

[0025] The calculation efficiency evaluation coefficient of the substitution model is based on the following formula:

[0026] ;

[0027] in, is the computational efficiency evaluation coefficient of the alternative model, is the running time of the alternative model, Total runtime for the neoclassical toroidal viscosity-torque model coupled with physics and neural networks.

[0028] Furthermore, a reliability threshold and a model evaluation threshold are set respectively. When the reliability coefficient is less than the reliability threshold and the computational efficiency evaluation coefficient of the surrogate model is greater than the model evaluation threshold, it means that the surrogate model needs to be optimized in terms of accuracy and computational efficiency. Otherwise, the surrogate model is not optimized.

[0029] The accuracy and computational efficiency optimization logic is as follows:

[0030] Get the weight of each neuron in each layer of the alternative model and the median of the neuron weight in each layer, set the pruning hyperparameters and initial values, and prune the neurons in each layer according to the pruning formula. The formula is as follows:

[0031] ;

[0032] in, Indicates the Tier neuron weights, is the pruning hyperparameter, For the The median neuron weight of the layer, Retrieve the variable for the neuron number, , , For the The total number of neurons in the layer, Retrieve variables for the layer number of the neural network model, , , is the total number of layers;

[0033] The neurons that meet the pruning formula are retained, and the neurons that do not meet the pruning formula are removed. The pruning hyperparameters use the initial values ​​during the first optimization. The pruned model is used for training again to obtain the reliability coefficient and the computational efficiency evaluation coefficient. The reliability threshold and the model evaluation threshold are used to determine whether optimization is needed again. If optimization is not needed, the current alternative model is used. If optimization is needed, the pruning hyperparameters are adjusted according to the change rate of the reliability coefficient and the computational efficiency evaluation coefficient. The adjustment is based on the following formula:

[0034] ;

[0035] in, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment factor and , Select the function for the maximum value, is the reliability coefficient of the surrogate model after pruning, is the reliability coefficient of the alternative model before pruning, is the computational efficiency evaluation coefficient of the pruned alternative model, is the computational efficiency evaluation coefficient of the alternative model before pruning;

[0036] Use the adjusted pruning hyperparameters to prune the surrogate model and determine whether optimization is needed again. This is a loop. During the loop, the adjustment sequence of the pruning hyperparameters is obtained according to the following formula:

[0037] ;

[0038] in, is the adjustment sequence of pruning hyperparameters, The pruning hyperparameters obtained for the first adjustment are: The pruning hyperparameters obtained for the second adjustment are: The pruning hyperparameters obtained for the third adjustment are: For the The pruning hyperparameters obtained by adjusting the Retrieve the variable for the number of adjustments, ;

[0039] The adjustment sequence of pruning hyperparameters is screened to obtain the latest continuously decreasing sequence, which is a subsequence containing the latest pruning hyperparameters and in which the subsequent pruning hyperparameters are all smaller than the previous pruning hyperparameters. The surrogate model obtained by the first pruning hyperparameter in the latest continuously decreasing sequence is pruned using the latest pruning hyperparameters. If the latest continuously decreasing sequence does not exist, the surrogate model is pruned using the current pruning hyperparameters.

[0040] Set the maximum number of pruning times. When the maximum number of pruning times is reached and the alternative model still needs to be optimized based on the reliability threshold and model evaluation threshold, the number of layers will be reduced. The logic for reducing the number of layers is as follows:

[0041] The activation variance of each layer is obtained, the layer with the smallest activation variance is removed, and the surrogate model is pruned again starting from the surrogate model before pruning. The maximum number of pruning layers is set. When the maximum number of pruning layers is reached or the non-optimization condition is met, the surrogate model is determined to be obtained.

[0042] Furthermore, a training set of the surrogate model is obtained, and the training set is input into the traditional neoclassical annular viscous torque physical model, and the output of the traditional neoclassical annular viscous torque physical model corresponding to each sample in the training set is obtained and calibrated as the true torque;

[0043] Each sample in the training set is input into the neoclassical annular viscous torque model coupled with physics and neural networks, and the output is obtained and calibrated as the model prediction value;

[0044] The coupling reliability coefficient of the neoclassical hoop viscous torque model for coupled physics and neural networks is obtained based on the following formula:

[0045] ;

[0046] in, is the coupling reliability coefficient, For the The model prediction value of samples, For the The true moment of the sample, is the average value of the true moment of all samples, is the number of training set samples, Retrieve variables for sample numbers, , ;

[0047] A coupling reliability threshold is set. When the coupling reliability coefficient is less than the coupling reliability threshold and the computational efficiency evaluation coefficient of the surrogate model is greater than the model evaluation threshold, it means that the surrogate model needs to be optimized for accuracy and computational efficiency. Otherwise, it is considered that the correct neoclassical toroidal viscous torque model of coupled physics and neural networks has been obtained. The accuracy and computational efficiency optimization logic is as follows:

