Nuclear reaction cross section data generation method and system based on machine learning

Abstract

The invention discloses a nuclear reaction cross section data generation method and system based on machine learning. The nuclear reaction cross section data generation method based on machine learning comprises the following steps: acquiring data of nuclide characteristic indexes; the data of the nuclide characteristic indexes are used to predict a nuclear reaction cross section by using a pre-trained ensemble learning model, the ensemble learning model comprises a plurality of base learners and a secondary model, and the base learners are used to predict according to the nuclide characteristic index data; the secondary model is used for integrating the prediction results of the base learners to obtain the nuclear reaction cross section. The invention aims to optimize the generation efficiency and accuracy of nuclear reaction cross section data by combining various machine learning and deep learning technologies.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of atomic energy science and technology, and particularly relates to a nuclear reaction cross-section data generation method and system based on machine learning. BACKGROUND

[0002] In nuclear science research and nuclear engineering applications, nuclear reaction cross-section data is an important physical quantity for evaluating the probability of particle interaction with atomic nuclei in nuclear reaction processes. These data are indispensable for nuclear reactor design, nuclear medicine applications, radiation protection calculations, and nuclear physics basic research. Traditionally, nuclear reaction cross-section data is mainly obtained through experimental measurements and physical model calculations. However, experimental methods are often limited by experimental conditions and equipment, and it is difficult to obtain data for many high-energy regions or rare isotopes. Physical models, including TALYS, can provide relatively comprehensive data, but their accuracy and reliability still face challenges in the face of complex reaction mechanisms and physical processes.

[0003] OpenMC is an open-source Monte Carlo program widely used in the field of nuclear energy. By analyzing the Monte Carlo program, it can be found that the bottleneck of cross-section data reading is the main bottleneck of GPU acceleration. By using deep learning to calculate nuclear reaction cross-section data, more accurate and reliable input data can be provided for open-source software such as OpenMC, improving the accuracy and reliability of simulation results, and further promoting the development and application of open-source software in the field of nuclear energy.

[0004] Machine learning methods replace the search process of nuclear reaction cross-section data with a calculation process, making it easier to predict nuclear reaction cross-section data and provide more accurate and comprehensive input data for open-source software. This helps improve the accuracy and reliability of simulation results and enhance the software's simulation and prediction capabilities. Accurate nuclear reaction cross-section data is crucial for simulating and designing reactors and studying nuclear materials. By using deep learning methods to obtain more accurate data, simulation efficiency can be improved, dependence on expensive experiments can be reduced, and software calculation speed and accuracy can be accelerated.

[0005] At the same time, the more accurate nuclear data provided by deep learning can support the development of new reactor technologies. For different types of reactors, providing accurate input data is key to driving the development of these technologies.

[0006] In the field of nuclear energy, deep learning methods can be used to optimize algorithms, improve the computational efficiency of simulations and predictions. This optimization helps to improve the performance and functionality of software, enhancing its applicability in the field of nuclear energy. By improving and optimizing open-source software and introducing new technologies such as deep learning, more developers and researchers can be attracted to participate in open-source projects in the field of nuclear energy. This will promote the development of the open-source community and technical exchange, driving more innovation and contributions.

[0007] The nuclear reaction cross-section data in OpenMC is obtained through traditional cross-section lookup, and the use of machine learning methods to access OpenMC has certain innovation, and the advantage of AI method is that it can greatly reduce the number of memory accesses, solve the problem of low cache hit rate, and greatly reduce the memory occupation of cross-section data, and has better generalization ability.

[0008] In recent years, with the rapid development of machine learning technology, its advantages in data prediction and pattern recognition provide a new way to solve the problem of insufficient nuclear data. Especially the deep learning method, with its powerful data processing and nonlinear modeling ability, shows its potential in nuclear science data processing. However, how to effectively use machine learning technology to improve the generation efficiency and accuracy of nuclear reaction cross-section data is still a technical problem that needs to be solved urgently.

[0009] Nuclear reaction cross-section data is the basic data in nuclear science research and nuclear engineering application, and its accuracy directly affects the design and operation safety of nuclear reactors. However, due to the limitations of experimental conditions and the complexity of physical models, it has always been a challenge to obtain high-accuracy nuclear reaction cross-section data. SUMMARY

[0010] The technical problem to be solved by the present application is to provide a nuclear reaction cross-section data generation method and system based on machine learning, which aims to optimize the generation efficiency and accuracy of nuclear reaction cross-section data by combining various machine learning and deep learning technologies.

