PINNs high Reynolds number flow field solving method based on regulatory factor optimization

Abstract

The invention discloses a PINNs high Reynolds number flow field solving method based on regulatory factor optimization, and the scheme comprises the steps: firstly building a physical model, on one hand, building a geometric model according to the actual condition of a reactor core rod bundle channel, and on the other hand, building a fluid mechanics model containing continuity, momentum conservation and energy conservation equations; a data set is obtained, and experimental data is preprocessed and then integrated with simulated data through experimental measurement and numerical simulation; and then training a physical information neural network, designing a neural network model of specific input and output, introducing a regulatory factor to balance the difference between a physical equation and data, constructing a comprehensive loss function containing internal data points, boundary data points and equation loss, and training the network by using a training data set until convergence. And finally, solving a flow field by using the trained neural network, outputting predicted values of a velocity field, a pressure field and a temperature field, and solving the high Reynolds number flow field of the reactor core.

Description

Technical Field

[0001] The present invention relates to the field of numerical calculation technology, and in particular to a PINNs high Reynolds number flow field solution method based on adjustment factor optimization. Background Art

[0002] The nuclear reactor core is the most important component of the reactor system, directly affecting the safety and efficiency of the reactor. The coolant flow process in the core is crucial for heat transfer, and the flow of coolant in the reactor core rod bundle channel is a typical complex flow field problem. The core rod bundle channel refers to the fluid channels formed between the rod bundle structures of the core assembly in the reactor. Through these channels, the coolant absorbs the heat released by the fuel rods, thereby keeping the reactor in a stable operating state.

[0003] In the actual operation of nuclear reactors, the core coolant flow usually has a very high Reynolds number (Re), especially in large commercial reactors, the core Reynolds number can reach the order of 105 or even higher. The Reynolds number is a dimensionless parameter to measure the flow properties of a fluid, characterizing the ratio of the inertial force to the viscous force in the flow. When the Reynolds number is high, the flow state of the coolant is often in a highly turbulent state. For such highly turbulent flows, it is extremely important to accurately predict the flow field characteristics, such as the velocity field, pressure field, and temperature field.

[0004] However, the calculation and simulation of high Reynolds number flow fields is a recognized problem. Traditional computational fluid dynamics (CFD) methods, such as numerical simulation techniques based on the finite element method (FEM) and the finite volume method (FVM), usually require very fine meshing of the flow field and simulation of complex turbulent characteristics. This places huge demands on computing resources, especially in nuclear reactor cores, where the rod bundle structure is complex, the flow channels are narrow, and the turbulence generation, development, and dissipation processes are complex, further increasing the difficulty of simulation. Common challenges include:

[0005] (1) High computational cost: In order to accurately capture the flow field characteristics under high Reynolds numbers, traditional CFD methods require the use of very fine grids, which significantly increases the computational cost, especially for three-dimensional models.

[0006] (2) The model is not accurate enough: Although common turbulence models (such as RANS, LES, etc.) can simplify calculations under certain conditions, their accuracy is insufficient in high Reynolds number flows, especially in flows with complex geometric structures.

[0007] (3) Experimental data is limited and mostly used for verification, and is difficult to integrate into the calculation process to enhance the solution: Due to the complexity of the core channel, it is difficult to obtain large-scale, high-precision data experimentally, resulting in a lack of sufficient verification of the numerical simulation results. Existing CFD calculation methods are difficult to integrate existing data in the solution process, and limited data are usually used to verify the model, resulting in a waste of data resources.

[0008] Therefore, how to accurately and effectively solve the flow field in the core rod bundle channel of a nuclear reactor under the condition of high Reynolds number flow is still a major challenge in the current nuclear energy engineering field. Summary of the invention

[0009] The present invention provides a PINNs high Reynolds number flow field solution method based on adjustment factor optimization, which is used to overcome at least one technical problem existing in the prior art.

[0010] The embodiment of the present invention provides a PINNs high Reynolds number flow field solution method based on adjustment factor optimization, comprising:

[0011] S1. Construct a physical model of the area to be analyzed in the core of the target nuclear reactor, including:

[0012] S11, based on the geometric structure and coolant flow characteristics of the core rod bundle channel of the target nuclear reactor, determining the size and relative position of each component of the core rod bundle channel, and constructing a geometric model of the rod bundle channel in the area to be analyzed;

[0013] S12. For the region to be analyzed, a fluid mechanics physical model including a continuity equation, a momentum conservation equation, and an energy conservation equation is established;

[0014] The continuity equation is used to describe the conservation of fluid mass, which is specifically expressed as:

[0015] ▽ u=0

[0016] The momentum conservation equation is used to describe the momentum change and viscosity effect of the fluid, which is specifically expressed as:

[0017]

[0018] In the core bundle channel, the first term on the left side of the momentum conservation equation is represents the rate of change of momentum with time, and the second term represents the convection term. The right side of the momentum conservation equation The term represents the pressure gradient term, The term represents the viscous diffusion term, and f represents the external force term;

[0019] The energy equation is used to describe heat transfer and is expressed as:

[0020]

[0021] in, represents the gradient symbol, u represents the fluid velocity vector, p represents the pressure, ρ represents the fluid density, ν represents the kinematic viscosity coefficient, f represents the volume force, T represents the temperature, and c represents the fluid velocity vector. p represents the specific heat capacity at constant pressure, the symbol k represents the thermal conductivity, and the symbol Q represents the volume heat source term; The term represents the rate of change of temperature with time, represents the convection term, The term represents the heat conduction term;

[0022] S2. Through experimental measurement and numerical simulation, the experimental data are pre-processed and integrated with the simulation data, so as to obtain a data set in the core rod bundle channel in the area to be analyzed;

[0023] S3. Training the physical information neural network, specifically including:

[0024] S31. Design a neural network model including an input layer, multiple hidden layers and an output layer, wherein the input of the neural network model is a parameterized description of a geometric structure, boundary conditions and parameters related to initial conditions, and the output of the neural network model is key physical quantities and adjustment factors of the flow field;

[0025] S32, constructing a comprehensive loss function including internal data point loss, boundary data point loss and equation loss, using data, boundary conditions and adaptively corrected physical equations to train the neural network until convergence, and adjusting model parameters of the neural network model according to the training results;

[0026] The comprehensive loss function consists of internal data point loss, boundary data point loss and equation loss, as follows:

[0027] The internal data point loss is used to calculate the difference between the predicted value of the physical quantity output by the neural network and the true value obtained by actual measurement or numerical simulation for each data point inside the core bundle channel; for the velocity field, the mean square error MSE is used to calculate the internal data point loss Among them, the symbol N represents the total number of internal data points, and the symbol u i Represents the actual speed value of the i-th internal data point, symbol represents the velocity value of the i-th internal data point predicted by the neural network;

[0028] For the pressure field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol p i Represents the actual pressure value of the i-th internal data point, symbol represents the pressure value of the i-th internal data point predicted by the neural network;

[0029] For the temperature field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol T i Represents the actual temperature value of the i-th internal data point, symbol represents the temperature value of the i-th internal data point predicted by the neural network;

[0030] The total internal data point loss L data is the weighted sum of the internal data point losses of velocity, pressure and temperature fields, i.e., L data =ω u L data-u +ω p L data-p +ω T L data-T , where the symbol ω u ,ω p and ω T are the weight coefficients of the internal data point loss of velocity, pressure and temperature fields, ω u +ω p +ω T =1;

