Machine learning method for new classical circumferential viscous torque

Abstract

The invention provides a new classical circumferential viscous torque machine learning method, which relates to the technical field of controllable nuclear fusion, and comprises the following steps of: screening out a module which has a calculation bottleneck and needs a replacement model by obtaining a calculation efficiency evaluation coefficient of each module, and obtaining the replacement model through training; judging and optimizing the substitution model according to the reliability coefficient, replacing the sub-module with a calculation bottleneck by the substitution model, forming a new classical circumferential viscous moment model coupled with a physical network and a neural network, obtaining a calculation evaluation efficiency coefficient of the substitution model, obtaining a coupling reliability coefficient, and carrying out calculation evaluation on the coupling reliability coefficient. According to the method, the calculation efficiency is improved, the time cost bottleneck of a traditional method is broken through, the input requirements of different physical parameters can be flexibly met, and accurate and rapid support is provided for experimental discharge control and scheme design.

Description

Technical Field

[0001] The present invention relates to the technical field of controlled nuclear fusion, and specifically to a machine learning method for neoclassical toroidal viscosity torque. Background Technique

[0002] Tokamak devices confine plasma inside through magnetic confinement and achieve 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 perturbations, the Tokamak magnetic field often exhibits toroidal asymmetry. This toroidal asymmetric magnetic field perturbation will generate an additional toroidal torque through the neoclassical toroidal viscosity effect. This generated additional toroidal torque is the NTV torque, which affects the toroidal rotation of the plasma, and further affects the toroidal plasma instability and the performance of the device.

[0003] Therefore, to achieve controlled nuclear fusion, it is necessary to conduct NTV torque analysis. Accurate and rapid NTV torque simulation analysis helps enhance the understanding of experimental phenomena and improve the prediction and control capabilities for future experiments. Currently, the traditional physical calculation process of neoclassical toroidal viscosity torque (NTV-PHY) solves the NTV torque numerically. However, this numerical method for NTV torque analysis is extremely time-consuming.

[0004] In the Chinese invention patent with the application number CN117371299A, a machine learning method for neoclassical toroidal viscosity torque of Tokamak is disclosed. Input and output data are extracted from the traditional calculation program of neoclassical toroidal viscosity torque of Tokamak to construct a data set required for model training, and a deep neural network model is designed and trained to enable it to predict the neoclassical toroidal viscosity torque based on the data set. This technical solution demonstrates the high computational efficiency of the AI method, but it belongs to a completely end-to-end implementation of neoclassical toroidal viscosity torque calculation, lacking physical completeness and interpretability.

[0005] In the Chinese invention patent with the application number CN119046590A, the implementation method of the AI proxy model for the linearized drift kinetic equation is disclosed. It still belongs to an end-to-end implementation method for the linearized drift kinetic equation and has not been connected to other physical processes of neoclassical toroidal viscosity torque, unable to carry out a complete calculation process for neoclassical toroidal viscosity torque, lacking physical completeness and practical operability.

[0006] Based on the above applications and the existing technology, in the existing calculation methods of neoclassical toroidal viscosity torque of Tokamak, the method of establishing equations based on physical principles has the problem of computational efficiency in NTV torque simulation, and the machine learning method has the problem of black box non-interpretability in NTV torque simulation. These contradictions restrict the development of physical research and the optimization of device performance.

[0007] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure. Therefore, it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0008] An object of the present invention is to provide a machine learning method for the new classical toroidal viscous torque to solve the problems raised in the above background art.

[0009] To achieve the above object, the present invention provides the following technical solutions: A machine learning method for the new classical toroidal viscous torque, the specific steps include: Step 1: Divide the process of the traditional new classical toroidal viscous torque physical model into three sub-modules, namely an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module. Obtain the running time of each sub-module respectively and obtain a calculation efficiency evaluation coefficient. Set a calculation efficiency evaluation coefficient threshold and judge the module with a calculation bottleneck. Step 2: Use the input of the sub-module with a calculation bottleneck as the training set and the output as the label, train in a fully connected neural network to obtain a surrogate model. Construct a reliability coefficient based on the input and output of the surrogate model, and replace the corresponding sub-module with a calculation bottleneck with the surrogate model to form a new classical toroidal viscous torque model that couples physics and neural networks. Step 3: Obtain the calculation efficiency evaluation coefficient of the surrogate model in the new classical toroidal viscous torque model that couples physics and neural networks. Set a reliability threshold and a model evaluation threshold, and combine the reliability coefficient, the calculation efficiency evaluation coefficient of the surrogate model with the reliability threshold and the model evaluation threshold to judge the optimization status of the surrogate model. Step 4: Input the training set into the traditional new classical toroidal viscous torque physical model to obtain the true torque, input the training set into the new classical toroidal viscous torque model that couples physics and neural networks to obtain the simulated prediction value. Construct a coupling reliability coefficient based on the true torque and the simulated prediction value. Set a coupling reliability threshold, and combine the coupling reliability coefficient, the calculation efficiency coefficient of the surrogate model with the coupling reliability threshold and the model evaluation threshold to judge the correct new classical toroidal viscous torque model that couples physics and neural networks.

[0010] Further, divide the traditional new classical toroidal viscous torque physical model into three sub-modules, namely an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module, and number them. Obtain the running time of each sub-module for solving respectively, and use the running time of the module to evaluate the calculation efficiency evaluation coefficient of each sub-module. The formula based on which the calculation efficiency evaluation coefficient is calculated is as follows: ; Among them, is the computational efficiency evaluation coefficient of the th sub-module, is the running time of the th sub-module, is the total running time of the traditional new classical toroidal viscous torque physical model, , is the module number retrieval variable, , ; Set the threshold of the computational efficiency evaluation coefficient. When the computational efficiency evaluation coefficient of the th sub-module exceeds the threshold of the computational efficiency evaluation coefficient, it means that the th sub-module has a computational bottleneck and needs to be replaced by a model.