[0011] In order to solve the above technical problems, the technical scheme adopted by the present application is: A nuclear reaction cross-section data generation method based on machine learning, comprising the following steps: S101, obtaining data of nuclear characteristic indicators; S102, using a pre-trained ensemble learning model to predict nuclear reaction cross-sections from nuclear characteristic indicator data, the ensemble learning model comprising a plurality of base learners and a secondary model, the base learners being used to predict nuclear reaction cross-sections from nuclear characteristic indicator data, and the secondary model being used to integrate the prediction results of each base learner to obtain nuclear reaction cross-sections.

[0012] Optionally, the nuclear characteristic indicators in step S101 include data of particle species, atomic number of nucleus, mass number of nucleus, particle energy, reaction mechanism type, and temperature, wherein the particle species includes neutrons and photons, and the reaction mechanism type includes total cross section of reaction between neutrons and target nucleus, elastic scattering between neutrons and target nucleus, inelastic scattering between neutrons and target nucleus, nuclear reaction between neutrons and tritium, production of other particles by reaction between neutrons and target nucleus, production of two neutrons by reaction between neutrons and target nucleus, production of three neutrons by reaction between neutrons and target nucleus, fission reaction between neutrons and target nucleus, production of protons by reaction between neutrons and target nucleus, nuclear reaction between neutrons and gamma rays, production of alpha particles by reaction between neutrons and target nucleus, production of two alpha particles by reaction between neutrons and target nucleus, complete absorption of neutrons by target nucleus, and continuous energy distribution of scattered neutrons after incidence.

[0013] Optionally, the base learner in step S102 is a regression model, and a functional expression of the regression model is: σ = f (Ψ, Z, A, E, MT, T) wherein σ is a nuclear reaction cross section, f represents the base learner, Ψ is a particle species, Z is an atomic number of nucleus, A is a mass number of nucleus, E is a particle energy, MT is a reaction mechanism type, and T is a temperature.

[0014] Optionally, the regression model is a lasso regression model, a Gaussian process regression model, a random forest regression model, a K-nearest neighbor regression model, a gradient boosting regression model, an elastic net regression model, a support vector regression model, a ridge regression model, a kernel support vector regression model, or a kernel ridge regression model.

[0015] Optionally, when the data of the nuclear characteristic indicators are predicted by using the pre-trained ensemble learning model in step S102, the data of the nuclear characteristic indicators are preprocessed before being input into the pre-trained ensemble learning model, and the preprocessing includes: S201, one-hot encoding is performed on the two discrete data of particle species and reaction mechanism type in the nuclear characteristic indicators; S202, the data of each nuclear characteristic indicator of the two one-hot encoded data of particle species and reaction mechanism type, and the data of atomic number of nucleus, mass number of nucleus, particle energy, and temperature are estimated by using maximum likelihood estimation to estimate an optimal transformation factor λ so that the data of the nuclear characteristic indicator is close to a normal distribution, and if the estimated optimal transformation factor λ is not equal to 0, Box-Cox transformation is performed according to the following formula: , if the estimated optimal transformation factor λ is equal to 0, Box-Cox transformation is performed according to the following formula: , wherein, is the data obtained by Box-Cox transformation, is the original data before Box-Cox transformation.

[0016] Optionally, the step S102 further comprises a step of training the ensemble learning model before the step S102: S201, obtaining data samples of the isotope characteristic indicators; S102, constructing a training data set after preprocessing the data samples of the isotope characteristic indicators and classifying them into k categories by using a pre-trained XGBoost model; S103, for the data samples of each of the k categories, respectively training each of a preset regression model set, the preset regression model set including part or all of a lasso regression model, a Gaussian process regression model, a random forest regression model, a K-nearest neighbor regression model, a gradient boosting regression model, an elastic net regression model, a support vector regression model, a ridge regression model, a kernel support vector regression model, and a kernel ridge regression model, and calculating a weighted sum of Akaike information criterion (AIC) and Bayesian information criterion (BIC) of each regression model after the training, and selecting the optimal regression model for each category according to the principle that the weighted sum of AIC and BIC is the maximum, and combining the optimal regression models of the k categories with a secondary model to construct an ensemble learning model, and completing the training of the ensemble learning model by using network parameters of the secondary model of the ensemble learning model.