[0031] Boundary data point loss: For the boundary area of ​​the core bundle channel, including the data points at the inlet, outlet and bundle surface boundary, the difference between the boundary physical quantity values ​​predicted by the calculation model and the known boundary conditions is calculated;

[0032] For the inlet boundary velocity field, calculate the boundary data point loss

[0033] Among them, the symbol M in is the number of entry boundary data points, symbol u in,j It represents the actual velocity value of the jth entry boundary data point, symbol represents the velocity value of the jth entry boundary data point predicted by the neural network;

[0034] For the outlet boundary pressure field, calculate the boundary data point loss Among them, the symbol M out Indicates the number of export boundary data points, symbol p out,k represents the actual pressure value of the kth outlet boundary data point, symbol represents the pressure value of the kth outlet boundary data point predicted by the neural network;

[0035] For the temperature field on the rod bundle surface boundary, calculate the loss of boundary data points

[0036]

[0037] Among them, the symbol M wall Indicates the number of data points on the rod bundle surface boundary, symbol T wall,l It represents the actual temperature value of the lth rod bundle surface boundary data point, symbol It represents the temperature value of the lth rod bundle surface boundary data point predicted by the neural network;

[0038] The total boundary data point loss L boundary It is the weighted sum of the boundary data point losses of different physical quantities at the inlet, outlet and bundle surface boundaries;

[0039] The equation loss includes the equation loss L of the continuity equation eq-c , the equation loss L of the momentum conservation equation eq-m and the energy conservation equation loss L eq-e ;

[0040] Among them, the equation loss of the continuity equation is

[0041] Equation loss for the momentum conservation equation

[0042] Equation loss for the energy conservation equation

[0043] The total equation loss L eq =ω c L eq-m +ω 2 L eq-m +ω e L eq-e , where the symbol S(x) represents the adjustment factor, and the symbol ω c ,ω m and ω e They represent the weight coefficients of the equation loss of the continuity equation, the equation loss of the momentum conservation equation, and the equation loss of the energy conservation equation, respectively, and ω c +ω m +ω e =1;

[0044] Comprehensive loss function L total It is expressed as:

[0045] L total =ω data L data +ω boundary L boundary +ω eq L eq

[0046] Among them, ω data ,ω boundary and ωeq are the weight coefficients of internal data point loss, boundary data point loss and equation loss respectively, and ω data +ω boundary +ω eq =1;

[0047] The neural network is trained using a training data set. During the training process, the parameters of the neural network are adjusted through an optimization algorithm according to the comprehensive loss function, so that the value of the comprehensive loss function gradually decreases until a preset convergence condition is met, thereby obtaining a trained neural network;

[0048] The trained neural network is used to solve the high Reynolds number flow field in the core of a nuclear reactor and output the corresponding predicted values ​​of the velocity field, pressure field and temperature field.

[0049] Preferably, a three-dimensional geometric model is accurately constructed based on the actual structural mapping or design documents of the nuclear reactor core, laser scanning and industrial CT imaging technology are used to obtain high-precision point cloud data or tomographic image data of the core internal structure, and the geometric structure of the rod bundle channel of the target nuclear reactor core is reconstructed by reverse engineering software; the scope of the area to be analyzed is defined according to the focus area of ​​the problem to be solved and the limitation of computing resources.

[0050] Preferably, the acquisition of the data set in the core rod bundle channel in the area to be analyzed includes: equipping a sensor array consisting of a high-precision flow sensor, a velocity sensor, a pressure sensor and a temperature sensor to collect data at axial intervals of 1-5 mm and 3-8 key positions in each radial layer of the rod bundle channel, the sampling frequency is adaptively set at the order of 10-20 Hz according to the transient change characteristics of the flow field to ensure the capture of high-frequency fluctuations, the collected raw data is identified and removed according to statistical methods, and smoothed by a filtering algorithm, the processed data is fused and corrected by data assimilation technology and numerical simulation data, and finally the data set in the core rod bundle channel in the area to be analyzed is obtained.

[0051] Preferably, in step S32, during the process of training the neural network until convergence, the solution points are adaptively adjusted according to the flow field gradient, the density of the solution points is adjusted to accurately analyze local details or capture macro trends, and the solution points are optimized according to the solution stability and solution accuracy.

[0052] Preferably, the hidden layer of the neural network model adopts a multilayer perceptron; Tanh is selected as the activation function to prevent the gradient vanishing phenomenon, and the number of neurons and the connection mode are adaptively configured according to the complexity of the problem; the network depth is optimized and determined in the range of 20-100 layers according to the nonlinearity of the physical quantities of the flow field.

[0053] One embodiment of this specification can achieve at least the following beneficial effects:

[0054] 1. By constructing a model containing physical equations such as the mass conservation equation, momentum conservation equation, and energy conservation equation, and combining it with the physical information neural network (PINN), on the one hand, the model can strictly follow these basic physical laws to describe the flow of coolant in the core of the nuclear reactor. On the other hand, by combining a small amount of experimental or numerical simulation data with the physical equations, the physical equations provide the basic physical laws that the flow field should follow, making up for the lack of information in small sample data. During the training process, the neural network not only learns from the data, but also constrains and guides the learning process based on the physical equations, so that the model can have a deeper understanding of the physical mechanism of the flow field.

[0055] 2. A comprehensive loss function consisting of internal data point loss, boundary data point loss and equation loss was constructed. The internal data point loss prompts the neural network to effectively fit the data actually measured or simulated inside the core bundle channel, so that the flow field physical quantities (velocity, pressure, temperature, etc.) output by the model are as close to the true value as possible; the boundary data point loss ensures that the model can accurately meet the boundary conditions such as the inlet, outlet and bundle surface, because the boundary conditions have a key impact on the propagation and evolution of the entire flow field. Accurate boundary processing can make the flow field at the boundary and its vicinity more in line with the actual situation; the equation loss ensures that the model follows the laws described by the physical equations. By reasonably setting the weights of each part of the loss in the comprehensive loss function, the neural network is guided to automatically find the best balance between fitting the data and following the physical laws during the training process, avoiding the problem of simply pursuing data fitting and violating physical principles or over-emphasizing physical laws and ignoring the actual situation of the data, so that the final flow field solution is both physically reasonable and well matched with the actual data.

[0056] 3. The introduced adjustment factor S(x) is added to the equation loss and can be automatically adjusted according to the error between the physical equation and the data during the network training process. This feature makes the calculation of the equation loss more flexible and accurate, and can better correct the deviation between the physical equation and the actual data due to model simplification, data error and other reasons. It further helps the neural network to optimize the balance between data fitting and physical law compliance during training, improves the generalization ability of the model, and enables it to output more accurate and reliable flow field solutions under different working conditions and different data quality conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 A flow chart of a method for solving a PINNs high Reynolds number flow field based on adjustment factor optimization provided in an embodiment of this specification. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of one or more embodiments of this specification clearer, the technical solutions of one or more embodiments of this specification will be clearly and completely described below in combination with the specific embodiments of this specification and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of one or more embodiments of this specification.

[0060] It should be understood that although the terms first, second, third, etc. may be used in this application document to describe various information, this information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other.

[0061] In the field of nuclear reactor core flow field solution, the difficulty of data acquisition has always restricted the progress of research. The internal environment of the nuclear reactor core is complex, the rod bundle structure is staggered, and the coolant flows in narrow and irregularly shaped channels. When conducting high-precision, large-scale experimental measurements, not only does it require specially designed complex experimental equipment to simulate the core environment, but it also faces many technical challenges, such as the reliability of measurement equipment in a strong radiation environment and the accuracy of measuring micro-scale flow field characteristics. These factors make it costly and difficult to obtain large-scale experimental data, resulting in data scarcity becoming the main bottleneck for flow field solution.