[0011] Furthermore, obtain the sub-module with a computational bottleneck, label it as the model replacement module, obtain the input and output of the sub-module with a computational bottleneck, use the input of the sub-module with a computational bottleneck as the training set, use the output of the sub-module with a computational bottleneck as the label, input them into a fully connected neural network for training, obtain the replacement model, and according to the input and output of the replacement model, obtain the reliability coefficient. The formula is as follows: ; Among them, is the reliability coefficient, is the number of training set samples, is the output corresponding to the th sample of the replacement model, is the mean value of the output of the model replacement module, is the th sample label, is the sample number retrieval variable, , ; Remove the sub-module with a computational bottleneck in the traditional new classical toroidal viscous torque physical model and replace it with the corresponding replacement model to form a new classical toroidal viscous torque model that couples physics and neural networks.

[0012] Furthermore, obtain the computational efficiency evaluation coefficient of the replacement model in the new classical toroidal viscous torque model that couples physics and neural networks. The logic is as follows: When obtaining the running time of each sub-module in step 1, each sub-module has a corresponding input. Input this input into the replacement model again. The replacement model obtains the output according to the input. At this time, the time consumed by the replacement model is the running time of the replacement model. Add the running time of the replacement model to the running time of the sub-module without a computational bottleneck, which is the total running time of the new classical toroidal viscous torque model that couples physics and neural networks; The formula for the calculation efficiency evaluation coefficient of the surrogate model is as follows: ; Among them, is the calculation efficiency evaluation coefficient of the surrogate model, is the running time of the surrogate model, is the total running time of the new classical toroidal viscous torque model that couples physics and neural networks.

[0013] Furthermore, a reliability threshold and a model evaluation threshold are set respectively. When the reliability coefficient is less than the reliability threshold and the calculation 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 calculation efficiency, otherwise the surrogate model is not optimized; The optimization logic for accuracy and calculation efficiency is as follows: Obtain the weights of each neuron in each layer of the surrogate model and the median of the neuron weights in each layer, set the pruning hyperparameter and the initial value, and prune the neurons in each layer according to the pruning formula. The formula is as follows: ;

[0014] Among them, represents the weight of the th neuron in the th layer, is the pruning hyperparameter, is the median of the neuron weights in the th layer, is the neuron number retrieval variable, , , is the total number of neurons in the th layer, is the layer number retrieval variable of the neural network model, , , is the total number of layers; Retain the neurons that satisfy the pruning formula and eliminate the neurons that do not satisfy the pruning formula. When optimizing for the first time, use the initial value for the pruning hyperparameter. Use the pruned model to train again and obtain the reliability coefficient and the calculation efficiency evaluation coefficient, and then judge again according to the reliability threshold and the model evaluation threshold whether further optimization is needed. If no optimization is needed, use the current surrogate model. If optimization is needed, adjust the pruning hyperparameter according to the change rate of the reliability coefficient and the calculation efficiency evaluation coefficient. The adjustment formula is as follows: ; Among them, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment coefficient and , is the maximum value selection function, is the reliability coefficient of the pruned surrogate model, is the reliability coefficient of the surrogate model before pruning, is the computational efficiency evaluation coefficient of the pruned surrogate model, is the computational efficiency evaluation coefficient of the surrogate model before pruning; Use the adjusted pruning hyperparameters to prune the surrogate model and judge again whether optimization is needed. Taking this as a loop, during the loop, obtain the adjustment sequence of the pruning hyperparameters. The formula is as follows: ; Among them, is the adjustment sequence of the pruning hyperparameters, is the pruning hyperparameter obtained from the first adjustment, is the pruning hyperparameter obtained from the second adjustment, is the pruning hyperparameter obtained from the third adjustment, is the pruning hyperparameter obtained from the th adjustment, is the adjustment times retrieval variable, ; Screen the adjustment sequence of the pruning hyperparameters to obtain the latest continuously decreasing sequence. The latest continuously decreasing sequence is a subsequence that contains the latest pruning hyperparameter and each subsequent pruning hyperparameter is smaller than the previous one. Use the latest obtained pruning hyperparameter to prune the surrogate model obtained from the first pruning hyperparameter in the latest continuously decreasing sequence. If there is no latest continuously decreasing sequence, use the current pruning hyperparameter to prune the surrogate model; Set the maximum number of pruning times. When the surrogate model still needs to be optimized according to the reliability threshold and the model evaluation threshold when the maximum number of pruning times is reached, then reduce the number of layers. The logic for reducing the number of layers is as follows: Obtain the activation variance of each layer, remove the layer with the smallest activation variance, and start pruning the surrogate model again with the surrogate model before pruning. Set the maximum number of layers to be reduced. When the maximum number of layers to be reduced is reached or the non-optimization condition is met, then judge to obtain the surrogate model.

[0015] Furthermore, obtain the training set of the surrogate model, input the training set into the traditional new classical toroidal viscous torque physical model, obtain the output of the traditional new classical toroidal viscous torque physical model corresponding to each sample in the training set, and calibrate it as the true torque; Input each sample in the training set into the new classical toroidal viscous torque model that couples physics and neural networks and obtain the output, which is calibrated as the model prediction value; To obtain the coupling reliability coefficient of the new classical toroidal viscosity moment model that couples physics and neural networks, the formula is as follows: ; Wherein, is the coupling reliability coefficient, is the model prediction value of the th sample, is the true moment of the th sample, is the average value of the true moments of all samples, is the number of samples in the training set, is the sample number retrieval variable, , ; Set the coupling reliability threshold. When the coupling reliability coefficient is less than the coupling reliability threshold and the calculation 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 calculation efficiency. Otherwise, it is determined that the correct new classical toroidal viscosity moment model that couples physics and neural networks has been obtained. The accuracy and calculation efficiency optimization logic is as follows: Optimize the surrogate model again with the optimization process in step 3, and replace the conditions for whether to perform pruning, layer reduction, and optimization with the coupling reliability coefficient, the calculation efficiency coefficient of the surrogate model, the coupling reliability threshold, and the model evaluation threshold. At the same time, replace the reliability coefficient in the pruning hyperparameter formula with the coupling reliability coefficient.