[0048] The surrogate model is optimized again using the optimization process of step 3, and the conditions for whether to perform pruning, layer reduction, and optimization are replaced with the coupling reliability coefficient, the computational efficiency coefficient of the surrogate model, the coupling reliability threshold, and the model evaluation threshold. At the same time, the reliability coefficient in the pruning hyperparameter formula is replaced with the coupling reliability coefficient.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] The present invention innovatively solves key problems in the background technology by coupling a deep neural network model with the new classical annular viscous torque physical equation. First, the coupling method overcomes the accuracy limitations of traditional calculation methods, achieves high accuracy and high reliability in the prediction of the new classical annular viscous torque, and avoids the prediction deviation caused by model simplification; second, the coupling of deep learning and physical equations significantly improves computational efficiency, allowing the simulation process to be completed under immediate or real-time conditions, breaking through the time cost bottleneck of traditional methods; in addition, the method couples the torque calculation module of the physical model and can interpret the simulation results according to physical laws; finally, the coupling method can flexibly adapt to the input requirements of different physical parameters, providing accurate and rapid theoretical support for experimental discharge control and scheme design, thereby effectively promoting the research and application of tokamak devices in the field of controlled nuclear fusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the overall method flow of the present invention;

[0052] Figure 2 A comparison diagram of the output of the neoclassical annular viscous torque model of coupled physics and neural networks and the output of the traditional neoclassical annular viscous torque physical model;

[0053] Figure 3 This is the calculation time diagram of the traditional neoclassical annular viscous torque physical model;

[0054] Figure 4 Computational time plot for the neoclassical toroidal viscous torque model for coupled physics and neural networks. DETAILED DESCRIPTION

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to specific embodiments.

[0056] It should be noted that, unless otherwise defined, the technical or scientific terms used in the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0057] Example:

[0058] See also Figure 1 , the present invention provides a technical solution:

[0059] A new classical annular viscous torque machine learning method, the specific steps include:

[0060] Step 1: Divide the traditional neoclassical hoop viscous torque physical model process into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. Obtain the runtime and computational efficiency evaluation coefficient of each submodule, set the computational efficiency evaluation coefficient threshold, and identify the module with computational bottlenecks.

[0061] The step 1 includes the following:

[0062] The traditional neoclassical annular viscous torque physical model is divided into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. These submodules are numbered and the running time of each submodule is obtained. The computational efficiency evaluation coefficient of each submodule is evaluated using the module running time. The computational efficiency evaluation coefficient is based on the following formula:

[0063] ;

[0064] in, For the The computational efficiency evaluation coefficient of each submodule, For the The running time of each submodule, is the total running time of the traditional neoclassical hoop viscous torque physical model, , Retrieve variable for module number, , ;

[0065] To quantify the The running time of each submodule accounts for the proportion of the total running time of the traditional neoclassical hoop viscosity torque physical model. When the running time of the submodule increases, if the total running time remains unchanged, then It will increase accordingly, indicating that the submodule occupies more computing resources in the overall model and is less efficient.

[0066] Set the calculation efficiency evaluation coefficient threshold. When the computational efficiency evaluation coefficient of a submodule exceeds the computational efficiency evaluation coefficient threshold, it means that the There are computational bottlenecks in each submodule, and model replacement is required.

[0067] Step 1 achieves modular management of the overall model by subdividing the traditional neoclassical annular viscous torque physics model into three independent submodules: an initial physical coefficient generation module, a linearized drift physics equation solution module, and a torque calculation module. This division not only helps clarify the specific responsibilities and functions of each submodule in the overall computational process, but also enables accurate evaluation of each module's computational efficiency evaluation coefficient by independently measuring the runtime of each submodule. This process effectively identifies specific modules within the overall model that present computational bottlenecks, providing clear targets for subsequent optimization steps. Furthermore, setting a computational efficiency evaluation coefficient threshold systematically prioritizes modules for replacement or optimization, improving the efficiency and responsiveness of the entire computational process. This modular division also enhances the maintainability and scalability of the model, allowing for flexible improvements to specific modules during future model upgrades or adjustments without requiring large-scale modifications to the entire system. This step lays a solid foundation for subsequent training and optimization of alternative models, ensuring the systematic and efficient nature of the overall approach.

[0068] Step 2: Using the input of the submodule with a computational bottleneck as the training set and the output as the label, a fully connected neural network is trained to obtain a surrogate model. A reliability coefficient is constructed based on the input and output of the surrogate model. The corresponding submodule with a computational bottleneck is replaced with the surrogate model to form a new classical hoop viscous torque model that couples physics and neural networks.

[0069] The step 2 includes the following:

[0070] Obtain the submodule with a computational bottleneck and mark it as a model replacement module. Obtain the input and output of the submodule with a computational bottleneck. Use the input of the submodule with a computational bottleneck as the training set and the output of the submodule with a computational bottleneck as the label. Input the training set into a fully connected neural network to obtain a replacement model. According to the input and output of the replacement model, obtain the reliability coefficient. The formula is as follows:

[0071] ;

[0072] in, is the reliability coefficient, is the number of training set samples, For the replacement model The output corresponding to the samples is is the mean of the output of the model replacement module, For the The labels of samples, Retrieve variables for sample numbers, , ;

[0073] Measured the model prediction value With label The degree of deviation between the two values. Values ​​closer to 1 indicate that the surrogate model's predictions are closer to the true value and have higher reliability; values ​​closer to 0 indicate that the model's predictions are poorer and less reliable. The reliability coefficient reflects the degree of fit of the model's predictions by comparing the ratio of the squared error between the output and the label to the squared error between the output and the mean value of the label (the denominator). When the denominator remains unchanged, This indicates that the prediction results of the alternative model are closer to the true value and the reliability is improved. In a real environment, this means that through training and optimization, the neural network model can more accurately simulate the behavior of the original physical module, thereby improving the performance of the entire system. Increase or decrease, and the output and tags The relationship remains unchanged, then the denominator will change accordingly, but The impact of depends on the specific changes in the forecast error. In general, the average level change of the true value will not directly affect Unless it also affects the prediction error.