[0062] Traditional pure data-driven machine learning methods, such as neural networks and support vector machines, rely on large amounts of high-quality data for training. Their learning process is mainly based on statistical laws in the data and lacks an understanding of the physical essence. In solving the core flow field of a nuclear reactor, due to data scarcity, such methods are difficult to learn sufficiently comprehensive and accurate flow field characteristics, and the model is prone to overfitting and poor generalization. For example, when faced with core flow field predictions under different operating conditions, the model may not be able to adapt accurately, resulting in large deviations in the prediction results.

[0063] In order to solve the defects in the prior art, the technical solution of the present application introduces a physical information neural network (PINN) and embeds fluid mechanics equations, such as the continuity equation, the momentum conservation equation, and the energy equation, into the neural network. In this way, a small amount of experimental or numerical simulation data can be combined with the physical equations. The physical equations provide the basic physical laws that the flow field should follow, making up for the defect of insufficient information in small sample data. During the training process, the neural network not only learns from the data, but also constrains and guides the learning process according to the physical equations, so that the model can have a deeper understanding of the physical mechanism of the flow field.

[0064] Figure 1 A flow chart of the method provided in the embodiment of this specification is as follows: Figure 1 As shown, the process may include the following steps.

[0065] Step S1: constructing a physical model of the area to be analyzed in the core of the target nuclear reactor, which may specifically include:

[0066] Step S11, based on the geometric structure and coolant flow characteristics of the core rod bundle channel of the target nuclear reactor, the size and relative position of each component of the core rod bundle channel are determined, and a geometric model of the rod bundle channel in the area to be analyzed is constructed;

[0067] Step S12: for the area to be analyzed, a fluid mechanics physical model including a continuity equation, a momentum conservation equation, and an energy conservation equation is established;

[0068] The continuity equation is used to describe the conservation of fluid mass, which is specifically expressed as:

[0069]

[0070] The momentum conservation equation is used to describe the momentum change and viscosity effect of the fluid, which is specifically expressed as:

[0071]

[0072] In the core bundle channel, the first term on the left side of the momentum conservation equation is represents the rate of change of momentum with time, and the second term represents the convection term. The right side of the momentum conservation equation The term represents the pressure gradient term, The term represents the viscous diffusion term, and f represents the external force term;

[0073] The energy equation is used to describe heat transfer and is expressed as:

[0074]

[0075] in, represents the gradient symbol, u represents the fluid velocity vector, p represents the pressure, ρ represents the fluid density, ν represents the kinematic viscosity coefficient, f represents the volume force, T represents the temperature, and c represents the fluid velocity vector. p represents the specific heat capacity at constant pressure, the symbol k represents the thermal conductivity, and the symbol Q represents the volume heat source term; The term represents the rate of change of temperature with time, represents the convection term, The term represents the heat conduction term;

[0076] Step S2: Through experimental measurement and numerical simulation, the experimental data is pre-processed and integrated with the simulation data, so as to obtain a data set in the core rod bundle channel in the area to be analyzed;

[0077] Step S3: training the physical information neural network, specifically including:

[0078] Step S31: designing a neural network model including an input layer, multiple hidden layers and an output layer, wherein the input of the neural network model is a parameterized description of the geometric structure, boundary conditions and initial condition related parameters, and the output of the neural network model is key physical quantities and adjustment factors of the flow field;

[0079] Step S32: constructing a comprehensive loss function including internal data point loss, boundary data point loss and equation loss, using data, boundary conditions and adaptively corrected physical equations to train the neural network until convergence, and adjusting model parameters of the neural network model according to the training results;

[0080] The comprehensive loss function consists of internal data point loss, boundary data point loss and equation loss, as follows:

[0081] The internal data point loss is used to calculate the difference between the predicted value of the physical quantity output by the neural network and the true value obtained by actual measurement or numerical simulation for each data point inside the core bundle channel; for the velocity field, the mean square error MSE is used to calculate the internal data point loss Among them, the symbol N represents the total number of internal data points, and the symbol u i Represents the actual speed value of the i-th internal data point, symbol represents the velocity value of the i-th internal data point predicted by the neural network;

[0082] For the pressure field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol p i Represents the actual pressure value of the i-th internal data point, symbol represents the pressure value of the i-th internal data point predicted by the neural network;

[0083] For the temperature field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol T i Represents the actual temperature value of the i-th internal data point, symbol represents the temperature value of the i-th internal data point predicted by the neural network;

[0084] The total internal data point loss L data is the weighted sum of the internal data point losses of velocity, pressure and temperature fields, i.e., L data =ω u L data-u +ω p L data-p +ω T L data-T , where the symbol ω u ,ω p and ω T are the weight coefficients of the internal data point loss of velocity, pressure and temperature fields, ω u +ω p +ω T =1;

[0085] Boundary data point loss: For the boundary area of ​​the core bundle channel, including the data points at the inlet, outlet and bundle surface boundary, the difference between the boundary physical quantity values ​​predicted by the calculation model and the known boundary conditions is calculated;

[0086] For the inlet boundary velocity field, calculate the boundary data point loss

[0087] Among them, the symbol M in is the number of entry boundary data points, symbol u in,j It represents the actual velocity value of the jth entry boundary data point, symbol represents the velocity value of the jth entry boundary data point predicted by the neural network;

[0088] For the outlet boundary pressure field, calculate the boundary data point loss Among them, the symbol M out Indicates the number of export boundary data points, symbol p out,k represents the actual pressure value of the kth outlet boundary data point, symbol represents the pressure value of the kth outlet boundary data point predicted by the neural network;

[0089] For the temperature field on the rod bundle surface boundary, calculate the loss of boundary data points

[0090]

[0091] Among them, the symbol Mwall Indicates the number of data points on the rod bundle surface boundary, symbol T wall,l It represents the actual temperature value of the lth rod bundle surface boundary data point, symbol It represents the temperature value of the lth rod bundle surface boundary data point predicted by the neural network;

[0092] The total boundary data point loss L boundary It is the weighted sum of the boundary data point losses of different physical quantities at the inlet, outlet and bundle surface boundaries;

[0093] The equation loss includes the equation loss L of the continuity equation eq-c , the equation loss L of the momentum conservation equation eq-m and the energy conservation equation loss L eq-e ;

[0094] Among them, the equation loss of the continuity equation is

[0095] Equation loss for the momentum conservation equation

[0096] Equation loss for the energy conservation equation

[0097] The total equation loss L eq =ω c L eq-m +ω 2 L eq-m +ω e L eq-e , where the symbol S(x) represents the adjustment factor, and the symbol ω c ,ω m and ω e They represent the weight coefficients of the equation loss of the continuity equation, the equation loss of the momentum conservation equation, and the equation loss of the energy conservation equation, respectively, and ω c +ω m +ω e =1;

[0098] Comprehensive loss function L total It is expressed as:

[0099] L total =ω data L data +ω boundary L boundary +ω eq L eq

[0100] Among them, ω data ,ω boundary and ω eqare the weight coefficients of internal data point loss, boundary data point loss and equation loss respectively, and ω data +ω boundary +ω eq =1;

[0101] The neural network is trained using a training data set. During the training process, the parameters of the neural network are adjusted through an optimization algorithm according to the comprehensive loss function, so that the value of the comprehensive loss function gradually decreases until a preset convergence condition is met, thereby obtaining a trained neural network;

[0102] The trained neural network is used to solve the high Reynolds number flow field in the core of a nuclear reactor and output the corresponding predicted values ​​of the velocity field, pressure field and temperature field.