[0016] Compared with the prior art, the beneficial effects of the present invention are: Through the coupling of the deep neural network model and the new classical toroidal viscosity moment physical equation, the present invention innovatively solves the key problems in the background technology. First, through the coupling method, the accuracy limitation of the traditional calculation method is overcome, achieving high accuracy and high reliability in the prediction of the new classical toroidal viscosity moment, and avoiding the prediction deviation caused by model simplification. Second, the coupling of deep learning and physical equations significantly improves the calculation efficiency, enabling the simulation process to be completed under instant or real-time conditions and breaking through the time cost bottleneck of traditional methods. In addition, the torque calculation module of the physical model can be coupled to explain 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, thus effectively promoting the research and application of tokamak devices in the field of controlled nuclear fusion. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a schematic diagram of the overall method flow of the present invention; Figure 2Comparison chart of the output of the new classical toroidal viscosity torque model that couples physics and neural networks with the output of the traditional new classical toroidal viscosity torque physical model; Figure 3 Chart of the calculation time of the traditional new classical toroidal viscosity torque physical model; Figure 4 Chart of the calculation time of the new classical toroidal viscosity torque model that couples physics and neural networks. Detailed implementation manners

[0018] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0019] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs. The "first", "second", and similar terms used in the present invention do not indicate any order, quantity, or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this term cover the elements or objects listed after this term and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right", etc. are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0020] Embodiment: Please refer to Figure 1 , the present invention provides a technical solution: A machine learning method for new classical toroidal viscosity torque, the specific steps include: Step 1: Divide the process of the traditional new classical toroidal viscosity torque physical model into three sub-modules, namely an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module, respectively obtain the running duration of each sub-module and obtain a calculation efficiency evaluation coefficient, set a calculation efficiency evaluation coefficient threshold, and determine the module with a calculation bottleneck; The said Step 1 includes the following contents: Divide the traditional new classical toroidal viscosity torque physical model into three sub-modules, namely an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module, and number them. Respectively obtain the running time for each sub-module to solve, and use the running time of the module to evaluate the calculation efficiency evaluation coefficient of each sub-module. The formula based on which the calculation efficiency evaluation coefficient is calculated is as follows: ; Among them, is the computational efficiency evaluation coefficient of the -th sub-module, is the running time of the -th sub-module, is the total running time of the traditional new classical toroidal viscous torque physical model, , is the module number retrieval variable, , ; is used to quantify the proportion of the running time of the -th sub-module in the total running time of the entire traditional new classical toroidal viscous torque physical model. When the running time of the sub-module increases, if the total running time remains unchanged, then will increase correspondingly, indicating that this sub-module occupies more computing resources in the overall model and has low efficiency.

[0021] Set the threshold of the computational efficiency evaluation coefficient. When the computational efficiency evaluation coefficient of the -th sub-module exceeds the threshold of the computational efficiency evaluation coefficient, it means that the -th sub-module has a computational bottleneck and needs to be replaced by a model.

[0022] Step 1 realizes the modular management of the overall model by dividing the traditional new classical toroidal viscous torque physical model into three independent sub-modules: an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module. This division not only helps to clarify the specific responsibilities and functions of each sub-module in the entire calculation process, but also can accurately evaluate the computational efficiency evaluation coefficient of each module by independently measuring the running time of each sub-module. This process can effectively identify the specific module with a computational bottleneck in the overall model, thus providing a clear goal for the subsequent optimization steps. In addition, setting the threshold of the computational efficiency evaluation coefficient can systematically identify which modules need to be replaced or optimized first, improving the efficiency and response speed of the entire calculation process. The modular division also enhances the maintainability and scalability of the model, making it possible to more flexibly improve specific modules in the future when the model is upgraded or adjusted, without the need to make large-scale modifications to the entire system. This step lays a solid foundation for the training and optimization of the replacement model in the subsequent steps, ensuring the systematicness and efficiency of the entire method.

[0023] Step 2: Use the input of the sub-module with a computational bottleneck as the training set and the output as the label to train in a fully connected neural network to obtain a replacement model. Construct a reliability coefficient based on the input and output of the replacement model, and replace the corresponding sub-module with a computational bottleneck with the replacement model to form a new classical toroidal viscous torque model that couples physics and neural networks; Step 2 includes the following steps: Obtain the sub-module with a computing bottleneck, which is designated as the model replacement module. Obtain the input and output of the sub-module with a computing bottleneck. Use the input of the sub-module with a computing bottleneck as the training set, and the output of the sub-module with a computing bottleneck as the label. Input them into a fully connected neural network for training to obtain a replacement model. According to the input and output of the replacement model, obtain the reliability coefficient. The formula is as follows: ; Where, is the reliability coefficient, is the number of training set samples, is the output corresponding to the th sample of the replacement model, is the mean value of the output of the model replacement module, is the th sample label, is the sample number retrieval variable, , ; measures the deviation between the model prediction value and the label . The closer the value is to 1, the closer the prediction result of the replacement model is to the true value, and the higher the reliability; the closer the value is to 0, the worse the prediction effect of the model, and the lower the reliability. The reliability coefficient reflects the fitting degree of the model prediction result by comparing the ratio between the squared error of the output and the label and the squared error of the output and the average value of the label (denominator). When decreases while the denominator remains unchanged, then increases. This indicates that the prediction result of the replacement model is 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. If increases or decreases, while the relationship between the output and the label remains unchanged, then the denominator will change accordingly, but the impact on depends on the specific change situation of the prediction error. Generally speaking, the change in the average level of the true value will not directly affect the calculation of , unless it affects the prediction error at the same time.