[0074] By calculating the reliability coefficient, we can quantify the predictive power of the surrogate model, guiding the model's training and optimization process and ensuring its sufficient reliability and accuracy in real-world environments. Furthermore, by combining the computational efficiency evaluation coefficient and model evaluation threshold, we can comprehensively evaluate and optimize the surrogate model, balancing computational efficiency with predictive accuracy, and improving the performance and practical value of the entire neoclassical hoop viscous torque model under complex working conditions. This not only improves the overall operational efficiency of the system but also enhances the model's adaptability and scalability in various application scenarios.

[0075] The sub-modules with computational bottlenecks in the traditional neoclassical toroidal viscous torque physical model are removed and replaced with corresponding alternative models to form a neoclassical toroidal viscous torque model that couples physics and neural networks.

[0076] Step 2 replaces computationally bottlenecked submodules with fully connected neural networks, significantly improving the model's computational efficiency while maintaining high torque calculation accuracy. Specifically, replacing bottleneck modules with machine learning techniques not only shortens computation time but also captures potential nonlinear characteristics within complex physical relationships, thereby improving the model's overall performance. Training the surrogate model using its input as the training set and its output as labels ensures that the neural network accurately mimics the behavior of the original physical model. Furthermore, a reliability coefficient is constructed to quantify the reliability of the surrogate model, making the replacement process verifiable and controllable. This step organically integrates the physical model with the neural network, leveraging the strengths of both. This ensures the scientific validity of the physical model while improving computational speed and efficiency. Furthermore, the introduction of the surrogate model provides greater flexibility and possibilities for optimization in subsequent steps, ensuring greater adaptability and scalability of the entire method to diverse computational requirements and scenarios. Through this process, the entire neoclassical hoop viscous torque model becomes more efficient, flexible, and reliable, significantly improving its performance in practical applications.

[0077] Step 3: Obtain the computational efficiency evaluation coefficient of the surrogate model in the new classical annular viscous torque model of coupled physics and neural networks, set the reliability threshold and model evaluation threshold, and judge the optimization status of the surrogate model by combining the reliability coefficient, the computational efficiency evaluation coefficient of the surrogate model, the reliability threshold, and the model evaluation threshold;

[0078] The step 3 includes the following:

[0079] Get the computational efficiency evaluation coefficient of the alternative model in the new classical toroidal viscous torque model that couples physics and neural networks. The logic is:

[0080] When obtaining the runtime of each submodule in step 1, each submodule has a corresponding input. This input is then fed back into the surrogate model, which then obtains an output based on the input. The time consumed by the surrogate model is the runtime of the surrogate model. The total runtime of the neoclassical circumferential viscous torque model that couples physics and neural networks is obtained by adding the runtime of the surrogate model to the runtime of the submodule without computational bottlenecks.

[0081] The calculation efficiency evaluation coefficient of the substitution model is based on the following formula:

[0082] ;

[0083] in, is the computational efficiency evaluation coefficient of the alternative model, is the running time of the alternative model, Total runtime for the neoclassical toroidal viscosity-torque model coupled with physics and neural networks.

[0084] This value reflects the computational burden of the surrogate model on the entire coupled model calculation process. Larger values ​​indicate that the surrogate model takes up more time and is less efficient. Smaller values ​​indicate that the surrogate model consumes fewer computational resources and is more efficient.

[0085] The reliability threshold and model evaluation threshold are set respectively. When the reliability coefficient is less than the reliability threshold and the computational efficiency evaluation coefficient of the alternative model is greater than the model evaluation threshold, it means that the alternative model needs to be optimized in terms of accuracy and computational efficiency. Otherwise, the alternative model will not be optimized.

[0086] The accuracy and computational efficiency optimization logic is as follows:

[0087] Get the weight of each neuron in each layer of the alternative model and the median of the neuron weight in each layer, set the pruning hyperparameters and initial values, and prune the neurons in each layer according to the pruning formula. The formula is as follows:

[0088] ;

[0089] in, Indicates the Tier neuron weights, is the pruning hyperparameter, For the The median neuron weight of the layer, Retrieve the variable for the neuron number, , , For the The total number of neurons in the layer, Retrieve variables for the layer number of the neural network model, , , is the total number of layers;

[0090] The neurons that meet the pruning formula are retained, and the neurons that do not meet the pruning formula are removed. The pruning hyperparameters use the initial values ​​during the first optimization. The pruned model is used for training again to obtain the reliability coefficient and the computational efficiency evaluation coefficient. The reliability threshold and the model evaluation threshold are used to determine whether optimization is needed again. If optimization is not needed, the current alternative model is used. If optimization is needed, the pruning hyperparameters are adjusted according to the change rate of the reliability coefficient and the computational efficiency evaluation coefficient. The adjustment is based on the following formula:

[0091] ;

[0092] in, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment factor and , Select the function for the maximum value, is the reliability coefficient of the surrogate model after pruning, is the reliability coefficient of the alternative model before pruning, is the computational efficiency evaluation coefficient of the pruned alternative model, is the computational efficiency evaluation coefficient of the alternative model before pruning;

[0093] Reflects the aggressiveness of pruning that should be used in the current optimization iteration to balance model accuracy and computational efficiency. represents the pruning hyperparameters at the previous iteration, A positive adjustment coefficient used to control the adjustment range. and They represent the reliability level of the alternative model at the current and previous iterations, respectively, reflecting the model's retention of the accuracy of the original physical module; and They represent the indicators of the computational burden of the alternative model in the overall coupling model in the current and previous iterations, respectively, reflecting the level of model computing resource utilization. The function ensures that only when Lower than A positive adjustment component will be generated only when Lower (i.e. is negative and its negative value is negated), it will contribute to the total adjustment; this shows that when the reliability of the model decreases or the evaluation of computational efficiency deteriorates (that is, the value decreases and increases), the negative correction of the pruning hyperparameter will be increased accordingly. Comparison Lower, then is positive, which increases the The deduction part leads to Compared to has decreased; similarly, if Compare Decline, then is also positive, thus further reducing .therefore, The adjustment is directly affected by the changes in the reliability coefficient and the computational efficiency evaluation coefficient. That is, when the model accuracy deteriorates or the computational efficiency decreases, the new pruning hyperparameter will be reduced accordingly, which means that a more conservative pruning strategy will be adopted in the subsequent pruning process to avoid excessive pruning and further reduction in accuracy. On the contrary, if there is no negative change in both indicators, then This adjustment relationship ultimately enables automatic adjustment of pruning intensity based on model performance feedback during real-world operation, ensuring that the overall neoclassical hoop viscous torque model achieves a more ideal balance between accuracy and efficiency.

[0094] Use the adjusted pruning hyperparameters to prune the surrogate model and determine whether optimization is needed again. This is a loop. During the loop, the adjustment sequence of the pruning hyperparameters is obtained according to the following formula:

[0095] ;

[0096] in, is the adjustment sequence of pruning hyperparameters, The pruning hyperparameters obtained for the first adjustment are: The pruning hyperparameters obtained for the second adjustment are: The pruning hyperparameters obtained for the third adjustment are: For the The pruning hyperparameters obtained by adjusting the Retrieve the variable for the number of adjustments, ;

[0097] The adjustment sequence of pruning hyperparameters is screened to obtain the latest continuously decreasing sequence, which is a subsequence containing the latest pruning hyperparameters and in which the subsequent pruning hyperparameters are all smaller than the previous pruning hyperparameters. The surrogate model obtained by the first pruning hyperparameter in the latest continuously decreasing sequence is pruned using the latest pruning hyperparameters. If the latest continuously decreasing sequence does not exist, the surrogate model is pruned using the current pruning hyperparameters.

[0098] By screening the latest continuously decreasing sequence, the adjustment process of the pruning hyperparameters is judged. By "using the latest obtained pruning hyperparameters to prune the alternative model obtained by the first pruning hyperparameter in the latest continuously decreasing sequence", excessive adjustment of the pruning hyperparameters is avoided, so that the optimization of the model proceeds steadily.

[0099] Set the maximum number of pruning times. When the maximum number of pruning times is reached and the alternative model still needs to be optimized based on the reliability threshold and model evaluation threshold, the number of layers will be reduced. The logic for reducing the number of layers is as follows:

[0100] The activation variance of each layer is obtained, the layer with the smallest activation variance is removed, and the surrogate model is pruned again starting from the surrogate model before pruning. The maximum number of pruning layers is set. When the maximum number of pruning layers is reached or the non-optimization condition is met, the surrogate model is determined to be obtained.

[0101] By pruning the weights of neurons in each layer of the surrogate model, setting pruning hyperparameters, and using the median weight as a reference, neurons that do not meet the set criteria are deleted. This step makes the model structure simpler and more efficient, significantly reducing computational resource consumption while ensuring stable prediction accuracy. During the optimization process, by continuously adjusting the pruning hyperparameters and forming a continuous decreasing sequence, the model's performance trends are keenly captured, ensuring that the surrogate model accurately simulates the behavior of the original physical module during iteration. This not only provides an optimized starting point for surrogate model training in step 2 after initially identifying computationally bottlenecked modules in step 1, but also ensures high consistency between the surrogate model's predicted values ​​and the actual torque when validating the overall coupled model in step 4 by constructing a coupling reliability coefficient. This achieves a balance between computational efficiency and accuracy, effectively reducing the computational workload during model runtime and improving overall system response speed while preventing oversimplification that could lead to a decrease in prediction accuracy. This provides a solid technical foundation for the stable operation and efficient application of the neoclassical hoop viscous torque model under various complex operating conditions.