[0103] In the technical solution of the present application, the adjustment factor S(x) is a function related to the spatial position, and x represents a specific spatial coordinate point in the core rod bundle channel of the nuclear reactor (for example, in three-dimensional space, x=(x 1 , x 2 , x 3 ), which correspond to the coordinate values ​​in different directions such as axial and radial directions. It means that at different spatial positions in the core, the value of can vary, reflecting the differences in its adjustment effect on the loss of the physical equation at different points in the entire flow field space.

[0104] At the same time, in the technical solution of the present application, the adjustment factor S (x) can correct the deviation between the physical equation and the data. Specifically, when using the physical information neural network PINN to solve the high Reynolds number flow field problem of the nuclear reactor core, it is necessary to substitute the flow field physical quantities (such as velocity, pressure, temperature, etc.) output by the neural network into physical control equations such as the continuity equation, the momentum conservation equation, and the energy conservation equation, and calculate the difference between the left and right sides of the equation to measure the equation loss. However, due to the existence of various complex factors in actual situations, such as the physical model itself is an idealized simplification of the actual complex flow field, there is a certain modeling error; or the data obtained by the experiment or numerical simulation itself has noise, uncertainty, and the data may have sparsity and other problems. Simply relying on the difference between the left and right sides of the equation calculated conventionally to measure the equation loss cannot accurately reflect the degree of fit between the model output and the actual physical situation. At this time, the adjustment factor S (x) comes into play. It is attached to the equation loss to correct the deviation between these physical equations and the actual data, so that the calculation of the equation loss can more reasonably and accurately reflect the model's compliance with the physical equation.

[0105] For example, in the momentum conservation equation After adding the adjustment factor S(x), it becomes When calculating the loss of the equation, the velocity field predicted by the neural network is Pressure Field Substitute the terms on the left side of the equation for calculation, and then compare them with the external force terms f on the right side of the equation. The difference at this time is used as the new equation loss (taking the influence of S(x) into account). In this way, the equation loss can better adapt to various complex situations in actual physical scenarios that cause the theoretical equation to not fully match the actual data.

[0106] The adjustment factor S(x) is not fixed, it can be automatically adjusted according to the error between the physical equation and the data during the network training process. Specifically, it is calculated by calculating the gradient of the loss function (including the loss of the equation with S(x) and the comprehensive loss function such as data loss) with respect to the adjustment factor S(x), and then using the optimization algorithm (such as the gradient descent algorithm, etc.) to update the value in the direction indicated by the gradient. In the early stage of training, S(x) will quickly adjust in the direction that can reduce the value of the comprehensive loss function. With the continuous iteration of training, it will gradually converge to a suitable value, so that the flow field output by the model is consistent with the physical laws (reflected by the reasonable adjustment of the equation loss) and can fit the actual data situation (combined with the joint effect of data loss, etc.), and finally achieve a more accurate solution to the high Reynolds number flow field of the nuclear reactor core.

[0107] In short, the adjustment factor S(x) is an important adjustment factor used to coordinate the relationship between physical equations and actual data and improve the accuracy of the model in the entire process of solving flow field problems based on physical information neural networks. It is related to the spatial position and can be adjusted adaptively.

[0108] The internal data point loss mentioned above mainly measures the difference between the predicted value of the physical quantity at each data point in the internal area of ​​the core bundle channel by the neural network model and the true value obtained by actual measurement or numerical simulation. In the high Reynolds number flow field of the nuclear reactor core, the internal data points are distributed throughout the core, and the true values ​​of the physical quantities (such as velocity, pressure, temperature, etc.) at these points are obtained through experimental measurement or high-precision numerical simulation. During training, the neural network model predicts the physical quantities of these internal data points and then calculates the deviation between the predicted value and the true value. For example, for the velocity field, the difference between the velocity vector predicted by the model and the actual measured velocity vector at each internal data point is calculated, and the velocity errors of all internal data points are combined through specific mathematical methods (such as mean square error) to obtain a value reflecting the size of the overall velocity prediction error of the model at the internal data point. This is the velocity-related internal data point loss. Similar methods are used to calculate the internal data point loss for physical quantities such as pressure and temperature. By minimizing the internal data point loss, the neural network can be guided to adjust internal parameters (such as weights and biases) so that the model can more accurately predict the distribution of physical quantities in the flow field inside the core. Because the flow field characteristics inside the core have an important impact on the performance and safety of the reactor, accurate prediction of the internal flow field can help optimize the reactor design, improve operating efficiency and ensure safety. For example, accurate prediction of velocity distribution can help optimize the flow path of the coolant in the core and improve the efficiency of heat transfer; accurate prediction of pressure distribution can help avoid damage to the core structure caused by excessive or low local pressure. Boundary data point loss is used to evaluate the performance of the model on the core bundle channel boundaries (including inlet boundaries, outlet boundaries, bundle surface boundaries, etc.). At these boundaries, the physical quantities of the flow field have specific conditions, such as the inlet boundary has given conditions such as velocity, temperature and pressure, the outlet boundary may have pressure or velocity constraints, and the bundle surface boundary may have no-slip conditions (zero velocity) or given heat exchange conditions. Boundary data point loss calculates the difference between the boundary physical quantity values ​​predicted by the model and these known boundary conditions. For example, at the inlet boundary, the difference between the velocity predicted by the calculation model and the actual given inlet velocity is calculated, and the velocity loss at the inlet boundary is calculated by the corresponding loss function; for the rod bundle surface boundary, the loss is calculated based on the difference between the temperature predicted by the model and the known wall temperature (if there is a heat exchange condition) or the velocity calculated based on the no-slip condition (should be zero) and the velocity predicted by the model. Similarly, similar calculations are performed for the prediction errors of physical quantities such as pressure on the boundary, and finally the losses of different physical quantities on each boundary are combined to obtain the boundary data point loss. Boundary conditions have an important influence on the distribution and evolution of the entire core flow field. By minimizing the loss of boundary data points, neural networks can better meet boundary conditions, thereby ensuring the prediction accuracy of the flow field near the boundary and in the entire calculation domain.For example, if the velocity condition at the inlet boundary cannot be accurately met, the subsequent flow field calculation will be biased from the beginning, which will affect the prediction results of the entire core flow field. Accurate boundary data point loss calculation and optimization can make the model's prediction at the boundary consistent with the actual situation, provide reasonable boundary constraints for the accurate calculation of the internal flow field, and ensure the physical rationality and accuracy of the entire flow field calculation. Equation loss mainly evaluates the degree of conformity of the model to the control equations (such as the continuity equation, momentum conservation equation, and energy conservation equation). For the nuclear reactor core flow field, these control equations are the basic laws that describe the physical process of the flow field. Equation loss is measured by substituting the flow field physical quantities (velocity, pressure, temperature, etc.) predicted by the neural network into the control equation and calculating the difference between the left and right sides of the equation. For example, for the momentum conservation equation, the velocity field predicted by the model is substituted into the convection term, pressure gradient term, viscous diffusion term, etc. on the left side of the equation for calculation to obtain a result, which is then compared with the external force term on the right side of the equation. The difference between the two is the loss of the momentum conservation equation at a certain data point or the entire calculation domain. Similarly, similar calculations are performed for the continuity equation and the energy conservation equation, and finally the losses of these equations at all data points are combined to obtain the equation loss. In this process, the adjustment factor (S(x) is added to the equation loss to correct the overall difference between the data and the equation caused by model simplification or calculation errors. The data size of the adjustment factor is consistent with the size of the total training points. The difference between the data and the equation is quantified through data approximation to help the model better follow the physical equation. The equation loss ensures that the flow field predicted by the model is physically reasonable and follows basic physical principles even when the data is limited or noisy. By minimizing the equation loss, the neural network can adjust the parameters so that the flow field output by the model satisfies the physical laws such as conservation of mass, momentum and energy. This helps to avoid the model predicting flow field solutions that are not in line with physical reality, such as avoiding unreasonable situations such as non-conservation of mass or the creation or disappearance of energy out of thin air. The equation loss works together with the internal data point loss and the boundary data point loss to guide the neural network to find a balance between fitting the data and following the physical laws during the training process, thereby obtaining accurate and reliable solutions to the high Reynolds number flow field in the core of a nuclear reactor.