[0024] By calculating the reliability coefficient, the prediction ability of the surrogate model can be quantified, guiding the training and optimization process of the model to ensure its sufficient reliability and accuracy in the actual environment. In addition, by combining the computational efficiency evaluation coefficient and the model evaluation threshold, the surrogate model can be comprehensively evaluated and optimized, balancing computational efficiency and prediction accuracy, and enhancing the application performance and practical value of the entire new classical toroidal viscous torque model under complex working conditions. This not only improves the overall operating efficiency of the system but also enhances the adaptability and scalability of the model in different application scenarios.

[0025] Remove the sub-module with computational bottlenecks in the traditional new classical toroidal viscous torque physical model and replace it with the corresponding surrogate model to form a new classical toroidal viscous torque model that couples physics and neural networks.

[0026] In Step 2, by introducing a fully connected neural network to replace the sub-module with computational bottlenecks, the computational efficiency of the model is significantly improved while maintaining high accuracy in torque calculation. Specifically, using machine learning techniques to replace the bottleneck module not only shortens the calculation time but also enables capturing potential non-linear features in complex physical relationships, thus improving the overall performance of the model. By using the input of the surrogate model as the training set and the output as the label for training, it is ensured that the neural network can accurately simulate the behavior of the original physical model. At the same time, constructing a reliability coefficient can quantify the reliability of the surrogate model, making the replacement process verifiable and controllable. This step realizes the organic combination of the physical model and the neural network, giving full play to the advantages of both, ensuring the scientific nature of the physical model while improving the calculation speed and efficiency. In addition, the introduction of the surrogate model provides more flexibility and possibilities for the optimization of subsequent steps, ensuring that the entire method can have higher adaptability and scalability when dealing with different computational requirements and scenarios. Through this process, the entire new classical toroidal viscous torque model becomes more efficient, flexible, and reliable, significantly improving its performance in practical applications.

[0027] Step 3: Obtain the computational efficiency evaluation coefficient of the surrogate model in the new classical toroidal viscous torque model that couples physics and neural networks, set the reliability threshold and the 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; The content of the above Step 3 includes: Obtain the computational efficiency evaluation coefficient of the surrogate model in the new classical toroidal viscous torque model that couples physics and neural networks, and the logic is as follows: When obtaining the running time of each sub-module in step 1, each sub-module has a corresponding input. This input is input into the surrogate model again, and the surrogate model obtains the output according to the input. At this time, the time consumed by the surrogate model is the running time of the surrogate model. The running time of the surrogate model is added to the running time of the sub-module without computational bottlenecks, which is the total running time of the new classical toroidal viscous torque model coupling physics and neural networks; The formula for the computational efficiency evaluation coefficient of the surrogate model is as follows: ; Among them, is the computational efficiency evaluation coefficient of the surrogate model, is the running time of the surrogate model, is the total running time of the new classical toroidal viscous torque model coupling physics and neural networks.

[0028] reflects the computational burden of the surrogate model in the entire coupled model calculation process. The larger the value, the more time the surrogate model occupies in the overall calculation, and the lower the computational efficiency; the smaller the value, the less computational resources the surrogate model occupies, and the higher the computational efficiency.

[0029] The reliability threshold and the 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 optimize the accuracy and computational efficiency, otherwise the surrogate model is not optimized; The accuracy and computational efficiency optimization logic is as follows: Obtain the weight of each neuron in each layer of the surrogate model and the median of the neuron weights in each layer. Set the pruning hyperparameter and the initial value, and prune the neurons in each layer according to the pruning formula. The formula is as follows: ; Among them, represents the weight of the rd neuron in the th layer, is the pruning hyperparameter, is the median of the neuron weights in the th layer, is the neuron number retrieval variable, , , is the th layer, is the layer number retrieval variable of the neural network model, , , is the total number of layers; Retain the neurons that satisfy the pruning formula and eliminate the neurons that do not satisfy the pruning formula. When performing the first optimization, use the initial values for the pruning hyperparameters. Use the pruned model to train again and obtain the reliability coefficient and the computational efficiency evaluation coefficient. Then, based on the reliability threshold and the model evaluation threshold, determine whether further optimization is needed. If no optimization is required, use the current surrogate model. If optimization is needed, adjust the pruning hyperparameters according to the change rates of the reliability coefficient and the computational efficiency evaluation coefficient. The adjustment formula is as follows: ; Where, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment coefficient and , is the maximum selection function, is the reliability coefficient of the surrogate model after pruning, is the reliability coefficient of the surrogate model before pruning, is the computational efficiency evaluation coefficient of the surrogate model after pruning, is the computational efficiency evaluation coefficient of the surrogate model before pruning; reflects the degree of pruning aggressiveness that should be adopted in the current optimization iteration to balance model accuracy and computational efficiency. represents the pruning hyperparameter in the previous iteration, is a positive adjustment coefficient used to control the adjustment amplitude. and respectively represent the reliability levels of the surrogate model in the current and previous iterations, reflecting the retention of the accuracy of the original physical module by the model; and respectively represent the indicators of the computational burden of the surrogate model in the overall coupled model in the current and previous iterations, reflecting the level of computational resource usage of the model. The function ensures that a positive adjustment component is generated only when is lower than . Similarly, only when is low (i.e., is negative and its negative value is taken), will it contribute to the total adjustment; this indicates that when the reliability of the model decreases or the computational efficiency evaluation deteriorates (i.e., the value increases), the negative correction of the pruning hyperparameter will be increased accordingly. If is lower than , then is positive, which increases the part deducted from , resulting in decreasing compared to ; similarly, if Ratio If it decreases, then is also positive, thus further reducing . Therefore, The adjustment of 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 decrease accordingly, meaning that a more conservative pruning strategy will be adopted in the subsequent pruning process to avoid further reduction in accuracy due to excessive pruning. Conversely, if there are no negative changes in both indicators, then remains basically stable. Through this adjustment relationship, the pruning intensity is finally automatically adjusted according to the model performance feedback during actual operation, ensuring a more ideal balance between the accuracy and efficiency of the overall new classical circumferential viscous torque model.

