Thermal hydraulic flow field prediction method based on evidence physical information neural network

Abstract

The invention discloses a thermal hydraulic flow field prediction method based on an evidence physical information neural network, and the method comprises the specific steps: collecting different physical quantity data sets in a thermal hydraulic system, and carrying out the preprocessing of the data; constructing data loss; constructing physical loss; constructing an evidence uncertainty modeling mechanism, and dynamically allocating evidence weights according to the reliability of different data and physical constraints; constructing a total loss function by integrating the data error, the physical residual error and the evidence reliability; and outputting the trained neural network model and prediction. According to the invention, by introducing an evidence learning mechanism, the uncertainty of the model is dynamically estimated in the network training process, and the adaptability of the model to data with inconsistent noise sensitivity degrees is significantly improved; the uncertainty of the evidence is mapped into a physical quantity weighting coefficient, a uniform normalized weighting loss function is constructed, and the subjectivity and robustness problems caused by manual setting of hyper-parameters for each physical quantity in a traditional physical information neural network are effectively avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of thermal hydraulic flow fields, and in particular relates to a thermal hydraulic flow field prediction method based on an evidence physics information neural network. Background Art

[0002] Thermal hydraulic flow field is an important physical process that describes the coupled changes of heat conduction, convective heat transfer, pressure distribution, and velocity field. It plays a key role in the design and safety assessment of major equipment such as nuclear energy, thermal power, hydropower, ships, spacecraft, and heat exchange equipment. Traditional thermal flow field analysis relies on computational fluid dynamics (CFD) methods based on governing equations. Although such methods have high accuracy, they often require huge computing resources under complex conditions of multiple parameters, multiple boundaries, and coupling, making it difficult to achieve real-time prediction and efficient optimization. With the development of deep learning technology, data-driven neural network models have gradually been introduced into thermal flow field prediction tasks, especially methods such as physical information neural network (PINN). By introducing the governing physical equations into neural network training, the generalization ability and physical consistency of the model have been effectively improved.

[0003] While existing physical information neural networks can integrate physical constraints with data-driven capabilities to a certain extent, they generally assume that all observed physical quantities are of equal quality. This ignores the significant differences in observation accuracy, sampling frequency, and interference intensity among different physical quantities (such as temperature, pressure, and velocity) in actual engineering scenarios. This results in the model being unable to distinguish between noise-dominated information and high-confidence data during training, leading to problems such as misleading learning, unstable convergence, and increased prediction errors. Therefore, effectively identifying the noise levels of different physical quantity constraint data during network training and dynamically assigning them corresponding confidence weights has become a key technical challenge urgently needed to be overcome in the field of thermal flow field modeling. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a thermal-hydraulic flow field prediction method based on an evidence-based physical information neural network, which can automatically perceive the data credibility of different constraints and physical quantities, assign differentiated evidence weights to them, and thus improve the robustness and accuracy of the prediction.

[0005] In order to solve the above technical problems, the present invention is implemented in the following ways:

[0006] A thermal hydraulic flow field prediction method based on evidence physics information neural network, the specific steps are as follows:

[0007] S1. Collect different physical quantity data sets in the thermal hydraulic system and preprocess the data;

[0008] S2, construction data loss;

[0009] S3, structural physical loss;

[0010] S4. Construct an evidence uncertainty modeling mechanism to dynamically assign evidence weights based on the reliability of different data and physical constraints;

[0011] S5. Construct a total loss function by integrating data error, physical residual and evidence credibility;

[0012] S6. The trained neural network model and prediction output.

[0013] Furthermore, the specific method of step S1 is as follows:

[0014] Acquire data sets of different physical quantities, including velocity fields , pressure field , temperature field and spatial coordinates and time ,in and Represent the velocity components of the fluid in the horizontal and vertical directions respectively;

[0015] In order to eliminate the dimensional differences between physical quantities and the influence of different data sources, this application normalizes the collected data. The normalized expression is as follows:

[0016]

[0017] in, Indicates the collected raw data. represents the normalized data, and Represent the minimum and maximum values ​​in the data set respectively. The normalized data compresses each physical quantity into the interval [0,1], which helps to improve the stability and convergence speed of neural network training.

[0018] The preprocessed dataset is divided into a training set, a validation set, and a test set in a ratio of 70%:20%:10%. The preprocessed data is used for data loss calculation in step S2 and physical residual calculation in step S3.

[0019] Furthermore, the specific method of step S2 is as follows:

[0020] During model training, the data loss is calculated to measure the difference between the predicted value of the neural network model and the actual observed value. The expression of data error loss is as follows:

[0021]

[0022] in, represents the number of samples of the jth type of physical quantity, represents the predicted value of the j-th physical quantity of the i-th sample, Represents the observed value of the jth physical quantity of the i-th sample.