[0109] The following is a comparison of the effects of the technical solution of the present application with the traditional pure data-driven model solution from the perspective of model stability and prediction accuracy.

[0110] From the perspective of model stability, assuming that the prediction result of the traditional pure data-driven model is y traditional , whose variance is Var(y traditional ), due to data scarcity, the model is sensitive to data fluctuations and has a large variance. The prediction result of the model of the present invention is y PINNAfter introducing the physical equation as a constraint, the model is restricted by the laws of physics and will not overfit the noise in the data. Let the constraint term of the physical equation be C, then y PINN =f(x)+C (f(x) is the part of the model based on data). From the perspective of mathematical expectation, E[C]=0. According to the variance property Var(y PINN )=Var(f(x)+C)=Var(f(x))+Var(C)+2Cov(f(x),C). Because the physical equation constraints are relatively stable, Var(C) is small, and Cov(f(x),C) approaches 0, so Var(y PINN )<Var(y traditional ), that is, the prediction results of the model of the present invention are more stable.

[0111] From the perspective of prediction accuracy, the mean square error (MSE) is used to measure the prediction accuracy. The mean square error of the traditional model is MSE traditional =E[(y true -y traditional ) 2 ], the mean square error of the model of the present invention is MSE PINN =E[(y true -y PINN ) 2 ]. Due to the constraints of the physical equations, the model of the present invention can better capture the real physical characteristics of the flow field. When the data is limited, the traditional model is easy to deviate from the real flow field distribution, while the model of the present invention, under the guidance of the physical equations, predicts the value y PINN Closer to the true value y true , that is E[(y true -y PINN ) 2 ]<E[(y true -y traditional ) 2 ], so MSE PINN <MSE traditional , indicating that the prediction accuracy of the model of the present invention is higher.

[0112] Figure 1The scheme in the paper constructs a model containing physical equations such as the mass conservation equation, momentum conservation equation, and energy conservation equation, and combines it with the physical information neural network (PINN). On the one hand, the model can strictly follow these basic physical laws to describe the flow of coolant in the core of the nuclear reactor. On the other hand, by combining a small amount of experimental or numerical simulation data with the physical equations, the physical equations provide the basic physical laws that the flow field should follow, making up for the lack of information in small sample data. During the training process, the neural network not only learns from the data, but also constrains and guides the learning process according to the physical equations, so that the model can have a deeper understanding of the physical mechanism of the flow field. At the same time, the scheme constructs a comprehensive loss function consisting of internal data point loss, boundary data point loss, and equation loss. Internal data point loss prompts the neural network to effectively fit the data actually measured or simulated inside the core bundle channel, so that the flow field physical quantities (velocity, pressure, temperature, etc.) output by the model are as close to the real value as possible; boundary data point loss ensures that the model can accurately meet the boundary conditions such as the inlet, outlet and bundle surface, because the boundary conditions have a key impact on the propagation and evolution of the entire flow field. Accurate boundary processing can make the flow field at the boundary and its vicinity more in line with the actual situation; equation loss ensures that the model follows the laws described by the physical equations. By reasonably setting the weights of each part of the loss in the comprehensive loss function, the neural network is guided to automatically find the best balance between fitting the data and following the physical laws during the training process, avoiding the problem of simply pursuing data fitting and violating physical principles or over-emphasizing physical laws and ignoring the actual data situation, so that the final flow field solution is both physically reasonable and well matched with the actual data. The introduced adjustment factor S(x) is added to the equation loss and can be automatically adjusted according to the error between the physical equation and the data during the network training process. This feature makes the calculation of the equation loss more flexible and accurate, and can better correct the deviation between the physical equation and the actual data due to model simplification, data error and other reasons. It further helps the neural network to optimize the balance between data fitting and compliance with physical laws during training, improves the generalization ability of the model, and enables it to output more accurate and reliable flow field solutions under different working conditions and different data quality conditions.

[0113] based on Figure 1 The method, the examples of this specification also provide some specific implementation plans of the method, which are described below.

[0114] In an optional embodiment technical solution, a three-dimensional geometric model can be accurately constructed based on the actual structural mapping or design documents of the nuclear reactor core, and laser scanning and industrial CT imaging technology can be used to obtain high-precision point cloud data or tomographic image data of the core internal structure. The geometric structure of the rod bundle channel of the target nuclear reactor core can be reconstructed by reverse engineering software; the scope of the area to be analyzed is defined according to the focus area of ​​the problem to be solved and the computing resource limitations.

[0115] In the technical solution of this embodiment, for the reactors that have been built, technicians can use professional measuring tools to conduct on-site measurements of the size, shape and relative position of each component of the core rod bundle channel. For example, a high-precision three-dimensional coordinate measuring instrument can accurately measure the three-dimensional coordinates of each component, and its measurement accuracy can reach sub-millimeter level, providing accurate basic data for model construction. For newly built reactors, detailed design documents contain the precise parameters of each component of the core, from the diameter and length of the fuel rods to the arrangement of components. The three-dimensional geometric model can be directly constructed based on these design parameters. An accurate geometric model can truthfully reflect the impact of the core structure on the coolant flow, laying the foundation for subsequent flow field simulation.

[0116] Laser scanning technology emits a laser beam to the core, measures the time from the laser being emitted to the laser being reflected back to the receiver, and uses the principle of the invariance of the speed of light to calculate the distance from the measurement point to the scanner, thereby obtaining a large number of three-dimensional coordinate points to form point cloud data. This technology has the characteristics of non-contact measurement, which can avoid physical damage to the core structure. It has a fast measurement speed and can obtain massive data in a short time, covering all parts of the complex structure of the core, including areas that are difficult to measure directly, such as the inside of narrow channels and corners. The acquired data is highly accurate and can accurately present the subtle features of the internal structure of the core, providing rich and accurate original information for subsequent model reconstruction.

[0117] Industrial CT imaging technology uses tomography to scan the core, emits X-rays from multiple angles to penetrate the core, and receives the attenuated ray signals on the other side. Using the principle of computed tomography, these signals are processed into a series of tomographic images, which can clearly show the distribution, boundaries and connections of different materials and components inside the core. Complementary to laser scanning technology, industrial CT imaging can obtain internal information of objects and is very effective for detecting defects and material inhomogeneities inside the core. By analyzing the tomographic images, the precise geometric information of the internal structure of the core can be extracted, providing more comprehensive data support for the reconstruction of the geometric model, ensuring that the model can accurately reflect the real structure inside the core. After obtaining point cloud data or tomographic image data, reverse engineering software needs to be used for processing and reconstruction. In the data preprocessing stage, the reverse engineering software can denoise the acquired point cloud data to remove abnormal points caused by measurement errors or environmental interference; smooth the data through filtering algorithms to reduce data fluctuations; streamline redundant data to reduce data volume and improve processing efficiency. During the modeling process, the software uses the fitting algorithm to construct the geometric shape based on the processed data, and generates a complete three-dimensional geometric model through surface reconstruction technology. During the reconstruction process, the model can be optimized and adjusted according to actual needs, such as adjusting the smoothness of the surface, repairing minor defects in the model, etc., to ensure that the model is highly consistent with the actual core structure.