[0030] Use the adjusted pruning hyperparameters to prune the surrogate model and then determine whether optimization is needed again. Taking this as a cycle, obtain the adjustment sequence of the pruning hyperparameters during the cycle. The formula is as follows: ; where is the adjustment sequence of the pruning hyperparameters, is the pruning hyperparameter obtained from the first adjustment, is the pruning hyperparameter obtained from the second adjustment, is the pruning hyperparameter obtained from the third adjustment, is the pruning hyperparameter obtained from the th adjustment, is the adjustment times retrieval variable, ; Screen the adjustment sequence of the pruning hyperparameters to obtain the latest continuously decreasing sequence. The latest continuously decreasing sequence is a subsequence that contains the latest pruning hyperparameter and each subsequent pruning hyperparameter is smaller than the previous one. Use the latest obtained pruning hyperparameter to prune the surrogate model obtained from the first pruning hyperparameter in the latest continuously decreasing sequence. If there is no latest continuously decreasing sequence, use the current pruning hyperparameter to prune the surrogate model; By screening the latest continuously decreasing sequence, judge the adjustment process of the pruning hyperparameters. In the way of "using the latest obtained pruning hyperparameter to prune the surrogate model obtained from the first pruning hyperparameter in the latest continuously decreasing sequence", avoid excessive adjustment of the pruning hyperparameters and make the optimization of the model proceed steadily.

[0031] Set the maximum number of pruning times. When the surrogate model still needs to be optimized according to the reliability threshold and the model evaluation threshold when the maximum number of pruning times is reached, then reduce the number of layers. The logic for reducing the number of layers is as follows: Obtain the activation variance of each layer, eliminate the layer with the smallest activation variance, and restart pruning the surrogate model starting from the surrogate model before pruning. Set the maximum number of layers to be reduced. When the maximum number of layers to be reduced is reached or the non-optimization condition is met, then judge to obtain the surrogate model.

[0032] By pruning the weights of each layer of neurons in the surrogate model, setting pruning hyperparameters, and using the weight median as a reference, neurons that do not meet the set standard are deleted. This step makes the structure of the model more concise and efficient, thus greatly reducing the consumption of computing resources and ensuring the stability of prediction accuracy at the same time. During the optimization process, by continuously adjusting the pruning hyperparameters and forming a continuously decreasing sequence, the changing trend of the model performance can be sensitively captured, so that the surrogate model always maintains an accurate simulation of the behavior of the original physical module during iteration. This not only provides an optimized starting point for training the surrogate model in step 2 after initially identifying the module with computational bottlenecks in step 1, but also ensures a high degree of consistency between the predicted value of the surrogate model and the true torque when verifying the overall coupling model by constructing the coupling reliability coefficient in the final step 4. The balance between computational efficiency and accuracy is achieved. It can not only effectively reduce the computational amount during model operation and improve the overall system response speed, but also prevent the prediction accuracy from decreasing due to over-simplification, thus providing a solid technical guarantee for the stable operation and efficient application of the entire new classical circumferential viscous torque model under different complex working conditions.

[0033] In step 3, by comprehensively evaluating the computational efficiency and reliability of the surrogate model, it is ensured that the surrogate process not only improves the computational speed but also maintains the high accuracy and stability of the model. First, obtain the computational efficiency evaluation coefficient of the surrogate model, which can specifically quantify the degree of efficiency improvement of the surrogate model in the overall model operation. Setting the reliability threshold and the model evaluation threshold provides clear criteria and a basis for evaluating the surrogate model, ensuring that the optimization process is controllable and targeted. By combining the reliability coefficient and the computational efficiency evaluation coefficient, the performance of the surrogate model in practical applications can be comprehensively reflected, avoiding a decrease in model accuracy caused by over-optimization. At the same time, when the computational efficiency evaluation coefficient of the surrogate model exceeds the model evaluation threshold and the reliability coefficient is insufficient, the model architecture can be adjusted in a timely manner, such as reducing the number of neurons and the number of layers in each layer of the fully connected neural network, so as to further improve the computational efficiency on the premise of ensuring the model performance. This step not only examines the actual effect of the surrogate model but also provides a feedback mechanism for continuous optimization, ensuring that the entire new classical circumferential viscous torque model always maintains the best performance in different application scenarios. Through this process, the optimization status of the model can be monitored and adjusted in real time to ensure its good adaptability and stability in a dynamic environment.

[0034] Step 4: Input the training set into the traditional new classical toroidal viscous torque physical model to obtain the true torque, input the training set into the new classical toroidal viscous torque model that couples physics and neural networks to obtain the simulated prediction values, construct the coupling reliability coefficient based on the true torque and the simulated prediction values, set the coupling reliability threshold, and combine the coupling reliability coefficient, the calculation efficiency coefficient of the surrogate model with the coupling reliability threshold and the model evaluation threshold to determine the correct new classical toroidal viscous torque model that couples physics and neural networks.

