Optimization method for fission product yield data based on gradient descent method

Abstract

The method for optimizing fission product yield data based on gradient descent method is mainly developed for multi-Gaussian model of yield. The yield data are optimized by optimizing the parameters of the model. Firstly, the yield is calculated based on the multi-Gaussian model and its original model parameters, and compared with the corresponding experimental data to construct a loss function. Then, the partial derivative of the loss function with respect to each model parameter is calculated to construct the gradient vector of the loss function, and the model parameters are updated by the gradient descent method. Based on the updated model parameters, the yield is calculated again by the multi-Gaussian model, and the loss function and its gradient vector are updated. Then, the model parameters are updated again by the gradient descent method. The above updating process is repeated until the loss function converges, and the corresponding model parameter value is the optimal value. The optimal value of the model parameters is input into the multi-Gaussian model for calculation, and the optimized fission product yield data can be obtained.

Description

Technical Field

[0001] This invention relates to the technical field of nuclear reactor physics calculations and nuclear data evaluation, specifically to a method for optimizing fission product quality and yield data based on gradient descent. Background Technology

[0002] Nuclear reactor core physics design relies on high-precision numerical simulations. Burnup calculation is a crucial component of nuclear reactor physics design and calculation, simulating the changes in various nuclide compositions within the fuel during reactor operation. This plays a vital guiding role in the safety and economics of reactor operation. Fission yield is a critical nuclear data point related to burnup calculation, representing the proportion of fission product nuclides produced through the fission reaction of the fuel. Simulating the changes in the stock of fission product nuclides within the fuel is essential in numerical calculations. The stock of fission product nuclides, in turn, plays a significant role in determining macroscopic parameters such as the effective multiplication factor, power distribution, burnup depth, decay heat, and photon source term after reactor shutdown during operation. Therefore, the accuracy of fission yield data directly impacts the accuracy of core physics design and calculation.

[0003] Currently, fission yield data used in nuclear reactor physics design and calculations are primarily obtained through a comprehensive evaluation of experimental measurement data and theoretical model calculation data. In recent years, with the development of experimental techniques, the accuracy of experimental fission yield data has significantly improved. Therefore, theoretical model calculations have become the main factor affecting the evaluation effect and accuracy of fission yield data. The mass yield of fission products is the distribution of fission yield with respect to the mass number of fission products; it is the sum of the yields of fission products with the same mass number. Mass yield is the foundation for accurate theoretical model calculations of fission yield. Mass yield is calculated using a multi-Gaussian model. The original model parameters were fitted using the least squares method. This fitting process is significantly influenced by human experience, and the experimental data used for fitting also has considerable uncertainty due to the early measurement years. The imperfections in the mass yield model limit the accuracy of theoretical fission yield calculations, which in turn affects the overall evaluation of fission yield. Consequently, in subsequent core physics design and calculations, fission yield data introduces non-negligible errors into the macroscopic parameters mentioned above, significantly impacting the accuracy of reactor core physics design, nuclear waste transportation, and disposal.

[0004] In summary, it is necessary to optimize the mass yield of fission products to improve the overall accuracy of fission yield data. To achieve this goal, we consider optimizing the parameters of the multi-Gaussian model for mass yield based on recent high-precision experimental data and numerical methods, thereby fundamentally optimizing the mass yield data. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a method for optimizing fission product quality and yield data based on gradient descent. This method optimizes the parameters of a multi-Gaussian model for quality and yield. By optimizing the model parameters, the accuracy of quality and yield data can be fundamentally improved, and the effectiveness of fission yield data evaluation can be substantially enhanced.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The method for optimizing fission product quality and yield data based on gradient descent includes the following steps:

[0008] Step 1: Based on the multi-Gaussian model of mass yield and its original model parameters, calculate the mass yield data of different fission product nuclides using the multi-Gaussian model expression shown in formula (1):

[0009]

[0010] In the formula:

[0011] MY(A) — Mass yield of fission product nuclides with mass number A;

[0012] N i —The intensity of the i-th Gaussian function in the multi-Gaussian model is a parameter of the first type of model;

[0013] —The average mass number of different fission products;

[0014] D i —In a multi-Gaussian model, the center position of the i-th Gaussian function is relative to the average mass. The offset is the parameter of the second type of model;

[0015] σ i —The standard deviation of the i-th Gaussian function in the multi-Gaussian model is a parameter of the third type of model;

[0016] Step 2: Compare the quality output calculation data obtained in Step 1 with the corresponding experimental data, and construct the loss function shown in formula (2):

[0017]

[0018] In the formula:

[0019] Loss—the value of the loss function;

[0020] N A —The number of mass spots of the fission product nuclides considered;