[0102] Step 3 comprehensively evaluates the computational efficiency and reliability of the surrogate model to ensure that the substitution process not only improves computational speed but also maintains high model accuracy and stability. First, the computational efficiency evaluation coefficient of the surrogate model is obtained to quantify the efficiency improvement of the surrogate model in the overall model operation. Setting a reliability threshold and a model evaluation threshold provides clear criteria and basis for evaluating the surrogate model, ensuring a controllable and targeted optimization process. Combining the reliability coefficient and the computational efficiency evaluation coefficient comprehensively reflects the performance of the surrogate model in practical applications, avoiding the degradation of model accuracy caused by over-optimization. Furthermore, when the computational efficiency evaluation coefficient of the surrogate model exceeds the model evaluation threshold and the reliability coefficient is insufficient, timely adjustments to the model architecture can be made, such as reducing the number of neurons per layer and the number of layers in the fully connected neural network, thereby further improving computational efficiency while maintaining model performance. This step not only verifies the actual effectiveness of the surrogate model but also provides a feedback mechanism for continuous optimization, ensuring that the entire neoclassical hoop viscosity torque model maintains optimal performance in different application scenarios. Through this process, the model's optimization status can be monitored and adjusted in real time, ensuring its good adaptability and stability in dynamic environments.

[0103] Step 4: Input the training set into the traditional neoclassical annular viscous torque physical model to obtain the true torque, and input the training set into the neoclassical annular viscous torque model of coupled physics and neural network to obtain the simulated prediction value. Construct the coupling reliability coefficient based on the true torque and the simulated prediction value, set the coupling reliability threshold, and combine the coupling reliability coefficient, the computational efficiency coefficient of the alternative model, the coupling reliability threshold, and the model evaluation threshold to determine the correct neoclassical annular viscous torque model of coupled physics and neural network.

[0104] The step 4 includes the following contents:

[0105] Obtain a training set of the surrogate model, input the training set into the traditional neoclassical annular viscous torque physical model, obtain the output of the traditional neoclassical annular viscous torque physical model corresponding to each sample in the training set, and calibrate it as the true torque;

[0106] Each sample in the training set is input into the neoclassical annular viscous torque model coupled with physics and neural networks, and the output is obtained and calibrated as the model prediction value;

[0107] The coupling reliability coefficient of the neoclassical hoop viscous torque model for coupled physics and neural networks is obtained based on the following formula:

[0108] ;

[0109] in, is the coupling reliability coefficient, For the The model prediction value of samples, For the The true moment of the sample, is the average value of the true moment of all samples, is the number of training set samples, Retrieve variables for sample numbers, , ;

[0110] Weighed the coupled model predictions Compared with the real torque of traditional physical model The degree of deviation between the two values. Values ​​closer to 1 indicate a high degree of agreement between the coupling model's predictions and the true torque, indicating higher reliability. Values ​​closer to 0 indicate a significant difference between the predictions and the true torque, indicating lower reliability. The goodness of fit of the model is reflected by comparing the ratio of the squared error between the coupling model's predictions and the true torque to the squared error of the true torque relative to its mean. decreases, while the denominator remains unchanged, then This indicates that the coupled model's predictions are closer to the actual torque, improving reliability. In practical applications, this means that by optimizing the neural network or adjusting the coupling strategy, the model's prediction accuracy can be improved, ensuring the accuracy of torque calculations. increases, while the denominator remains unchanged, then This means that the difference between the coupling model's predictions and the actual torque increases, and reliability decreases. In a real-world setting, this may indicate that the neural network model has not been fully trained or that there is an overfitting / underfitting problem, requiring further optimization and adjustment. Increase or decrease, and and The change of remains unchanged, then the denominator Will change accordingly, affecting If a change in the mean causes the denominator to increase while the numerator remains constant, then will decrease and vice versa. However, usually The change in reflects the overall trend of the data and does not directly affect the evaluation of a single prediction error.

[0111] A coupling reliability threshold is set. When the coupling reliability coefficient is less than the coupling reliability threshold and the computational efficiency evaluation coefficient of the surrogate model is greater than the model evaluation threshold, it means that the surrogate model needs to be optimized for accuracy and computational efficiency. Otherwise, it is considered that the correct neoclassical toroidal viscous torque model of coupled physics and neural networks has been obtained. The accuracy and computational efficiency optimization logic is as follows:

[0112] The surrogate model is optimized again using the optimization process of step 3, and the conditions for whether to perform pruning, layer reduction, and optimization are replaced with the coupling reliability coefficient, the computational efficiency coefficient of the surrogate model, the coupling reliability threshold, and the model evaluation threshold. At the same time, the reliability coefficient in the pruning hyperparameter formula is replaced with the coupling reliability coefficient.

[0113] The alternative model is further optimized through the results of the entire coupled physics and neural network model to make the model more in line with the needs.