[0035] The said Step 4 includes the following contents: Obtain the training set of the surrogate model, input the training set into the traditional new classical toroidal viscous torque physical model, and obtain the output of the traditional new classical toroidal viscous torque physical model corresponding to each sample in the training set, which is calibrated as the true torque; Input each sample in the training set into the new classical toroidal viscous torque model that couples physics and neural networks and obtain the output, which is calibrated as the model prediction value; Obtain the coupling reliability coefficient of the new classical toroidal viscous torque model that couples physics and neural networks. The formula is as follows: ; where, is the coupling reliability coefficient, is the th model prediction value of the sample, is the th true torque of the sample, is the average value of the true torques of all samples, is the number of samples in the training set, is the sample number retrieval variable, , ; measures the deviation degree between the coupling model prediction value and the true torque of the traditional physical model. The closer the value is to 1, the higher the consistency between the prediction result of the coupling model and the true torque, and the higher the reliability; the closer the value is to 0, the greater the difference between the prediction result and the true torque, and the lower the reliability. By comparing the ratio between the squared error between the coupling model prediction value and the true torque and the squared error of the true torque relative to its average value, the goodness of fit of the model is reflected. decreases while the denominator remains unchanged, then increases. This indicates that the prediction result of the coupling model is closer to the true torque and the reliability is improved. In practical applications, this means that by optimizing the neural network or adjusting the coupling strategy, the prediction accuracy of the model can be improved to ensure the accuracy of torque calculation. increases while the denominator remains unchanged, then Decrease. This means that the difference between the prediction result of the coupling model and the true torque increases, and the reliability decreases. In the actual environment, this may indicate that the neural network model has not been fully trained, or there are problems of model overfitting / underfitting, and further optimization and adjustment are required. increases or decreases, while and the change of remains unchanged, then the denominator will change accordingly, affecting the value of. If the change in the average value causes the denominator to increase while the numerator remains unchanged, then will decrease, and vice versa. However, usually

[0036] Set the coupling reliability threshold. 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 determined that the new classical circumferential viscous torque model that correctly couples physics and neural networks has been obtained. The accuracy and computational efficiency optimization logic is as follows: Optimize the surrogate model again with the optimization process in step 3, and replace the conditions for pruning, layer reduction, and optimization 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, replace the reliability coefficient in the pruning hyperparameter formula with the coupling reliability coefficient.

[0037] Further optimize the surrogate model through the results of the entire coupled physics and neural network model to make the model more in line with requirements.

[0038] Step 4 comprehensively verifies the accuracy of the surrogate model and the reliability of the overall system by comparing the output results of the traditional physical model and the coupled physical and neural network model. Specifically, the training set is input into the traditional physical model to obtain the true torque, and then input into the coupled model to obtain the simulated prediction value, which can accurately measure the performance of the surrogate model in practical applications. Constructing the coupling reliability coefficient provides an intuitive index for evaluating the consistency between the prediction value of the coupled model and the true torque, ensuring that the surrogate model improves the calculation efficiency without sacrificing the prediction accuracy of the model. Setting the coupling reliability threshold makes the evaluation process have clear criteria and operability. When the coupling reliability coefficient is lower than the threshold and the calculation efficiency evaluation coefficient of the surrogate model is higher than the model evaluation threshold, it can be identified and optimized in a timely manner to further improve the overall performance of the model. In addition, through the verification of actual data, this step ensures the applicability and stability of the entire coupled model under different conditions, enhancing the credibility and practicality of the model in practical applications. Combining the optimization and evaluation mechanisms of the foregoing steps, Step 4 not only consolidates the effectiveness of the surrogate model, but also provides a solid theoretical basis and empirical support for the deployment and popularization of the entire new classical toroidal viscous torque model in practical engineering applications, ensuring its reliable operation under various complex working conditions.

[0039] Please refer to Figures 2 to 4 , the present invention also includes a preferred embodiment: As a preferred embodiment, the traditional new classical toroidal viscous torque physical calculation process is divided into three sub-modules, namely, an initial physical coefficient generation module, a linearized drift kinetic equation solving module, and a torque calculation module; based on the calculation efficiency evaluation coefficients of each sub-module, it is determined that the calculation efficiency evaluation coefficient of the linearized drift kinetic equation calculation module is higher than the threshold, which is the module that needs to be replaced by training the model; As a preferred embodiment, the input of the linearized drift kinetic equation calculation module is used as the training set. The specific situation of the sample is 8 equation coefficients, among 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 this module (referred to as 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 the data set of the surrogate model for the linearized drift kinetic equation solving module; As a preferred embodiment, the data set for constructing the surrogate model of the linearized drift kinetic equation solving module is input into a fully connected neural network for training. The designed fully connected neural network consists of 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 obtains an output value according to the activation function and bias in the neuron . Finally, 512 outputs are obtained as features and input into 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 obtains an output value according to the activation function and bias in the neuron . Finally, 512 outputs are obtained as features and input into 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 obtains an output value according to the activation function and bias in the neuron . Finally, 400 outputs are obtained as the final result, which is consistent with the sample label dimension. Finally, the training and testing of the surrogate model for constructing the linearized drift kinetic equation solving module are carried out. The surrogate model for constructing the linearized drift kinetic equation solving module is trained on the data set using the supervised learning method; As a preferred embodiment, after the surrogate model of the linearized drift kinetic equation solving module is trained, the cross-validation method is used according to the model reliability coefficient . If it is less than 0.8, the calculation accuracy of the perturbation distribution function prediction model is optimized. This optimization uses the Adam optimizer. The parameters adjusted during optimization include the weights and biases of the model, the learning rate, and the model initialization method. The Glorit Uniform model initialization method is used, and the learning rate is set to 0.0001 until the reliability coefficient is greater than 0.8; As a preferred embodiment, multi-source information is integrated through the environment and data fusion interface, and the model fusion technology is adopted to couple the surrogate models of the initial physical coefficient generation module, the linearized drift kinetics equation solving module and the torque calculation module. Specifically: Based on MATLAB, the Python computing framework is called, the Python path is confirmed using the pyenv command, and data type conversion and communication are achieved through the py library of MATLAB, so as to call the scientific computing, machine learning, data processing and visualization functions of Python; This process enables the Python data involved in the surrogate model of the linearized drift kinetics equation solving module to be integrated with the MATLAB data involved in the initial physical coefficient generation module and the torque calculation module; Then, the model fusion of the surrogate models of the initial physical coefficient generation module, the linearized drift kinetics equation solving module and the torque calculation module is carried out in the order of "physics - AI - physics". Specifically, the output of the initial physical coefficient generation module is used as the input of the surrogate model of the linearized drift kinetics equation solving module, the output of the surrogate model of the linearized drift kinetics equation solving module is used as the input of the torque calculation module, and the output of the torque calculation module is the new classical toroidal viscous torque; Through this sequential fusion, a new classical toroidal viscous torque model coupling a physical model and a neural network is finally obtained; Construct the computational efficiency evaluation coefficient of the surrogate model of the linearized drift kinetics equation solving module If the computational efficiency evaluation coefficient is greater than 0.5, optimize the calculation time of the model. When optimizing, first reduce the number of neurons in each layer. If the condition is still not met, reduce the number of layers of the model; As a preferred embodiment, obtain the coupling reliability coefficient of the new classical toroidal viscous torque model coupling a physical model and a neural network. If it does not exceed 0.8, optimize the model accuracy of the surrogate model of the linearized drift kinetics equation solving module. This optimization uses the L - BFGS optimizer, and the parameters to be adjusted during optimization include the weights and biases of the model, the learning rate and the initialization method of the model; If the coupling reliability coefficient exceeds 0.8, obtain the computational efficiency evaluation coefficient of the surrogate model of the linearized drift kinetics equation solving module in the new classical toroidal viscous torque model coupling a physical model and a neural network again. If the computational efficiency evaluation coefficient exceeds 0.5, optimize the calculation time of the surrogate model of the linearized drift kinetics equation solving module. First, reduce the number of neurons in each layer. If the condition is still not met, reduce the number of layers of the model; When the computational efficiency evaluation coefficient of the surrogate model of the linearized drift kinetics equation solving module is also lower than 0.5, the new classical toroidal viscous torque model coupling physics and neural network is obtained.