[0017] Optionally, in the step S102 of constructing a training data set after preprocessing the data samples of the isotope characteristic indicators and classifying them into k categories by using a pre-trained XGBoost model, k is determined according to the size of the training data set, the larger the size of the training data set is, the larger k is, and the loss function used by the XGBoost model in the training adopts a cross-entropy loss function.

[0018] In addition, the present application also provides a nuclear reaction cross-section data generation system based on machine learning, comprising a microprocessor and a memory connected to each other, the microprocessor being programmed or configured to execute the nuclear reaction cross-section data generation method based on machine learning.

[0019] In addition, the present application also provides a computer readable storage medium, which stores a computer program / instruction programmed or configured to execute the nuclear reaction cross-section data generation method based on machine learning by using a processor.

[0020] Furthermore, the present invention also provides a computer program product, including a computer program / instructions programmed or configured to execute the machine learning-based nuclear reaction cross-section data generation method via a processor.

[0021] Compared with existing technologies, this invention has the following main advantages: In an advanced version of the deep learning-based method for generating nuclear reaction cross-section data, this invention proposes an innovative and comprehensive computational framework—the XGBoost-Regression-Ensemble (XRE model)—to optimize the generation efficiency and accuracy of nuclear reaction cross-section data by combining multiple machine learning and deep learning techniques. The XRE model aims to optimize the generation of nuclear reaction cross-section data through a comprehensive, end-to-end computational method. The XRE model integrates the XGBoost algorithm and traditional machine learning algorithms, and improves prediction accuracy through ensemble learning techniques. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram illustrating the principle of the method in an embodiment of the present invention. Detailed Implementation

[0024] like Figure 1 As shown, the method for generating nuclear reaction cross-section data based on machine learning in this embodiment includes the following steps: S101, acquire data on nuclide characteristic indicators; S102, the data of nuclide feature indicators are used to predict the nuclear reaction cross section using a pre-trained ensemble learning model (XRE model). The ensemble learning model includes multiple base learners and a secondary model. The base learners are used to make predictions based on the nuclide feature indicator data, and the secondary model is used to integrate the prediction results of each base learner to obtain the nuclear reaction cross section.

[0025] By analyzing nuclides, such as Figure 2As shown, six nuclear characteristic indexes are found in the embodiment, which are particle type, atomic number of nucleus, mass number of nucleus, particle energy, reaction mechanism type and temperature data. The particle type includes neutron and photon. The reaction mechanism type includes total cross section of reaction between neutron and target nucleus, elastic scattering between neutron and target nucleus, inelastic scattering between neutron and target nucleus, nuclear reaction between neutron and tritium, other particles produced by reaction between neutron and target nucleus, two neutrons produced by reaction between neutron and target nucleus, three neutrons produced by reaction between neutron and target nucleus, fission reaction between neutron and target nucleus, proton produced by reaction between neutron and target nucleus, nuclear reaction between neutron and gamma ray, reaction between neutron and target nucleus, alpha particle produced by reaction between neutron and target nucleus, two alpha particles produced by reaction between neutron and target nucleus, complete absorption of neutron and target nucleus, and continuous energy distribution of scattered neutron after incidence, as shown in Table 1.