[0118] The scope of the computational domain must be closely centered around the focal area of ​​the problem to be solved. If the research focus is on the flow field characteristics of a specific area of ​​the core, such as the flow of coolant near a group of fuel rods, the computational domain must include the area and a certain range around it to ensure that the interaction between the flow field in the area and the surrounding environment can be accurately simulated. Because the flow field is continuous, the flow state in the surrounding area will have an impact on the focal area. If the overall flow characteristics of the core are studied, the computational domain must cover the entire core area to obtain comprehensive flow field information. Clearly defining the focal area of ​​the problem to be solved can avoid the computational domain being too large or too small. A computational domain that is too large will increase the computational cost and consume too much computing resources and time; a computational domain that is too small may lead to unreasonable boundary condition settings, affect the accuracy of the calculation results, and fail to truly reflect the actual situation of the flow field.

[0119] At the same time, computing resources are an important factor that must be considered when defining the scope of the computational domain. Accurate simulation of the high Reynolds number flow field in the core of a nuclear reactor requires extremely high computing resources, including computing time and memory. When computing resources are limited, the scope of the computational domain must be reasonably reduced while ensuring the computational accuracy. One method is to optimize the grid division strategy and perform encrypted grid division on the key focus area in the computational domain to improve the computational accuracy of the area; use coarser grids for secondary areas to reduce the amount of calculation without affecting the overall accuracy, thereby balancing the computational accuracy and computational cost. Parallel computing technology can also be used to distribute computing tasks to multiple processors or computing nodes for simultaneous calculations, making full use of multi-core processors or cluster computing resources to alleviate the pressure on computing resources to a certain extent. This can not only expand the scope of the computational domain under limited resources, but also improve the computational accuracy while keeping the computational domain unchanged, providing a guarantee for accurate simulation of the core flow field.

[0120] In an optional embodiment technical solution, the acquisition of the data set in the core rod bundle channel in the area to be analyzed may include: equipping a sensor array consisting of a high-precision flow sensor, a velocity sensor, a pressure sensor and a temperature sensor to collect data at axial intervals of 1-5 mm and 3-8 key positions in each radial layer of the rod bundle channel, the sampling frequency is adaptively set at the order of 10-20 Hz according to the transient change characteristics of the flow field to ensure the capture of high-frequency fluctuations, the collected raw data is identified and removed of abnormal points according to statistical methods, and smoothed by a filtering algorithm, the processed data is fused and corrected by data assimilation technology and numerical simulation data, and finally the data set in the core rod bundle channel in the area to be analyzed is obtained.

[0121] In the technical solution of this embodiment, in order to comprehensively and accurately collect the flow field data in the core bundle channel, a sensor array consisting of a high-precision flow sensor, a velocity sensor, a pressure sensor and a temperature sensor is used, wherein the flow sensor is used to measure the flow rate of the coolant, the pressure sensor is responsible for monitoring the pressure change, and the temperature sensor captures the temperature information. They are arranged at key positions of the bundle channel, and the interval in the axial direction is set to 1-5mm. This small interval can carefully capture the changes in the flow field in the axial direction, because in the core, even within a small axial distance, the flow characteristics of the coolant may change significantly. In each radial layer, 3-8 sensors are arranged. This number setting can not only fully cover the radial flow field information, but also take into account the cost and feasibility of data processing. Through such an arrangement, the sensor array can collect data from multiple dimensions and provide rich information for subsequent analysis.

[0122] The transient change characteristics of the flow field are the key basis for determining the sampling frequency. Since the flow of the core coolant is in a highly turbulent state with a high Reynolds number, there may be high-frequency fluctuations. To ensure that these high-frequency fluctuations are captured, the sampling frequency needs to be adaptively set at the 10-20Hz level. When the flow field changes more drastically and the high-frequency fluctuations are obvious, the sampling frequency will automatically approach 20Hz to ensure that the instantaneous changes in the flow field can be recorded quickly and accurately. On the contrary, if the flow field is relatively stable, the sampling frequency may be reduced to about 10Hz. While ensuring the acquisition of key information, it reduces unnecessary data collection and reduces the pressure of data processing. This adaptive setting of the sampling frequency can not only effectively capture the dynamic changes of the flow field, but also improve the efficiency of data collection.

[0123] Considering that the collected raw data may contain outliers and noise, preprocessing is required. Statistical methods can be used to identify and remove outliers. By setting a reasonable threshold and comparing the relationship between each data point and the overall data distribution, data points that deviate from the normal range are considered outliers and removed, thereby ensuring the accuracy of the data. The data is smoothed using a filtering algorithm. Commonly used filtering algorithms such as mean filtering and median filtering can effectively remove noise from the data, make the data curve smoother, and reduce the impact of data fluctuations on subsequent analysis. In this way, the preprocessed data is more reliable and provides a good data foundation for subsequent data fusion and model training. The preprocessed data also needs to be fused and corrected with the numerical simulation data. Numerical simulation can provide more comprehensive flow field information, but there may be certain errors due to model assumptions and other reasons. Although the experimental data is real, there may be problems such as measurement errors and data sparsity. Data assimilation technology integrates the two. It establishes a connection between data and model, uses mathematical methods to optimize the combination of the two, takes some physical quantities measured in the experiment as constraints, and adjusts the numerical simulation results. At the same time, with the help of numerical simulation information, the experimental data is supplemented and corrected. After fusion and correction, the quality and representativeness of the data are significantly improved, which can more accurately reflect the actual flow field conditions in the core rod bundle channel, and can provide high-quality data sets for solving the high Reynolds number flow field in the nuclear reactor core.

[0124] In an optional embodiment technical solution, in step S32, during the process of training the neural network until convergence, the solution points can be adaptively adjusted according to the flow field gradient, by adjusting the density of the points to accurately analyze local details or capture macro trends, and optimizing the solution points based on solution stability and solution accuracy.

[0125] In the solution of the high Reynolds number flow field in the core of a nuclear reactor, the reasonable setting of the matching points is important for the accuracy and stability of the solution results. In the technical solution of the embodiment of the present application, the strategy of adaptively adjusting the matching points according to the flow field gradient can significantly improve the calculation efficiency and accuracy. The following will be elaborated in detail from its principle, implementation method and optimization effect on the stability and accuracy of the solution. From the perspective of the principle of adaptive adjustment, the flow field gradient reflects the degree of spatial variation of physical quantities (such as velocity, pressure, temperature, etc.) in the flow field. In the high Reynolds number flow field of the nuclear reactor core, the flow field characteristics are complex and changeable. In some areas, such as near the fuel rods or at the corners of the flow channel, the flow field gradient is large and the physical quantities change rapidly; while in other areas, the flow field is relatively stable and the gradient is small. The matching points are adaptively adjusted according to the flow field gradient, that is, in the area with large flow field gradient, the number of matching points is increased to make the matching points more densely distributed; in the area with small flow field gradient, the number of matching points is appropriately reduced, and the matching points are relatively sparsely distributed. This ensures that in areas where the physical quantity changes dramatically, there are enough points to accurately capture the details of its changes, while in areas where the changes are gentle, it avoids wasting computing resources due to too many points. In order to achieve adaptive adjustment of the solution points according to the flow field gradient, numerical calculation methods and algorithms are usually required. In the calculation process, the gradient of each position in the flow field is first calculated using the existing flow field data or preliminary calculation results. For example, the physical equations are discretized using numerical methods such as the difference method, the finite element method, or the finite volume method to obtain the rate of change of the flow field physical quantity in space, thereby determining the flow field gradient. According to the calculated flow field gradient size, a point adjustment strategy is formulated. When the flow field gradient in a certain area exceeds the set threshold, the points are encrypted in the area; if the gradient is lower than the threshold, the points are appropriately reduced. This process usually needs to be iterative. As the calculation progresses, the flow field information and point distribution are continuously updated to adapt to the dynamic changes of the flow field.