[0040] As a preferred embodiment, such as Figure 3As shown, the solution time of the traditional new classical toroidal viscous torque physical model is 67.542 seconds. As Figure 4 shown, the solution time of the new classical toroidal viscous torque model coupling physics and neural network is 23.744 seconds.

[0041] The above formulas are all dimensionless and take their numerical calculations. The formula is a formula obtained by collecting a large amount of data for software simulation to approximate the real situation as closely as possible. The preset parameters in the formula are set by those skilled in the art according to the actual situation.

[0042] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any 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 realize that the units and algorithm steps of each example described in connection with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0043] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units. They can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0044] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, and all should be covered by the protection scope of the present application.

Claims

1. A machine learning method for a new classical toroidal viscous torque, characterized in that The specific steps include: Step 1: Divide the process of the traditional neoclassical toroidal viscous torque physical model into three sub-modules, namely the initial physical coefficient generation module, the linearized drift kinetic equation solving module, and the torque calculation module. Obtain the running duration of each sub-module respectively and obtain the calculation efficiency evaluation coefficient. Set the calculation efficiency evaluation coefficient threshold and judge the module with a calculation bottleneck; Step 2: Use the input of the sub-module with a calculation bottleneck as the training set and the output as the label, and train in a fully connected neural network to obtain a surrogate model. Construct a reliability coefficient based on the input and output of the surrogate model, and replace the corresponding sub-module with a calculation bottleneck with the surrogate model to form a neoclassical toroidal viscous torque model that couples physics and neural networks; Step 3: Obtain the calculation efficiency evaluation coefficient of the surrogate model in the neoclassical toroidal viscous torque model that couples physics and neural networks. Set the reliability threshold and the model evaluation threshold, and combine the reliability coefficient, the calculation efficiency evaluation coefficient of the surrogate model, the reliability threshold, and the model evaluation threshold to judge the optimization status of the surrogate model; Step 4: Input the training set into the traditional neoclassical toroidal viscous torque physical model to obtain the true torque, input the training set into the neoclassical toroidal viscous torque model that couples physics and neural networks to obtain the simulated prediction value. Construct a 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 calculation efficiency coefficient of the surrogate model, the coupling reliability threshold, and the model evaluation threshold to judge the correct neoclassical toroidal viscous torque model that couples physics and neural networks.

2. A machine learning method for a new classical circumferential viscous torque according to claim 1, characterized in that: Divide the traditional neoclassical toroidal viscous torque physical model into three sub-modules, namely the initial physical coefficient generation module, the linearized drift kinetic equation solving module, and the torque calculation module, and number them. Obtain the running time for each sub-module to solve respectively, and use the running time of the module to evaluate the calculation efficiency evaluation coefficient of each sub-module. The formula based on which the calculation efficiency evaluation coefficient is calculated is as follows: ； Among them, is the calculation efficiency evaluation coefficient of the th sub-module, is the running time of the th sub-module, is the total running time of the traditional new classical toroidal viscous torque physical model, , is the module number retrieval variable, , ; Set the threshold of the calculation efficiency evaluation coefficient. When the calculation efficiency evaluation coefficient of the th sub-module exceeds the threshold of the calculation efficiency evaluation coefficient, it means that there is a calculation bottleneck in the th sub-module and a model replacement is required.

3. A machine learning method for a new classical circumferential viscous torque according to claim 2, characterized in that: Obtain the sub-module with a calculation bottleneck, label it as the model replacement module, obtain the input and output of the sub-module with a calculation bottleneck. Use the input of the sub-module with a calculation bottleneck as the training set and the output of the sub-module with a calculation bottleneck as the label, and input it into a fully connected neural network for training to obtain a surrogate model. Based on the input and output of the surrogate model, obtain the reliability coefficient. The formula based on which it is calculated is as follows: ； Among them, is the reliability coefficient, is the number of training set samples, is the output corresponding to the th sample of the surrogate model, is the mean value of the output of the model replacement module, is the th sample label, is the sample number retrieval variable, , ; Remove the sub-module with a calculation bottleneck in the traditional neoclassical toroidal viscous torque physical model and replace it with the corresponding surrogate model to form a neoclassical toroidal viscous torque model that couples physics and neural networks.