[0114] Step 4 comprehensively verifies the accuracy of the surrogate model and the reliability of the overall system by comparing the outputs of the traditional physical model with those of the coupled physical and neural network models. Specifically, the training set is input into the traditional physical model to obtain the true torque, which is then input into the coupled model to obtain the simulated predicted value. This accurately measures the performance of the surrogate model in practical applications. Constructing a coupling reliability coefficient provides an intuitive metric for evaluating the consistency between the coupled model's predicted value and the true torque, ensuring that the surrogate model improves computational efficiency without sacrificing its prediction accuracy. Setting a coupling reliability threshold ensures clear standards and operability in the evaluation process. When the coupling reliability coefficient is below the threshold and the computational efficiency evaluation coefficient of the surrogate model is above the model evaluation threshold, timely identification and optimization adjustments can be made to further improve the overall performance of the model. In addition, this step, through verification with real data, ensures the applicability and stability of the entire coupled model under different conditions, enhancing the model's credibility and practicality in practical applications. Combined with the optimization and evaluation mechanisms of the previous steps, step 4 not only consolidates the effectiveness of the alternative model but also provides a solid theoretical basis and empirical support for the deployment and promotion of the entire new classical annular viscous torque model in practical engineering applications, ensuring its reliable operation under various complex working conditions.

[0115] Please refer to Figures 2 to 4 , the present invention also includes a preferred embodiment:

[0116] As a preferred embodiment, the traditional neoclassical annular viscous torque physical calculation process is divided into three submodules: an initial physical coefficient generation module, a linearized drift dynamic equation solution module, and a torque calculation module. Based on the computational efficiency evaluation coefficients of each submodule, it is determined that the computational efficiency evaluation coefficient of the linearized drift dynamic equation calculation module is higher than a threshold, indicating that the module needs to be replaced by a training model.

[0117] As a preferred embodiment, the input of the linearized drift dynamics equation calculation module is used as a training set. The specific situation of the sample is 8 equation coefficients, of which 7 equation coefficients are 200-dimensional and 1 equation coefficient is 1-dimensional, that is, each sample has 1401 input features (7*200+1). The output of the module (called the perturbation distribution function value) is used as the label of the fully connected neural network. Specifically, the perturbation distribution function value is essentially a complex number, where the real part of the complex number is 200-dimensional and the imaginary part is also 200-dimensional, that is, the label corresponding to each sample is a 400-dimensional vector (200+200), thereby constructing a data set of an alternative model of the linearized drift dynamics equation solving module;

[0118] As a preferred embodiment, the data set of the alternative model for constructing the linearized drift physics equation solving module is input into the fully connected neural network for training. The designed fully connected neural network contains 4 layers. The first layer consists of 1401 neurons, which is the same as the input feature dimension. The second layer consists of 512 neurons. Each neuron in the second layer receives 1401 feature data from the first layer and activates the neurons according to the activation function in the neuron. and bias Get the output value , and finally get 512 outputs as feature input to the third layer; the third layer consists of 512 neurons, each neuron in the third layer receives 512 feature data from the second layer and activates it according to the activation function in the neuron and bias Get the output value , and finally get 512 outputs as feature input to the fourth layer; the fourth layer consists of 400 neurons, each neuron in the fourth layer receives 512 feature data from the third layer and according to the activation function in the neuron and bias Get the output value , and finally obtain 400 outputs as the final result, which is consistent with the sample label dimension; Finally, the training and testing of the alternative model for the linearized drift dynamic equation solving module is carried out. The alternative model for the linearized drift dynamic equation solving module is trained on the dataset using supervised learning;

[0119] As a preferred embodiment, after the replacement model training of the linearized drift physics equation solving module is completed, a cross-validation method is used to calculate the reliability coefficient of the model. If it is less than 0.8, the calculation accuracy of the disturbance distribution function prediction model is optimized. The Adam optimizer is used for optimization. The parameters adjusted during optimization include the weight and bias of the model, the learning rate and the initialization method of the model. The Glorit Uniform model initialization method is used, and the learning rate is set to 0.0001 until the reliability coefficient Greater than 0.8;

[0120] As a preferred embodiment, multi-source information is integrated through the environment and data fusion interface, and the model fusion technology is used to realize the coupling of the initial physical coefficient generation module, the alternative model of the linearized drift dynamic equation solving module and the torque calculation module. Specifically, the calculation framework of Python is called based on MATLAB, the Python path is confirmed using the pyenv command, and the data type conversion and communication are realized through the py library of MATLAB, thereby calling Python's scientific computing, machine learning, data processing and visualization functions; this process enables the Python data involved in the alternative model of the linearized drift dynamic equation solving module to be compatible with the initial physical coefficient. The MATLAB data involved in the generation module and the torque calculation module are integrated; then the "physics-AI-physics" sequence is adopted to fuse the models of the initial physical coefficient generation module, the alternative model of the linearized drift dynamic equation solving module, and the torque calculation module. Specifically, the output of the initial physical coefficient generation module is used as the input of the alternative model of the linearized drift dynamic equation solving module, and the output of the alternative model of the linearized drift dynamic equation solving module is used as the input of the torque calculation module. The output of the torque calculation module is the neoclassical circumferential viscous torque; through this sequential fusion, a neoclassical circumferential viscous torque model that couples the physical model and the neural network is finally obtained;

[0121] Computational efficiency evaluation coefficient of alternative model for constructing linearized drift dynamic equation solving module If the computational efficiency evaluation coefficient is greater than 0.5, the computational time of the model is optimized. During the optimization, the number of neurons in each layer is first reduced. If the conditions are still not met, the number of layers of the model is reduced.