[0126] In order to improve the accuracy of the solution, in the local area with large flow field gradient, the encrypted point distribution can more accurately describe the change of physical quantity. Near the surface of the fuel rod, the velocity and temperature of the fluid may change drastically. By adding points in these areas, the flow characteristics and heat transfer process in the boundary layer can be accurately captured, avoiding information loss and calculation errors caused by insufficient points, thereby significantly improving the accuracy of the flow field solution. For the entire flow field, a reasonable distribution of points can more comprehensively and accurately reflect the macroscopic trend of the flow field. In the mainstream area of ​​the flow channel, although the flow field gradient is relatively small, the macroscopic characteristics of the overall flow direction, velocity distribution, etc. of the flow field can be accurately described through the appropriately distributed points, so that the solution results are more in line with the actual physical situation. From the perspective of enhancing the stability of the solution, a reasonable distribution of points helps to improve the stability of the calculation process. If there are too few points in the area with large flow field gradient, numerical oscillation may occur in the calculation process, resulting in unstable results. By adaptively adjusting the points, ensuring that there are enough calculation points in these key areas to balance the errors and fluctuations in the numerical calculation, the occurrence of numerical oscillation can be effectively reduced, making the calculation process more stable, and thus obtaining reliable solution results. During long-term calculations, as the flow field changes dynamically, adaptive adjustment of the points can adapt to the changes in the flow field in real time, maintain the stability of the calculation, and avoid calculation interruptions or erroneous results caused by unreasonable point allocation.

[0127] In an optional embodiment technical solution, the hidden layer of the neural network model can adopt a multi-layer perceptron; Tanh is selected as the activation function to prevent the gradient disappearance phenomenon, and the number of neurons and the connection method are adaptively configured according to the complexity of the problem; the network depth is optimized and determined in the range of 20-100 layers according to the nonlinearity of the physical quantities of the flow field.

[0128] In the technical solution of this application, in the process of solving the high Reynolds number flow field of the nuclear reactor core using physical information neural network (PINNs), a PINNs model consisting of 40 layers of fully connected neural networks is constructed and trained. The model architecture and training process are described below. First, the PINNs model architecture is explained. The PINNs model consists of 40 layers of fully connected neural networks, each layer contains 100 neurons. In the technical solution of this application, the deeper network structure helps to improve the accuracy of solving complex physical problems, and even under sparse data conditions, the network can still rely on the constraints of physical equations to maintain high accuracy outside the data points, showing good generalization ability, and many hidden layers can perform deep feature extraction on the input data and mine the complex patterns and intrinsic relationships in the data. Each layer of 100 neurons can process information in parallel and capture the characteristics of physical problems at different levels of abstraction. When dealing with the flow field problem of the nuclear reactor core, it is possible to gradually extract features related to key physical quantities of the flow field from input information such as geometric structure parameters, boundary conditions and initial conditions, laying the foundation for accurate prediction of velocity field, pressure field and temperature field. The model can use Tanh as the main activation function. The Tanh function can map the input value to the interval of -1 to 1. Compared with the Sigmoid function, its output is centered on 0, which helps to alleviate the gradient disappearance problem. In the training process of the neural network, the activation function determines the output state of the neuron. The nonlinear characteristics of the Tanh function enable the neural network to learn the complex nonlinear relationship between input and output, which is suitable for modeling complex physical systems such as high Reynolds number flow fields in nuclear reactor cores. Because there are highly nonlinear interactions between physical quantities in the flow field, the Tanh function allows the model to better capture these relationships and improve the expressive power of the model. To ensure effective training of the network, the initial learning rate can be set to 0.0001. The learning rate determines the step size each time the parameters are updated. The appropriate initial learning rate enables the model to iterate stably towards the optimal solution in the early stage of training. In the technical solution of this application, the Adam optimizer is used in the training process. It combines the advantages of Adagrad and Adadelta and can adaptively adjust the learning rate of each parameter. The Adam optimizer dynamically adjusts the learning rate based on the first-order moment estimate and the second-order moment estimate of the gradient. It can accelerate convergence during training and adopt different learning rate adjustment strategies for different parameters. It is suitable for processing large-scale data and complex neural network training, which helps to improve training efficiency and reduce training time. At the same time, the cosine annealing restart learning rate algorithm can be used in the first 5000 steps of training. This algorithm helps the model jump out of the local optimum by periodically reducing the learning rate and restarting. The initial cycle length can be set to 50 steps, and the cycle length is multiplied by 2 after each restart.In the early stage of training, a relatively large learning rate allows the model to quickly explore the approximate optimal solution direction in the parameter space. As the training progresses, the learning rate gradually decreases according to the law of the cosine function, allowing the model to make more detailed parameter adjustments when approaching the optimal solution. When the cycle length is reached, the learning rate is restarted, and the model re-explores the parameter space with a larger learning rate to avoid falling into the local optimum. This strategy helps the model balance the relationship between exploration and utilization at different stages, enhances convergence ability, and improves the generalization performance of the model, so that it can better adapt to the complex characteristics of the nuclear reactor core flow field. After 5000 steps of training, the model can switch to the ReduceLROnPlateau algorithm, which dynamically adjusts the learning rate according to the change in loss. In the verification loss minimum mode, the learning rate attenuation factor can be set to 0.6, and the patience value is 20 steps. When the verification loss does not show a significant decrease within 20 consecutive steps, the algorithm believes that the model may be trapped in a local optimum or the convergence speed is too slow. At this time, the learning rate is reduced by a decay factor of 0.6. This dynamic adjustment mechanism can fine-tune the learning rate according to the training situation of the model in the later stage of model training, so that the model can converge more smoothly when it is close to the optimal solution, avoiding oscillation near the optimal solution due to excessive learning rate, or slow convergence due to too small learning rate, thereby further improving the accuracy of the model and enabling the model to more accurately predict the physical quantity distribution of the high Reynolds number flow field in the nuclear reactor core. This optimization strategy combines the advantages of cosine annealing restart and ReduceLROnPlateau algorithm, which can not only speed up the convergence speed in the early stage of training, but also perform fine tuning in the later stage, thereby significantly improving the training effect and final solution accuracy of the PINNs model.