4. A machine learning method for a new classical circumferential viscous torque according to claim 3, characterized in that: Obtain the calculation efficiency evaluation coefficient of the surrogate model in the neoclassical toroidal viscous torque model that couples physics and neural networks. The logic is: When obtaining the running time of each sub-module in Step 1, each sub-module has a corresponding input. This input is input into the surrogate model again, and the surrogate model obtains an output based on the input. At this time, the time consumed by the surrogate model is the running time of the surrogate model. Adding the running time of the surrogate model to the running time of the sub-module without computational bottlenecks gives the total running time of the new classical toroidal viscous torque model that couples physics and neural networks; The formula for the computational efficiency evaluation coefficient of the surrogate model is as follows: ； Among them, is the computational efficiency evaluation coefficient of the surrogate model, is the running time of the surrogate model, is the total running time of the new classical toroidal viscous torque model that couples physics and neural networks.

5. A machine learning method for a new classical circumferential viscous torque according to claim 4, characterized in that: Set the reliability threshold and the model evaluation threshold 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 for accuracy and computational efficiency; otherwise, the surrogate model is not optimized; The accuracy and computational efficiency optimization logic is as follows: Obtain the weights of each neuron in each layer of the surrogate model and the median of the neuron weights in each layer. Set the pruning hyperparameter and its initial value, and prune the neurons in each layer according to the pruning formula, which is as follows: ； Among them, represents the weight of the th neuron in the layer, is the pruning hyperparameter, is the median of the neuron weights in the layer, is the neuron number retrieval variable, is the neuron number retrieval variable, is the neuron number retrieval variable, is the total number of neurons in the layer, is the neural network model layer number retrieval variable, is the neural network model layer number retrieval variable, is the total number of layers; Retain the neurons that satisfy the pruning formula and eliminate the neurons that do not satisfy the pruning formula. Use the initial value of the pruning hyperparameter for the first optimization. Retrain the pruned model and obtain the reliability coefficient and the computational efficiency evaluation coefficient, and then judge again according to the reliability threshold and the model evaluation threshold whether further optimization is needed. If no optimization is needed, use the current surrogate model. If optimization is needed, adjust the pruning hyperparameter according to the change rate of the reliability coefficient and the computational efficiency evaluation coefficient. The adjustment formula is as follows: ； Among them, is the adjusted pruning hyperparameter, is the pruning hyperparameter before adjustment, is the adjustment coefficient and , is the maximum value selection function, is the reliability coefficient of the surrogate model after pruning, is the reliability coefficient of the surrogate model before pruning, is the computational efficiency evaluation coefficient of the surrogate model after pruning, is the computational efficiency evaluation coefficient of the surrogate model before pruning; Prune the surrogate model using the adjusted pruning hyperparameter and judge again whether optimization is needed. This is used as a loop. During the loop, obtain the adjustment sequence of the pruning hyperparameter, which is as follows: ； Among them, is the adjustment sequence of pruning hyperparameters, is the pruning hyperparameter obtained from the first adjustment, is the pruning hyperparameter obtained from the second adjustment, is the pruning hyperparameter obtained from the third adjustment, is the th pruning hyperparameter obtained from the adjustment, is the adjustment times retrieval variable, ; Screen the adjustment sequence of the pruning hyperparameter to obtain the latest continuously decreasing sequence. The latest continuously decreasing sequence is a subsequence that contains the latest pruning hyperparameter and each subsequent pruning hyperparameter is less than the previous one. Prune the surrogate model obtained with the first pruning hyperparameter in the latest continuously decreasing sequence using the latest obtained pruning hyperparameter. If there is no latest continuously decreasing sequence, prune the surrogate model using the current pruning hyperparameter; Set the maximum number of pruning times. When the surrogate model still needs to be optimized according to the reliability threshold and the model evaluation threshold when the maximum number of pruning times is reached, reduce the number of layers. The logic for reducing the number of layers is as follows: Obtain the activation variance of each layer, eliminate the layer with the smallest activation variance, and start pruning the surrogate model again starting from the surrogate model before pruning. Set the maximum number of layers to be reduced. When the maximum number of layers to be reduced is reached or the non-optimization condition is met, then judge to obtain the surrogate model.

6. A machine learning method for a new classical circumferential viscous torque according to claim 5, characterized in that: Obtain the training set of the surrogate model, input the training set into the traditional new classical toroidal viscous torque physical model, and obtain the output of the traditional new classical toroidal viscous torque physical model corresponding to each sample in the training set, which is calibrated as the true torque; Input each sample in the training set into the new classical toroidal viscous torque model that couples physics and neural networks and obtain the output, which is calibrated as the model prediction value; Obtain the coupling reliability coefficient of the new classical toroidal viscous torque model that couples physics and neural networks. The formula is as follows: ； Among them, is the coupling reliability coefficient, is the model prediction value of the th sample, is the true moment of the th sample, is the average value of the true moments of all samples, is the number of samples in the training set, is the sample number retrieval variable, , ; Set the coupling reliability threshold. 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 determined that the new classical toroidal viscous torque model that correctly couples physics and neural networks has been obtained. The accuracy and computational efficiency optimization logic is as follows: Optimize the surrogate model again with the optimization process in step 3, and replace the conditions for whether to perform pruning, layer reduction, and optimization 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, replace the reliability coefficient in the pruning hyperparameter formula with the coupling reliability coefficient.

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