[0026] Table 1. Reaction mechanism type table

[0027] The reaction cross section of particle and atomic nucleus mainly depends on the energy of incident particle and the properties of target nucleus. Since the task is a regression task, the base learner in step S102 can adopt a required machine learning model as needed. For example, as an optional implementation, the base learner in step S102 of the embodiment is a regression model, and the function expression of the regression model is: σ = f (Ψ, Z, A, E, MT, T) wherein σ is the nuclear reaction cross section, f represents the base learner, Ψ is the particle type, Z is the atomic number of nucleus, A is the mass number of nucleus, E is the particle energy, MT is the reaction mechanism type, and T is the temperature. As Figure 2As shown, the regression model in this embodiment is a lasso regression model, a Gaussian process regression model, a random forest regression model, a K-nearest neighbor regression model, a gradient boosting regression model, an elastic net regression model, a support vector regression model, a ridge regression model, a kernel support vector regression model, or a kernel ridge regression model, as described below: (1) Random forest regression, an ensemble learning method based on decision trees, which performs regression tasks by constructing multiple decision trees and combining their prediction results. Each tree is built based on a randomly selected subset of features. (2) Gradient boosting regression, which iteratively trains a series of decision trees, with each tree trained on the residual of the previous tree, gradually reducing the residual and ultimately obtaining the model. (3) Support vector regression, a regression method based on support vector machines (SVM), which finds the hyperplane that best fits the data for regression prediction, while allowing some degree of error. The optimization goal is to minimize the loss function while satisfying the fitting of data points and the control of errors. Common loss functions include Huber loss function and ε-insensitive loss function. (4) Kernel support vector regression, which uses kernel functions to map input features to high-dimensional space to learn nonlinear relationships. (5) K-nearest neighbor regression, KNN is based on the distance between samples to make predictions, which assumes that similar samples have similar target values. When predicting, the average or weighted average of the K nearest neighbors is selected as the prediction value. (6) Ridge regression, a linear regression method that adds a regularization term to the ordinary least squares method to prevent model overfitting. (7) Kernel ridge regression, a method that uses kernel methods to perform nonlinear regression based on ridge regression. It learns nonlinear relationships by mapping features to high-dimensional space. (8) Lasso regression, a linear regression method that adds an L1 regularization term to the ordinary least squares method to promote sparsity of model coefficients. (9) Elastic net regression, a combination of lasso and ridge regression, which uses both L1 and L2 regularization terms to balance sparsity and smoothness. (10) Gaussian process regression, a non-parametric regression method based on Bayesian methods, which assumes that the joint distribution of target variables satisfies Gaussian distribution. It should be noted that the above regression models are known regression models, and therefore the detailed details of their implementation are not described here.

[0028] In step S102, when predicting the nuclear reaction cross section using the pre-trained ensemble learning model, the data of the nuclide characteristic index is pre-processed as follows before being input into the trained ensemble learning model: S201, one-hot encoding is performed on the particle species and reaction mechanism type in the isotope characteristic index; one-hot encoding is a commonly used data encoding method, which is usually used to convert categorical variables into a format that machine learning algorithms can understand. It converts each categorical variable into a vector with a length equal to the number of categories, where only one element is 1 and the rest are 0. Such encoding makes the model better understand the relationship between the classification variables, while avoiding the influence of the numerical size of different categories on the model; S202, the data of each isotope characteristic index in the one-hot encoded particle species and reaction mechanism type data and the data of the atomic number of the nucleus, the mass number of the nucleus, the particle energy and the temperature are estimated by using maximum likelihood estimation to estimate the optimal transformation factor λ to make the data of the isotope characteristic index close to normal distribution, if the estimated optimal transformation factor λ is not equal to 0, Box-Cox transformation is performed according to the following formula: , if the estimated optimal transformation factor λ is equal to 0, Box-Cox transformation is performed according to the following formula: , wherein, is the data obtained by Box-Cox transformation, is the original data before Box-Cox transformation, Box-Cox transformation is a method for adjusting the distribution of data to meet the assumptions of statistical models. It can be used to deal with non-normal distribution and heteroscedasticity of data. The transformation factor λ can be any real number.

[0029] The embodiment step S102 further includes the step of training the integrated learning model: S201, obtaining data samples of isotope characteristic indexes; S102, constructing a training data set after preprocessing the data samples of isotope characteristic indexes and classifying them into k categories by using a pre-trained XGBoost model; S103, for each data sample of each of the k categories, respectively train each regression model in a preset regression model set, the preset regression model set including part or all of a lasso regression model, a Gaussian process regression model, a random forest regression model, a K-nearest neighbor regression model, a gradient boosting regression model, an elastic net regression model, a support vector regression model, a ridge regression model, a kernel support vector regression model, and a kernel ridge regression model, and after the training, calculate a weighted sum of Akaike information criterion (AIC) and Bayesian information criterion (BIC) of each regression model, and select the optimal regression model for each category according to the principle that the weighted sum of AIC and BIC is the maximum, and combine the optimal regression models of the k categories and the secondary model to construct an ensemble learning model, and train the ensemble learning model by training the network parameters of the secondary model of the ensemble learning model. After selecting the regression model, in order to ensure that each category after multi-classification adopts the most appropriate regression model, Akaike information criterion (AIC) and Bayesian information criterion (BIC) need to be calculated respectively. They are statistical criteria commonly used for model selection, which consider both the goodness of model fitting and the complexity of the model, but differ slightly in calculation. Akaike information criterion (AIC) is proposed by Japanese statistician Hirotugu Akaike, and its core idea is to balance the goodness of fit and the complexity of the model. AIC assumes that the data comes from a real model, estimates the parameters of the model by maximizing the likelihood function of the data, and then punishes the model with the number of parameters to avoid overfitting. The calculation function expression of Akaike information criterion (AIC) is as follows: , where, L is the maximum likelihood function value of the model, k is the number of parameters of the regression model.