[0023] Furthermore, the specific method of step S3 is as follows:

[0024] Physical loss is used to measure the deviation between the physical quantity output by the neural network model and the physical equation. and , the governing equation is the momentum equation, the temperature field The governing equation of is the energy conservation equation, then for the velocity field Physical residual loss The expression is as follows:

[0025]

[0026] in, represents the number of samples used for physical residuals, Represents the speed loss of the i-th sample. Combined with the physical partial differential equation of the control system, the expression of the speed loss is as follows:

[0027]

[0028] in, represents the fluid density, represents the dynamic viscosity of the fluid, and Represent the predicted values ​​of the velocity field in the horizontal and vertical directions, represents the predicted value of the pressure field, and represent the first-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. and represent the second-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. Represents the predicted value The rate of change over time t;

[0029] The pressure field is constrained by the mass conservation of the continuity equation, and the expression of pressure loss is as follows:

[0030]

[0031] The temperature field satisfies the energy conservation equation constraint, and the expression of temperature loss is as follows:

[0032]

[0033] in, represents the specific heat capacity at constant pressure, represents thermal conductivity, and represents the first-order spatial derivative of the temperature field, and represents the second-order spatial derivative of the temperature field, It represents the rate of change of the predicted value of temperature at a certain point with time t.

[0034] Furthermore, the specific method of step S4 is as follows:

[0035] The amount of evidence is used to characterize the degree of trust in different physical quantities in network training, which is used to quantify the uncertainty of physical quantity prediction. For each type of physical quantity j, the amount of evidence is introduced. , and construct the parameters of the evidence distribution according to the amount of evidence , which is expressed as follows:

[0036]

[0037] Set the weight of evidence for each physical quantity in the total loss function , which is expressed as follows:

[0038]

[0039] in, represents the evidence parameter of the j-th type of physical quantity, Represents the sum of all physical quantity evidence parameters.

[0040] Furthermore, the specific method of step S5 is as follows:

[0041] Combining data error, physical residual and evidence uncertainty, the total loss function is constructed, and its specific expression is as follows:

[0042]

[0043] in, Indicates data error loss, represents the physical residual loss, It represents the weight of evidence and the degree of confidence of the physical quantity.

[0044] Furthermore, the specific method of step S6 is as follows:

[0045] The neural network is trained using the Adam optimizer combined with the L-BFGS optimizer. An early stopping strategy is implemented based on the error changes in the validation set. After training, new boundary conditions and physical parameters are input. The model outputs velocity, pressure, and temperature predictions for various physical quantities in the thermal-hydraulic system, and provides corresponding evidence weights and uncertainty estimates, providing a reliable basis for subsequent flow field optimization and sensitivity analysis.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1) Effectively modeling data confidence differences between different physical quantities: By introducing an evidence learning mechanism, the amount of evidence (confidence level) is automatically learned for each type of physical quantity data, and its uncertainty is dynamically estimated during network training, significantly improving the model's adaptability to data with inconsistent noise sensitivity.

[0048] 2) Adaptive weighting to achieve joint modeling of multiple physical fields: By mapping the uncertainty of evidence into weighted coefficients of physical quantities and constructing a unified normalized weighted loss function, we can effectively avoid the subjectivity and robustness problems caused by manually setting hyperparameters for each physical quantity in traditional physical information neural networks.

[0049] 3) Improving flow field prediction accuracy and robustness: When data is insufficient or incomplete and observation conditions are complex, the model can automatically reduce the interference of low-confidence physical quantities on the results, improve overall prediction performance and physical consistency, and effectively alleviate the pathological conditions in inverse problem modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the process prediction process of the present invention. DETAILED DESCRIPTION

[0051] The specific implementation of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples.

[0052] This invention aims to address the modeling errors and generalization deficiencies of existing physical information neural networks, which are unable to identify imbalances in noise levels between different physical quantities when processing multi-source heterogeneous thermal-hydraulic flow field data. To address the reality of uneven data quality under different constraints, this invention automatically assesses the uncertainty of various physical quantity observations during training and assigns dynamic weights based on their credibility. This improves the model's ability to utilize high-confidence physical information, suppresses the impact of noise interference on prediction results, and significantly enhances the stability and accuracy of flow field predictions under complex boundary conditions.

[0053] like Figure 1 As shown in FIG, a thermal hydraulic flow field prediction method based on evidence physics information neural network is shown in FIG. The specific steps are as follows:

[0054] S1. Collect different physical quantity data sets in the thermal hydraulic system and preprocess the data. The specific method is as follows:

[0055] Before model training, data sets of different physical quantities are collected, including velocity field , pressure field , temperature field and spatial coordinates and time ,in and Represent the velocity components of the fluid in the horizontal and vertical directions respectively;

[0056] In order to eliminate the dimensional differences between physical quantities and the influence of different data sources, this application normalizes the collected data. The normalized expression is as follows:

[0057]

[0058] in, Indicates the collected raw data. represents the normalized data, and Represent the minimum and maximum values ​​in the data set respectively. The normalized data compresses each physical quantity into the interval [0,1], which helps to improve the stability and convergence speed of neural network training.