[0122] As a preferred embodiment, a coupling reliability coefficient of the coupled physical model and the neoclassical annular viscous torque model of the neural network is obtained. If it does not exceed 0.8, the model accuracy of the alternative model of the linearized drift dynamic equation solving module is optimized. The optimization adopts the L-BFGS optimizer. The parameters adjusted during the optimization include the model weight and bias, the learning rate and the model initialization method. If the coupling reliability coefficient exceeds 0.8, the computational efficiency evaluation coefficient of the alternative model of the linearized drift dynamic equation solving module in the neoclassical annular viscous torque model of the coupled physical model and the neural network is obtained again. If the computational efficiency evaluation coefficient exceeds 0.5, the computational time of the alternative model of the linearized drift dynamic equation solving module is optimized. The number of neurons in each layer is first reduced. If the conditions are still not met, the number of layers of the model is reduced.

[0123] When the computational efficiency evaluation coefficient of the alternative model of the linearized drift physics equation solving module is also lower than 0.5, the new classical annular viscous torque model of coupled physics and neural network is obtained.

[0124] As a preferred embodiment, Figure 3 As shown in , the solution time of the traditional neoclassical annular viscous torque physical model is 67.542 seconds, as shown in Figure 4 As shown, the solution time of the new classical annular viscous torque model with coupled physics and neural networks is 23.744 seconds.

[0125] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0126] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software depends on the specific application and design constraints of the technical solution.

[0127] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, and may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment as needed.

[0128] The above is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed in this application, which should be covered by the scope of protection of the present application.

Claims

1. A new classical machine learning method for annular viscous torque, characterized by: The specific steps include: Step 1: Divide the traditional neoclassical hoop viscous torque physical model process into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. Obtain the runtime and computational efficiency evaluation coefficient of each submodule, set the computational efficiency evaluation coefficient threshold, and identify the module with computational bottlenecks. Step 2: Using the input of the submodule with a computational bottleneck as the training set and the output as the label, a fully connected neural network is trained to obtain a surrogate model. A reliability coefficient is constructed based on the input and output of the surrogate model. The corresponding submodule with a computational bottleneck is replaced with the surrogate model to form a new classical hoop viscous torque model that couples physics and neural networks. Step 3: Obtain the computational efficiency evaluation coefficient of the surrogate model in the new classical annular viscous torque model of coupled physics and neural networks, set the reliability threshold and model evaluation threshold, and judge the optimization status of the surrogate model by combining the reliability coefficient, the computational efficiency evaluation coefficient of the surrogate model, the reliability threshold, and the model evaluation threshold; Step 4: Input the training set into the traditional neoclassical annular viscous torque physical model to obtain the true torque, and input the training set into the neoclassical annular viscous torque model of coupled physics and neural network to obtain the simulated prediction value. Construct the coupling reliability coefficient based on the true torque and the simulated prediction value, set the coupling reliability threshold, and combine the coupling reliability coefficient, the computational efficiency coefficient of the alternative model, the coupling reliability threshold, and the model evaluation threshold to determine the correct neoclassical annular viscous torque model of coupled physics and neural network.

2. The machine learning method for the new classical hoop viscous moment according to claim 1, characterized in that: The traditional neoclassical annular viscous torque physical model is divided into three submodules: the initial physical coefficient generation module, the linearized drift physical equation solution module, and the torque calculation module. These submodules are numbered and the running time of each submodule is obtained. The computational efficiency evaluation coefficient of each submodule is evaluated using the module running time. The computational efficiency evaluation coefficient is based on the following formula: ； in, For the The computational efficiency evaluation coefficient of each submodule, For the The running time of each submodule, is the total running time of the traditional neoclassical hoop viscous torque physical model, , Retrieve variable for module number, , ; Set the calculation efficiency evaluation coefficient threshold. When the computational efficiency evaluation coefficient of a submodule exceeds the computational efficiency evaluation coefficient threshold, it means that the There are computational bottlenecks in each submodule, and model replacement is required.

3. The machine learning method for the new classical hoop viscous moment according to claim 2, characterized in that: Obtain the submodule with a computational bottleneck and mark it as a model replacement module. Obtain the input and output of the submodule with a computational bottleneck. Use the input of the submodule with a computational bottleneck as the training set and the output of the submodule with a computational bottleneck as the label. Input the training set into a fully connected neural network to obtain a replacement model. According to the input and output of the replacement model, obtain the reliability coefficient. The formula is as follows: ； in, is the reliability coefficient, is the number of training set samples, For the replacement model The output corresponding to the samples is is the mean of the output of the model replacement module, For the The labels of samples, Retrieve variables for sample size, , ; The sub-modules with computational bottlenecks in the traditional neoclassical toroidal viscous torque physical model are removed and replaced with corresponding alternative models to form a neoclassical toroidal viscous torque model that couples physics and neural networks.

4. The machine learning method for the new classical hoop viscous moment according to claim 3, characterized in that: Obtain the computational efficiency evaluation coefficient of the alternative model in the new classical toroidal viscous torque model that couples physics and neural networks. The logic is: When obtaining the runtime of each submodule in step 1, each submodule has a corresponding input. This input is then fed back into the surrogate model, which then obtains an output based on the input. The time consumed by the surrogate model is the runtime of the surrogate model. The total runtime of the neoclassical circumferential viscous torque model that couples physics and neural networks is obtained by adding the runtime of the surrogate model to the runtime of the submodule without computational bottlenecks. The calculation efficiency evaluation coefficient of the substitution model is based on the following formula: ； in, is the computational efficiency evaluation coefficient of the alternative model, is the running time of the alternative model, Total runtime for the neoclassical toroidal viscosity-torque model coupled with physics and neural networks.