[0030] BIC is proposed by Stuart L. Schwartz, which considers the idea of Bayesian estimation in model selection. BIC not only considers the goodness of fit and the complexity of the model, but also considers the prior penalty on the parameter space, which usually punishes the number of parameters more strictly.

[0031] The calculation function expression of Bayesian information criterion (BIC) is as follows: , where, L represents the maximum likelihood function value of the model,k This represents the number of parameters in the regression model. n This represents the sample size. In both formulas, -2log(L) is a measure of goodness of fit; a higher maximum likelihood function value indicates a better fit to the data. k This refers to the number of parameters in the model, representing its complexity. Both the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are based on information theory principles, selecting the optimal model by balancing goodness of fit and complexity. Therefore, the smaller the values ​​of the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), the better the regression model performs. Evaluation metrics for regression problems are used to measure the model's predictive ability on the target variable. The following are evaluation metrics for regression problems: Mean Squared Error (MSE) represents the average of the squared errors between the predicted and actual values. The smaller the value, the more accurate the model prediction.

[0032] , Root Mean Square Error (RMSE) is the square root of MSE, and it more intuitively represents the magnitude of the error between the predicted and actual values. Similar to MSE, a smaller RMSE value indicates a more accurate model prediction.

[0033] , Mean Absolute Error (MAE) represents the average absolute error between the predicted and the actual values. It focuses on the actual difference between the predicted and the actual values, rather than considering the square of the error.

[0034] , Coefficient of determination (R) 2 ), R 2 This indicates the model's ability to explain changes in the target variable. The value ranges from [0,1]. The closer it is to 1, the stronger the model's ability to explain the target variable.

[0035] , like Figure 1 As shown, in this embodiment, the label data of the nuclear reaction cross section used in training the regression model is obtained by instrument measurement or physical model (for example, see the literature: Koning AJ, Rochman D. Modern nuclear data evaluation with the TALYS code system[J]. Nuclear data sheets, 2012, 113(12): 2841-2934.).

[0036] In step S102 of this embodiment, after preprocessing the data samples of nuclide feature indicators to construct a training dataset, and classifying them into k categories using a pre-trained XGBoost model, k is determined based on the size of the training dataset; the larger the training dataset, the larger the value of k. The XGBoost model uses the cross-entropy loss function during training. Since the input features are sparse data, to accelerate the training process and handle large amounts of sparse data, the XGBoost method is used to classify this data. XGBoost constructs the final model by integrating multiple decision trees. Each tree is built based on the residual of the previous tree, gradually reducing the residual and thus progressively optimizing the model's predictive performance. The cross-entropy loss function is expressed as follows: , In the above formula, y It is a one-hot encoding vector where only the elements of the true class are 1, and the rest are 0. It is the probability distribution vector of the model's predicted output. i It is a category index. It is the first in the actual tag i The probability of each category It is the model's prediction of the first i The probability of each category. In this embodiment, the XRE model first uses the XGBoost model to preprocess and classify the input data. The features of the input data include particle type (including neutrons and photons), atomic nucleus charge number, atomic nucleus mass number, reaction mechanism type, temperature, and particle energy. After classification, the processing of large-scale datasets with rich classification features is particularly optimized. This step significantly reduces the complexity of data preprocessing and training time.