[0059] The preprocessed dataset is split into training, validation, and test sets in a 70%:20%:10% ratio. The preprocessed data is used for data loss calculation in step S2 and physical residual calculation in step S3. The training set is used for model training, the validation set is used to adjust hyperparameters and monitor model overfitting, and the test set is used for final performance evaluation. This dataset partitioning ensures independence and generalization during model training.

[0060] S2. Construct data loss. The data loss term is used to measure the degree of fit between the neural network output and the observed data to form a supervisory signal. The specific method is as follows:

[0061] During model training, the data loss is calculated to measure the difference between the predicted value of the neural network model and the actual observed value. The expression of data error loss is as follows:

[0062]

[0063] in, represents the number of samples of the jth type of physical quantity, represents the predicted value of the j-th physical quantity of the i-th sample, Represents the observed value of the jth physical quantity of the i-th sample.

[0064] S3. Construct physical losses and combine them with the physical partial differential equations that control the system to enhance the physical consistency of the model. The specific methods are as follows:

[0065] For each physical quantity, the model prediction not only needs to fit the data, but also needs to satisfy the relevant physical control equations. The physical loss is used to measure the deviation between the physical quantity output by the neural network model and the physical equation. For the velocity field and , the governing equation is the momentum equation, the temperature field The governing equation of is the energy conservation equation, then for the velocity field Physical residual loss The expression is as follows:

[0066]

[0067] in, represents the number of samples used for physical residuals, Represents the speed loss of the i-th sample. Combined with the physical partial differential equation of the control system, the expression of the speed loss is as follows:

[0068]

[0069] in, represents the fluid density, represents the dynamic viscosity of the fluid, and Represent the predicted values ​​of the velocity field in the horizontal and vertical directions, represents the predicted value of the pressure field, and represent the first-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. and represent the second-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. Represents the predicted value The rate of change over time t;

[0070] The pressure field is constrained by the mass conservation of the continuity equation, and the expression of pressure loss is as follows:

[0071]

[0072] The temperature field satisfies the energy conservation equation constraint, and the expression of temperature loss is as follows:

[0073]

[0074] in, represents the fluid density, represents the specific heat capacity at constant pressure, represents thermal conductivity, and represents the first-order spatial derivative of the temperature field, and represents the second-order spatial derivative of the temperature field, It represents the rate of change of the predicted value of temperature at a certain point with time t.

[0075] S4. Construct an evidence uncertainty modeling mechanism to dynamically assign evidence weights based on the reliability of different data and physical constraints. The specific method is as follows:

[0076] In order to consider the uncertainty of data, this paper introduces evidence theory, which uses evidence quantity to characterize the degree of trust of different physical quantities in network training, and is used to quantify the uncertainty of physical quantity prediction; for each type of physical quantity j, the evidence quantity is introduced , and construct the parameters of the evidence distribution according to the amount of evidence , which is expressed as follows:

[0077]

[0078] Set the weight of evidence for each physical quantity in the total loss function , which is expressed as follows:

[0079]

[0080] in, represents the evidence parameter of the j-th type of physical quantity, Represents the sum of all physical quantity evidence parameters.

[0081] S5. Construct a total loss function by integrating data error, physical residual and evidence credibility. The specific method is as follows:

[0082] Combining data error, physical residual and evidence uncertainty, a total loss function is constructed to balance data fitting, physical consistency and uncertainty penalty. Its specific expression is as follows:

[0083]

[0084] in, Indicates data error loss, represents the physical residual loss, The weight of evidence represents the confidence level of the physical quantity. The final loss function takes into account the prediction accuracy of each physical quantity (measured by data error), the degree of conformity to the physical equation (measured by physical residuals), and the uncertainty of the physical quantity (quantified by evidence uncertainty). Through this mechanism, the model can dynamically adjust the weights of various physical constraints based on data uncertainty during training, effectively preventing misleading models from low-quality data and improving the stability and accuracy of overall predictions.

[0085] S6. The trained neural network model and prediction output are as follows:

[0086] The neural network is trained using the Adam optimizer combined with the L-BFGS optimizer. An early stopping strategy is implemented based on the error changes in the validation set. After training, new boundary conditions and physical parameters are input. The model outputs velocity, pressure, and temperature predictions for various physical quantities in the thermal-hydraulic system, and provides corresponding evidence weights and uncertainty estimates, providing a reliable basis for subsequent flow field optimization and sensitivity analysis.