5. The machine learning method for the new classical hoop viscous moment according to claim 4, characterized in that: The reliability threshold and model evaluation threshold are set respectively. When the reliability coefficient is less than the reliability threshold and the computational efficiency evaluation coefficient of the alternative model is greater than the model evaluation threshold, it means that the alternative model needs to be optimized in terms of accuracy and computational efficiency. Otherwise, the alternative model will not be optimized. The accuracy and computational efficiency optimization logic is as follows: Get the weight of each neuron in each layer of the alternative model and the median of the neuron weight in each layer, set the pruning hyperparameters and initial values, and prune the neurons in each layer according to the pruning formula. The formula is as follows: ； in, Indicates the Tier neuron weights, is the pruning hyperparameter, For the The median neuron weight of the layer, Retrieve the variable for the neuron number, , , For the The total number of neurons in the layer, Retrieve variables for the layer number of the neural network model, , , is the total number of layers; The neurons that meet the pruning formula are retained, and the neurons that do not meet the pruning formula are removed. The pruning hyperparameters use the initial values ​​during the first optimization. The pruned model is used for training again to obtain the reliability coefficient and the computational efficiency evaluation coefficient. The reliability threshold and the model evaluation threshold are used to determine whether optimization is needed again. If optimization is not needed, the current alternative model is used. If optimization is needed, the pruning hyperparameters are adjusted according to the change rate of the reliability coefficient and the computational efficiency evaluation coefficient. The adjustment is based on the following formula: ； in, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment factor and , Select the function for the maximum value, is the reliability coefficient of the surrogate model after pruning, is the reliability coefficient of the alternative model before pruning, is the computational efficiency evaluation coefficient of the pruned alternative model, is the computational efficiency evaluation coefficient of the alternative model before pruning; Use the adjusted pruning hyperparameters to prune the surrogate model and determine whether optimization is needed again. This is a loop. During the loop, the adjustment sequence of the pruning hyperparameters is obtained according to the following formula: ； in, is the adjustment sequence of pruning hyperparameters, The pruning hyperparameters obtained for the first adjustment are: The pruning hyperparameters obtained for the second adjustment are: The pruning hyperparameters obtained for the third adjustment are: For the The pruning hyperparameters obtained by adjusting the Retrieve the variable for the number of adjustments, ; The adjustment sequence of pruning hyperparameters is screened to obtain the latest continuously decreasing sequence, which is a subsequence containing the latest pruning hyperparameters and in which the subsequent pruning hyperparameters are all smaller than the previous pruning hyperparameters. The surrogate model obtained by the first pruning hyperparameter in the latest continuously decreasing sequence is pruned using the latest pruning hyperparameters. If the latest continuously decreasing sequence does not exist, the surrogate model is pruned using the current pruning hyperparameters. Set the maximum number of pruning times. When the maximum number of pruning times is reached and the alternative model still needs to be optimized based on the reliability threshold and model evaluation threshold, the number of layers will be reduced. The logic for reducing the number of layers is as follows: The activation variance of each layer is obtained, the layer with the smallest activation variance is removed, and the surrogate model is pruned again starting from the surrogate model before pruning. The maximum number of pruning layers is set. When the maximum number of pruning layers is reached or the non-optimization condition is met, the surrogate model is determined to be obtained.

6. The machine learning method for the new classical hoop viscous moment according to claim 5, characterized in that: Obtain a training set of the surrogate model, input the training set into the traditional neoclassical annular viscous torque physical model, obtain the output of the traditional neoclassical annular viscous torque physical model corresponding to each sample in the training set, and calibrate it as the true torque; Each sample in the training set is input into the neoclassical hoop viscosity torque model of coupled physics and neural network and the output is obtained and calibrated as the model prediction value; The coupling reliability coefficient of the neoclassical hoop viscous torque model for coupled physics and neural networks is obtained based on the following formula: ； in, is the coupling reliability coefficient, For the The model prediction value of samples, For the The true moment of the sample, is the average value of the true moment of all samples, is the number of training set samples, Retrieve variables for sample size, , ; A coupling reliability threshold is set. When the coupling reliability coefficient is less than the coupling reliability threshold and the computational efficiency evaluation coefficient of the surrogate model is greater than the model evaluation threshold, it means that the surrogate model needs to be optimized for accuracy and computational efficiency. Otherwise, it is considered that the correct neoclassical toroidal viscous torque model of coupled physics and neural networks has been obtained. The accuracy and computational efficiency optimization logic is as follows: The surrogate model is optimized again using the optimization process of step 3, and the conditions for whether to perform pruning, layer reduction, and optimization are replaced with the coupling reliability coefficient, the computational efficiency coefficient of the surrogate model, the coupling reliability threshold, and the model evaluation threshold. At the same time, the reliability coefficient in the pruning hyperparameter formula is replaced with the coupling reliability coefficient.

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