[0037] In summary, accurate nuclear reaction cross-section data is crucial for various aspects of nuclear science, including nuclear reactor design, radiation protection, and nuclear medicine applications. This embodiment proposes an innovative computational framework—the XRE model—for generating nuclear reaction cross-section data based on machine learning. This model combines the XGBoost algorithm, multiple machine learning algorithms, and ensemble learning techniques. By constructing and combining multiple learners, it completes the learning task, achieving better predictive performance than a single model. Figure 1As shown, due to the large size of the data set and the uneven distribution of the data set size among different nuclides, the established label is the range of different sizes of the data set by using XGBoost to perform multi-classification according to the size of the data set, and the classification is performed from the least to the most. Then, a plurality of different models are trained by using lasso regression, Gaussian process regression, random forest regression, K-nearest neighbor regression, gradient boosting regression, elastic net regression, support vector regression, kernel support vector regression, ridge regression, and kernel ridge regression as base learners, and then a secondary model is trained to integrate the predictions of these models, thereby improving the accuracy of the prediction. The ensemble learning model can use different types of algorithms as base learners, and the secondary model integrates the optimal combination according to the prediction results of different base learners to make the final prediction. In this embodiment, the XRE model can generally achieve higher accuracy than a single model by combining the prediction results of a plurality of base learners, especially when dealing with high-variance and high-bias problems. Therefore, finally, the XRE model uses ensemble learning technology to integrate the outputs of each prediction model, selects the optimal model combination to improve the accuracy of the prediction of the nuclear reaction cross-section data, and this strategy not only enhances the robustness of the model, but also ensures that a higher prediction accuracy can be achieved when facing variable and complex nuclear data. The method of this embodiment converts discrete cross-section data into continuous cross-section data and can simultaneously input multiple nuclides and simultaneously predict multiple sets of cross-section data, which solves the problem of incomplete data and enhances the scalability of the algorithm. By describing the architecture, key technologies and methods of the XRE model in detail, this embodiment shows the advantages and application potential of the model in the generation of nuclear reaction cross-section data. The method of this embodiment can apply artificial intelligence methods to OpenMC, and this research becomes the first to apply artificial intelligence technology to the generation of nuclear reaction cross-section data. OpenMC has a wide range of applications in nuclear physics simulation as an open-source software, and the method of this embodiment based on machine learning for generating nuclear reaction cross-section data will provide more accurate and reliable input data for OpenMC, and provide a new platform for the application of artificial intelligence methods in nuclear physics.

[0038] In addition, the embodiment also provides a nuclear reaction cross-section data generation system based on machine learning, which comprises a microprocessor and a memory connected to each other, and the microprocessor is programmed or configured to execute the nuclear reaction cross-section data generation method based on machine learning.

[0039] In addition, the embodiment also provides a computer readable storage medium, which stores computer programs / instructions programmed or configured to execute the nuclear reaction cross-section data generation method based on machine learning by a processor.

[0040] In addition, the embodiment further provides a computer program product comprising computer programs / instructions programmed or configured to execute the machine learning based nuclear reaction cross section data generation method by a processor.

[0041] Those skilled in the art will appreciate that embodiments of the present application can be supplied as methods, systems, or computer program products. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-readable storage media (including, but not limited to, disk memory, CD-ROMs, optical storage media, etc.) having computer usable program code embodied thereon. The present application is described in reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and / or block in the flowchart illustrations and / or block diagrams, and combinations of flows and / or blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 one or more flows and / or blocks Figure 1 one or more flows and / or blocks Figure 1 one or more flows and / or blocks Figure 1 one or more flows and / or blocks Figure 1 one or more flows and / or blocks

[0042] The above only describes the preferred embodiments of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled in the art, some improvements and refinements without departing from the principles of the present application shall also be considered as falling within the protection scope of the present application.

Claims

1. A method for generating nuclear reaction cross-section data based on machine learning, characterized in that, Includes the following steps: S101, acquire data on nuclide characteristic indicators; S102, the data of nuclide feature indicators are used to predict the nuclear reaction cross section using a pre-trained ensemble learning model. The ensemble learning model includes multiple base learners and a secondary model. The base learners are used to make predictions based on the nuclide feature indicator data, and the secondary model is used to synthesize the prediction results of each base learner to obtain the nuclear reaction cross section.

2. The method for generating nuclear reaction cross-section data based on machine learning according to claim 1, characterized in that, The nuclide characteristic indicators in step S101 include data on particle type, atomic nucleus charge number, atomic nucleus mass number, particle energy, reaction mechanism type, and temperature. The particle type includes neutrons and photons. The reaction mechanism type includes the total cross-section of the reaction between neutrons and the target nucleus, elastic scattering between neutrons and the target nucleus, inelastic scattering between neutrons and the target nucleus, nuclear reaction between neutrons and tritium, reaction between neutrons and the target nucleus producing other particles, reaction between neutrons and the target nucleus producing two neutrons, reaction between neutrons and the target nucleus producing three neutrons, fission reaction between neutrons and the target nucleus, reaction between neutrons and the target nucleus producing protons, nuclear reaction between neutrons and gamma rays, reaction between neutrons and the target nucleus producing alpha particles, reaction between neutrons and the target nucleus producing two alpha particles, complete absorption of neutrons and the target nucleus, and neutron scattering with a continuous energy distribution after incident.