[0087] The above description is merely an embodiment of the present invention. It is stated again that, for a person skilled in the art, several improvements can be made to the present invention without departing from the principles of the present invention, and these improvements are also included in the scope of protection of the claims of the present invention.

Claims

1. A thermal hydraulic flow field prediction method based on an evidence physics information neural network, characterized by: The specific steps are as follows: S1. Collect different physical quantity data sets in the thermal hydraulic system and preprocess the data; S2, construction data loss; S3, structural physical loss; S4. Construct an evidence uncertainty modeling mechanism to dynamically assign evidence weights based on the reliability of different data and physical constraints; S5. Construct a total loss function by integrating data error, physical residual and evidence credibility; S6. The trained neural network model and prediction output.

2. The method for predicting thermal hydraulic flow fields based on an evidence-based physics information neural network according to claim 1, characterized in that: The specific method of step S1 is as follows: Acquire data sets of different physical quantities, including velocity fields , pressure field , temperature field and spatial coordinates and time ,in and Represent the velocity components of the fluid in the horizontal and vertical directions respectively; The collected data is normalized, and the normalized expression is as follows: in, Indicates the collected raw data. represents the normalized data, and Represent the minimum and maximum values ​​in the data set respectively. The normalized data compresses each physical quantity into the interval [0,1], which helps to improve the stability and convergence speed of neural network training. The preprocessed dataset is divided into a training set, a validation set, and a test set in a ratio of 70%:20%:10%. The preprocessed data is used for data loss calculation in step S2 and physical residual calculation in step S3.

3. The method for predicting thermal hydraulic flow fields based on an evidence-based physics information neural network according to claim 1, characterized in that: The specific method of step S2 is as follows: During model training, the data loss is calculated to measure the difference between the predicted value of the neural network model and the actual observed value. The expression of data error loss is as follows: in, represents the number of samples of the jth type of physical quantity, represents the predicted value of the j-th physical quantity of the i-th sample, Represents the observed value of the jth physical quantity of the i-th sample.

4. The method for predicting thermal hydraulic flow fields based on an evidence-based physics information neural network according to claim 1, characterized in that: The specific method of step S3 is as follows: Physical loss is used to measure the deviation between the physical quantity output by the neural network model and the physical equation. and , the governing equation is the momentum equation, the temperature field The governing equation of is the energy conservation equation, then for the velocity field Physical residual loss The expression is as follows: in, represents the number of samples used for physical residuals, Represents the speed loss of the i-th sample. Combined with the physical partial differential equation of the control system, the expression of the speed loss is as follows: in, represents the fluid density, represents the dynamic viscosity of the fluid, and Represent the predicted values ​​of the velocity field in the horizontal and vertical directions, represents the predicted value of the pressure field, and represent the first-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. and represent the second-order spatial derivatives of the velocity field in the horizontal and vertical directions, respectively. Represents the predicted value The rate of change over time t; The pressure field is constrained by the mass conservation of the continuity equation, and the expression of pressure loss is as follows: The temperature field satisfies the energy conservation equation constraint, and the expression of temperature loss is as follows: in, represents the specific heat capacity at constant pressure, represents thermal conductivity, and represents the first-order spatial derivative of the temperature field, and represents the second-order spatial derivative of the temperature field, It represents the rate of change of the predicted value of temperature at a certain point with time t.

5. The method for predicting thermal hydraulic flow field based on evidence physics information neural network according to claim 1, characterized in that: The specific method of step S4 is as follows: The amount of evidence is used to characterize the degree of trust in different physical quantities in network training, which is used to quantify the uncertainty of physical quantity prediction. For each type of physical quantity j, the amount of evidence is introduced. , and construct the parameters of the evidence distribution according to the amount of evidence , which is expressed as follows: Set the weight of evidence for each physical quantity in the total loss function , which is expressed as follows: in, represents the evidence parameter of the j-th type of physical quantity, Represents the sum of all physical quantity evidence parameters.

6. The method for predicting thermal hydraulic flow fields based on an evidence physics information neural network according to claim 1, characterized in that: The specific method of step S5 is as follows: Combining data error, physical residual and evidence uncertainty, the total loss function is constructed, and its specific expression is as follows: in, Indicates data error loss, represents the physical residual loss, Indicates the weight of evidence.

7. The method for predicting thermal hydraulic flow fields based on an evidence physics information neural network according to claim 1, characterized in that: The specific method of step S6 is as follows: The neural network is trained using the Adam optimizer combined with the L-BFGS optimizer. An early stopping strategy is implemented based on the error changes in the validation set. After training, new boundary conditions and physical parameters are input. The model outputs velocity, pressure, and temperature predictions for various physical quantities in the thermal-hydraulic system, and provides corresponding evidence weights and uncertainty estimates, providing a reliable basis for subsequent flow field optimization and sensitivity analysis.

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