[0129] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A PINNs high Reynolds number flow field solution method based on adjustment factor optimization, characterized in that: The method comprises: S1. Construct a physical model of the area to be analyzed in the core of the target nuclear reactor, including: S11, based on the geometric structure and coolant flow characteristics of the core rod bundle channel of the target nuclear reactor, determining the size and relative position of each component of the core rod bundle channel, and constructing a geometric model of the rod bundle channel in the area to be analyzed; S12. For the region to be analyzed, a fluid mechanics physical model including a continuity equation, a momentum conservation equation, and an energy conservation equation is established; The continuity equation is used to describe the conservation of fluid mass, which is specifically expressed as: The momentum conservation equation is used to describe the momentum change and viscosity effect of the fluid, which is specifically expressed as: In the core bundle channel, the first term on the left side of the momentum conservation equation is represents the rate of change of momentum with time, and the second term represents the convection term. The right side of the momentum conservation equation The term represents the pressure gradient term, The term represents the viscous diffusion term, and f represents the external force term; The energy equation is used to describe heat transfer and is expressed as: in, represents the gradient symbol, u represents the fluid velocity vector, p represents the pressure, ρ represents the fluid density, ν represents the kinematic viscosity coefficient, f represents the volume force, T represents the temperature, and c represents the fluid velocity vector. p represents the specific heat capacity at constant pressure, the symbol k represents the thermal conductivity, and the symbol Q represents the volume heat source term; The term represents the rate of change of temperature with time, represents the convection term, The term represents the heat conduction term; S2. Through experimental measurement and numerical simulation, the experimental data are pre-processed and integrated with the simulation data, so as to obtain a data set in the core rod bundle channel in the area to be analyzed; S3. Training the physical information neural network, specifically including: S31. Design a neural network model including an input layer, multiple hidden layers and an output layer, wherein the input of the neural network model is a parameterized description of a geometric structure, boundary conditions and parameters related to initial conditions, and the output of the neural network model is key physical quantities and adjustment factors of the flow field; S32, constructing a comprehensive loss function including internal data point loss, boundary data point loss and equation loss, using data, boundary conditions and adaptively corrected physical equations to train the neural network until convergence, and adjusting model parameters of the neural network model according to the training results; The comprehensive loss function consists of internal data point loss, boundary data point loss and equation loss, as follows: The internal data point loss is used to calculate the difference between the predicted value of the physical quantity output by the neural network and the true value obtained by actual measurement or numerical simulation for each data point inside the core bundle channel; for the velocity field, the mean square error MSE is used to calculate the internal data point loss Among them, the symbol N represents the total number of internal data points, and the symbol u i Represents the actual speed value of the i-th internal data point, symbol represents the velocity value of the i-th internal data point predicted by the neural network; For the pressure field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol p i Represents the actual pressure value of the i-th internal data point, symbol represents the pressure value of the i-th internal data point predicted by the neural network; For the temperature field, the mean square error (MSE) is used to calculate the internal data point loss. Among them, the symbol T i Represents the actual temperature value of the i-th internal data point, symbol represents the temperature value of the i-th internal data point predicted by the neural network; The total internal data point loss L data is the weighted sum of the internal data point losses of velocity, pressure and temperature fields, i.e., L data =ω u L data-u +ω p L data-p +ω T L data-T , where the symbol ω u ,ω p and ω T are the weight coefficients of the internal data point loss of velocity, pressure and temperature fields, ω u +ω p +ω T =1; Boundary data point loss: For the boundary area of ​​the core bundle channel, including the data points at the inlet, outlet and bundle surface boundary, the difference between the boundary physical quantity values ​​predicted by the calculation model and the known boundary conditions is calculated; For the inlet boundary velocity field, calculate the boundary data point loss Among them, the symbol M in is the number of entry boundary data points, symbol u in,j Represents the actual velocity value of the jth entry boundary data point, symbol represents the velocity value of the jth entry boundary data point predicted by the neural network; For the outlet boundary pressure field, calculate the boundary data point loss Among them, the symbol M out Indicates the number of export boundary data points, symbol p out,k represents the actual pressure value of the kth outlet boundary data point, symbol represents the pressure value of the kth outlet boundary data point predicted by the neural network; For the temperature field on the rod bundle surface boundary, calculate the loss of boundary data points Among them, the symbol M wall Indicates the number of data points on the rod bundle surface boundary, symbol T wall,l It represents the actual temperature value of the lth rod bundle surface boundary data point, symbol It represents the temperature value of the lth rod bundle surface boundary data point predicted by the neural network; The total boundary data point loss L boundary It is the weighted sum of the boundary data point losses of different physical quantities at the inlet, outlet and bundle surface boundaries; The equation loss includes the equation loss L of the continuity equation eq-c , the equation loss L of the momentum conservation equation eq-m and the energy conservation equation loss L eq-e ; Among them, the equation loss of the continuity equation is Equation loss for the momentum conservation equation Equation loss for the energy conservation equation The total equation loss L eq =ω c L eq-m +ω2L eq-m +ω e L eq-e , where the symbol S(x) represents the adjustment factor, and the symbol ω c ,ω m and ω e They represent the weight coefficients of the equation loss of the continuity equation, the equation loss of the momentum conservation equation, and the equation loss of the energy conservation equation, respectively, and ω c +ω m +ω e =1; Comprehensive loss function L total It is expressed as: L total =ω data L data +oh boundary L boundary +oh eq L eq Among them, ω data ,ω boundary and ω eq are the weight coefficients of internal data point loss, boundary data point loss and equation loss respectively, and ω data +ω boundary +ω eq =1; The neural network is trained using a training data set. During the training process, the parameters of the neural network are adjusted through an optimization algorithm according to the comprehensive loss function, so that the value of the comprehensive loss function gradually decreases until a preset convergence condition is met, thereby obtaining a trained neural network; The trained neural network is used to solve the high Reynolds number flow field in the core of a nuclear reactor and output the corresponding predicted values ​​of the velocity field, pressure field and temperature field.

2. The PINNs high Reynolds number flow field solution method based on adjustment factor optimization according to claim 1 is characterized in that: The determination of the geometric structure of the target nuclear reactor core rod bundle channel specifically includes: A three-dimensional geometric model is accurately constructed based on the actual structural mapping or design documents of the nuclear reactor core, and laser scanning and industrial CT imaging technology are used to obtain high-precision point cloud data or tomographic image data of the core internal structure. The geometric structure of the rod bundle channel of the target nuclear reactor core is reconstructed through reverse engineering software; the scope of the area to be analyzed is defined according to the focus area of ​​the problem to be solved and the limitation of computing resources.

3. The PINNs high Reynolds number flow field solution method based on adjustment factor optimization according to claim 1 is characterized in that: The step of acquiring the data set in the core rod bundle channel in the area to be analyzed comprises: A sensor array consisting of high-precision flow sensors, velocity sensors, pressure sensors and temperature sensors is equipped to collect data at 1-5mm intervals in the axial direction and 3-8 key positions in each radial layer of the rod bundle channel. The sampling frequency is adaptively set at 10-20Hz according to the transient change characteristics of the flow field to ensure the capture of high-frequency fluctuations. The collected raw data is identified and removed of abnormal points by statistical methods, and smoothed by a filtering algorithm. The processed data is fused and corrected by data assimilation technology and numerical simulation data, and finally the data set in the core rod bundle channel in the area to be analyzed is obtained.

4. The PINNs high Reynolds number flow field solution method based on adjustment factor optimization according to claim 1 is characterized in that: In step S32, during the process of training the neural network until convergence, the solution points are adaptively adjusted according to the flow field gradient, and the density of the solution points is adjusted to accurately analyze local details or capture macro trends, and the solution points are optimized according to the solution stability and solution accuracy.

5. The PINNs high Reynolds number flow field solution method based on adjustment factor optimization according to claim 1 is characterized in that: The hidden layer of the neural network model adopts a multi-layer perceptron; the activation function selects Tanh to prevent the gradient disappearance phenomenon, and the number of neurons and the connection method are adaptively configured according to the complexity of the problem; the network depth is optimized and determined in the range of 20-100 layers according to the nonlinearity of the physical quantity of the flow field.

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