[0021] A L—Lower limit of the mass number of fission products considered;

[0022] A H —Upper limit of the mass number of fission products considered;

[0023] MY E (A) — Experimental data on the mass yield of fission product nuclides with mass number A;

[0024] Step 3: Based on the loss function constructed in Step 2, calculate its partial derivatives with respect to the various model parameters given in Step 1, construct the gradient vector of the loss function, and update the model parameters using the gradient descent method shown in formula (3):

[0025]

[0026] In the formula:

[0027] p (1) —The vector formed by the parameters of the three types of models after the update;

[0028] p (0) —Update the vector formed by the parameters of the first three types of models;

[0029] lr — learning rate, representing the magnitude of each parameter update;

[0030] —The gradient vector of the loss function;

[0031] Step 4: Re-input the model parameters obtained in Step 3 into the multi-Gaussian model, and then repeat the process of Steps 1 to 3 to update the model parameters repeatedly; observe the trend of the loss function. When the loss function converges and no longer changes significantly, end the update process. The model parameter values ​​at this time are the optimal values.

[0032] Step 5: Input the optimal values ​​of the model parameters into the Gaussian model, and the calculated result is the optimized mass yield data of the fission product nuclides.

[0033] Preferably, the convergence condition of the loss function is: after two consecutive updates of the model parameters, the relative change in the loss function value is less than 1.0 × 10⁻⁶. -8 .

[0034] Compared with existing technologies, it has the following advantages:

[0035] 1. Mass yield is a key quantity in the calculation of fission yield in related theoretical models, and it has a significant impact on the accuracy of fission yield data in nuclear reactor physics calculations. The method of this invention optimizes the parameters of the multi-Gaussian model for mass yield. By optimizing the model parameters, the accuracy of mass yield data can be fundamentally improved, and the effectiveness of fission yield data evaluation can be substantially enhanced.

[0036] 2. The method of this invention optimizes the parameters of a multi-Gaussian model for quality yield based on gradient descent. Gradient descent is simple in concept, easy to implement, and has low requirements for experimental data. It can incorporate the physical laws contained in the experimental data into the model parameters through repeated updates. Attached Figure Description

[0037] Figure 1 This is a flowchart of the method of the present invention.

[0038] Figure 2 Based on the optimized method of this invention 235 Mass yield distribution of U thermal neutron-induced fission.

[0039] Figure 3 Based on the optimized method of this invention 238 Mass yield distribution of U-fast neutron-induced fission. Detailed Implementation

[0040] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0041] This invention relates to a method for optimizing fission product quality yield data based on gradient descent. It constructs a loss function by introducing experimental quality yield data and comparing it with theoretical model calculations. The gradient vector of the loss function is then constructed by calculating the partial derivatives of the loss function with respect to the parameters of the multi-Gaussian model of quality yield. The model parameters are updated using gradient descent, and the quality yield is recalculated based on the updated model parameters, thus achieving the goal of optimizing the quality yield data. The specific steps are as follows:

[0042] Step 1: Based on the multi-Gaussian model of mass yield and its original model parameters, calculate the mass yield data of different fission product nuclides using the multi-Gaussian model expression shown in formula (1):

[0043]

[0044] In the formula:

[0045] MY(A) — Mass yield of fission product nuclides with mass number A;

[0046] N i —The intensity of the i-th Gaussian function in the multi-Gaussian model is a parameter of the first type of model;

[0047] —The average mass number of different fission products;

[0048] D i —In a multi-Gaussian model, the center position of the i-th Gaussian function is relative to the average mass. The offset is the parameter of the second type of model;

[0049] σ i —The standard deviation of the i-th Gaussian function in the multi-Gaussian model is a parameter of the third type of model;

[0050] Step 2: Compare the quality output calculation data obtained in Step 1 with the corresponding experimental data, and construct the loss function shown in formula (2):

[0051]

[0052] In the formula:

[0053] Loss—the value of the loss function;

[0054] N A —The number of mass spots of the fission product nuclides considered;

[0055] A L —Lower limit of the mass number of fission products considered;

[0056] A H —Upper limit of the mass number of fission products considered;

[0057] MY E (A) — Experimental data on the mass yield of fission product nuclides with mass number A;

[0058] Step 3: Based on the loss function constructed in Step 2, calculate its partial derivatives with respect to the various model parameters given in Step 1, construct the gradient vector of the loss function, and update the model parameters using the gradient descent method shown in formula (3):

[0059]

[0060] In the formula:

[0061] p (1) —The vector formed by the parameters of the three types of models after the update;

[0062] p (0) —Update the vector formed by the parameters of the first three types of models;

[0063] lr — learning rate, representing the magnitude of each parameter update;

[0064] —The gradient vector of the loss function;

[0065] Step 4: Re-input the model parameters obtained in Step 3 into the multi-Gaussian model, and then repeat the process of Steps 1 to 3 to update the model parameters repeatedly; observe the trend of the loss function. When the loss function converges and no longer changes significantly, end the update process. The model parameter values ​​at this time are the optimal values.