3. The method for generating nuclear reaction cross-section data based on machine learning according to claim 1, characterized in that, The base learner in step S102 is a regression model, and the functional expression of the regression model is: σ=f(Ψ,Z,A,E,MT,T) Where σ is the nuclear reaction cross section, f represents the basis learner, Ψ is the particle type, Z is the nucleus charge number, A is the nucleus mass number, E is the particle energy, MT is the reaction mechanism type, and T is the temperature.

4. The method for generating nuclear reaction cross-section data based on machine learning according to claim 1, characterized in that, The regression model is a lasso regression model, a Gaussian process regression model, a random forest regression model, a K nearest neighbor regression model, a gradient boosting regression model, an elastic network regression model, a support vector regression model, a ridge regression model, a kernel support vector regression model, or a kernel ridge regression model.

5. The method for generating nuclear reaction cross-section data based on machine learning according to claim 1, characterized in that, In step S102, when using the pre-trained ensemble learning model to predict the nuclear reaction cross section using the data of nuclide characteristic indicators, the data of nuclide characteristic indicators is preprocessed as follows before being input into the trained ensemble learning model: S201 performs one-hot encoding on two discrete data points in the nuclide characteristic index: particle type and reaction mechanism type. S202, for each nuclide characteristic index in the data of particle type and reaction mechanism type after unique thermal encoding, as well as the data of nuclear charge number, nuclear mass number, particle energy and temperature, the optimal transformation factor λ is estimated using maximum likelihood estimation so that the data of that nuclide characteristic index approximates a normal distribution. If the estimated optimal transformation factor λ is not equal to 0, then a Box-Cox transformation is performed according to the following formula: ， If the estimated optimal transformation factor λ is equal to 0, then the Box-Cox transformation is performed according to the following formula: ， in, The data obtained from the Box-Cox transformation. This is the original data before the Box-Cox transformation.

6. The method for generating nuclear reaction cross-section data based on machine learning according to claim 1, characterized in that, Step S102 also includes the step of training the ensemble learning model: S201, Obtain data samples of nuclide characteristic indicators; S102, after preprocessing the data samples of nuclide feature indicators, construct a training dataset and classify it into k categories using a pre-trained XGBoost model; S103. For each of the k categories of data samples, train each regression model in the preset regression model set. The preset regression model set includes lasso regression, Gaussian process regression, random forest regression, K nearest neighbor regression, gradient boosting regression, elastic network regression, support vector regression, ridge regression, kernel support vector regression, and some or all of the kernel ridge regression models. After training, calculate the weighted sum of the Akaike information criterion factor (AIC) and the Bayesian information criterion factor (BIC) for each regression model. Based on the principle of maximizing the weighted sum of the Akaike information criterion factor (AIC) and the Bayesian information criterion factor (BIC), select the best pre-trained regression model for each category. Combine the best regression models of the k categories with the secondary models to construct an ensemble learning model. Train the ensemble learning model by training the network parameters of the secondary model of the ensemble learning model.

7. The method for generating nuclear reaction cross-section data based on machine learning according to claim 6, characterized in that, In step S102, after preprocessing the data samples of nuclide feature indicators to construct a training dataset, the XGBoost model is used to classify them into k categories. Here, k is determined according to the size of the training dataset. The larger the size of the training dataset, the larger the value of k. The XGBoost model uses the cross-entropy loss function during training.

8. A machine learning-based system for generating nuclear reaction cross-section data, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the machine learning-based nuclear reaction cross-section data generation method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program / instructions, characterized in that, The computer program / instructions are programmed or configured to execute, via a processor, the machine learning-based nuclear reaction cross-section data generation method of any one of claims 1 to 7.

10. A computer program product comprising a computer program / instructions, characterized in that, The computer program / instructions are programmed or configured to execute, via a processor, the machine learning-based nuclear reaction cross-section data generation method of any one of claims 1 to 7.

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