[0066] Step 5: Input the optimal values ​​of the model parameters into the Gaussian model, and the calculated result is the optimized mass yield data of the fission product nuclides.

[0067] In this invention, the average mass number of different fission products in formula (1) of step 1 is... The calculations used empirical formulas employed in the fission yield calculation program CYFP developed by Los Alamos National Laboratory in the United States.

[0068] This invention does not restrict the experimental data on mass yield in step 2, and the data can be obtained from publicly available experimental databases, such as the EXFOR database developed by the International Atomic Energy Agency.

[0069] This invention does not impose upper or lower limits on the mass number of fission products in step 2; these limits can be determined based on the upper and lower limits of the mass number in experimental data.

[0070] The present invention does not impose a specific limit on the learning rate in step 3, which can be determined based on different experimental data and fission nuclides.

[0071] In this invention, the convergence condition of the loss function in step 4 is: after two consecutive updates of the model parameters, the relative change in the loss function value is less than 1.0 × 10⁻⁶. -8 .

[0072] To verify the effectiveness of the present invention, Figure 2 This demonstrates the improvements made before and after optimization based on the present invention. 235 Mass yield distribution of U thermal neutron-induced fission Figure 3 This demonstrates the improvements made before and after optimization based on the present invention. 238 The mass yield distribution of U-fast neutron-induced fission was analyzed. The results show that the mass yield data calculated based on the optimized model parameters of this invention achieves a better agreement with the experimental data compared to the mass yield calculated based on the original model parameters. Overall, the mass yield curve calculated based on the optimized model parameters maintains the same trend as the experimental data, representing a significant improvement over the original results.

[0073] Based on more accurate fission product quality and yield data, the effectiveness of fission yield data evaluation can be significantly improved, and its overall accuracy can be enhanced, thereby improving the accuracy of reactor core physics design and providing an effective basis for the safety and economy of reactor operation.

Claims

1. A method for optimizing fission product quality and yield data based on gradient descent, characterized in that: Includes the following steps: Step 1: Based on the multi-Gaussian model of mass yield and its original model parameters, calculate the mass yield data of different fission product nuclides using the multi-Gaussian model expression shown in formula (1): In the formula: MY(A) — Mass yield of fission product nuclides with mass number A; N i —The intensity of the i-th Gaussian function in the multi-Gaussian model is a parameter of the first type of model; —The average mass number of different fission products; D i —In a multi-Gaussian model, the center position of the i-th Gaussian function is relative to the average mass. The offset is the parameter of the second type of model; σ i —The standard deviation of the i-th Gaussian function in the multi-Gaussian model is a parameter of the third type of model; Step 2: Compare the quality output calculation data obtained in Step 1 with the corresponding experimental data, and construct the loss function shown in formula (2): In the formula: Loss—the value of the loss function; N A —The number of mass spots of the fission product nuclides considered; A L —Lower limit of the mass number of fission products considered; A H —Upper limit of the mass number of fission products considered; MY E (A) — Experimental data on the mass yield of fission product nuclides with mass number A; Step 3: Based on the loss function constructed in Step 2, calculate its partial derivatives with respect to the various model parameters given in Step 1, construct the gradient vector of the loss function, and update the model parameters using the gradient descent method shown in formula (3): p (1) =p (0) -lr·▽Loss(p (0) ) Equation (3) In the formula: p (1) —The vector formed by the parameters of the three types of models after the update; p (0) —Update the vector formed by the parameters of the first three types of models; lr — learning rate, representing the magnitude of each parameter update; ▽Loss(p (0) - The gradient vector of the loss function; Step 4: Re-input the model parameters obtained in Step 3 into the multi-Gaussian model, and then repeat the process of Steps 1 to 3 to update the model parameters repeatedly; observe the trend of the loss function. When the loss function converges and no longer changes significantly, end the update process. The model parameter values ​​at this time are the optimal values. Step 5: Input the optimal values ​​of the model parameters into the Gaussian model, and the calculated result is the optimized mass yield data of the fission product nuclides.

2. The method for optimizing fission product quality and yield data based on gradient descent according to claim 1, characterized in that: The convergence condition of the loss function is: after two consecutive updates of the model parameters, the relative change in the loss function value is less than 1.0 × 10⁻⁶. -8 .

Images