A parameter optimization method and system based on surrogate model and multi-algorithm gradient collaboration

Abstract

This invention discloses a parameter optimization method and system based on a surrogate model and multi-algorithm gradient collaboration, relating to the fields of nuclear engineering and nuclear safety technology. The method includes: first, determining the parameter combination of a nuclear facility; obtaining the Keff value through high-fidelity calculation using a Monte Carlo program; and constructing a training set. Then, training a differentiable surrogate model that can predict Keff values ​​and gradient information using a feedforward neural network combined with a backpropagation algorithm; using this model as the objective function; and minimizing the absolute error between the predicted Keff value and the target value as the optimization objective. A hybrid optimization algorithm is used to globally explore and generate candidate parameter solutions. Gradient-assisted local optimization is then used to obtain the optimal parameter combination candidate solution. Finally, the solution is verified using a Monte Carlo program; if the error meets the standard, it is taken as the final parameter combination solution. This invention solves the problem that existing parameter optimization methods cannot simultaneously achieve both computational efficiency and accuracy.

Description

Technical Field

[0001] This invention relates to the fields of nuclear engineering and nuclear safety technology, and in particular to a parameter optimization method and system based on a surrogate model and multi-algorithm gradient collaboration. Background Technology

[0002] Nuclear criticality safety is a core technical requirement in the nuclear industry. In nuclear facilities such as nuclear power plants, nuclear fuel processing plants, and nuclear waste storage facilities, the design and parameter optimization of equipment such as spent fuel storage racks, transport containers, and geometrically complex containers for reprocessing must all use the effective multiplication factor Keff value as the core judgment indicator. It is necessary to ensure that nuclear facilities maintain a subcritical state under all operating conditions and meet the nuclear safety guidelines in "HAD 301 / 02-2015: Critical Safety Requirements for Facility for the Handling, Processing and Handling of Fissile Materials".

[0003] In existing technologies, the calculation of the effective multiplication factor Keff and related safety margins during the optimization of nuclear criticality safety parameters for nuclear facilities mainly relies on Monte Carlo methods to perform multiple neutron transport calculations. While this type of high-fidelity calculation method can guarantee the accuracy of the Keff value calculation, it suffers from extremely long computation time. In scenarios where nuclear facility parameter space has high dimensionality and numerous variable combinations, in order to determine the design parameter combination that meets nuclear safety requirements, repeated Monte Carlo high-fidelity calculations are required for a large number of parameter combinations, directly leading to a significant extension of the parameter optimization design cycle for nuclear facilities.

[0004] To address these issues, some existing solutions attempt to optimize nuclear critical safety parameters by combining a single optimization algorithm with a simple prediction model, or by screening combinations of nuclear facility parameters through manual trial calculations. However, these improved solutions still have several technical shortcomings: First, single optimization algorithms are prone to getting trapped in local optima in the high-dimensional nonlinear parameter space of nuclear facilities, making it difficult to achieve a global search of the parameter space. This makes it impossible to balance the safety and economy of equipment design while meeting nuclear safety requirements, such as maximizing container loading capacity and minimizing the amount of shielding material used. Second, manual trial calculations or optimization methods using a single algorithm make the parameter optimization process heavily reliant on the industry experience of senior experts, lacking systematic and automated design. The robustness of the optimization process is poor, and the convergence and optimization effect are significantly affected by algorithm parameter debugging and problem characteristics. The optimization success rate is unstable under different nuclear facilities and different optimization scenarios.

[0005] Therefore, existing methods for optimizing nuclear critical safety parameters cannot balance computational efficiency and accuracy. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a parameter optimization method and system based on surrogate model and multi-algorithm gradient collaboration, which aims to solve the problem that the parameter optimization methods in the prior art cannot balance computational efficiency and accuracy.

[0007] This invention proposes a parameter optimization method based on a surrogate model and multi-algorithm gradient collaboration, the method comprising:

[0008] The nuclear facility equipment to be analyzed is obtained, and the combination of nuclear facility parameters of the nuclear facility equipment is determined. The Monte Carlo calculation program is called to perform high-fidelity calculation on the combination of nuclear facility parameters to obtain the effective multiplication coefficient Keff value corresponding to the parameter combination in order to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value.

[0009] A feedforward neural network combined with a backpropagation algorithm is used to train the training set to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information.

[0010] Using a differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective, a pre-defined hybrid optimization algorithm is used to globally explore the parameter space of the nuclear facility and generate multiple sets of candidate parameter solutions.

[0011] The gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters is calculated based on the differentiable surrogate model. The gradient is then used to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution.

[0012] The candidate solution of the optimal parameter combination is input again into the Monte Carlo calculation program for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is less than the threshold, the candidate solution of the optimal parameter combination is taken as the final parameter combination solution.

[0013] Furthermore, in the parameter optimization method based on the surrogate model and multi-algorithm gradient collaboration described above, the formula for calculating the gradient of the input kernel facility parameters is as follows:

[0014] ;

[0015] in, For the input nuclear facility parameters, This is the predicted value of the effective multiplication coefficient Keff output by the differentiable surrogate model.

[0016] Furthermore, in the above parameter optimization method based on surrogate model and multi-algorithm gradient collaboration, the calculation formula for using gradients to perform auxiliary local optimization on multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution is as follows:

[0017] ;

[0018] in, This represents a candidate solution for the optimal parameter combination after local optimization. For the current candidate parameter solution, The gradient step size is adjusted adaptively.

[0019] Furthermore, in the above-mentioned parameter optimization method based on surrogate model and multi-algorithm gradient collaboration, the step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions includes:

[0020] The nuclear facility parameter optimization problem is constructed as a Markov decision process. A proximal policy optimization algorithm is used to learn the parameter adjustment strategy. A reward function is set for the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff. The parameter adjustment strategy is updated iteratively by maximizing the reward value. A gradual adjustment method is adopted in the strategy update process to limit the magnitude of a single strategy update, and candidate parameter solutions are obtained.

[0021] A genetic algorithm is used to simulate the natural selection mechanism. Through selection, crossover, and mutation operations, the combination of nuclear facility parameters is iterated and selected as candidate parameter solutions by selecting parameter combinations with high fitness.

[0022] An evolutionary strategy is adopted to randomly sample near the current parameter point to generate offspring parameter combinations. By evaluating the predicted value of the effective proliferation coefficient Keff value corresponding to the offspring parameter combination, excellent offspring are selected and the parent parameters are updated. The candidate parameter solutions are obtained by gradually approaching the dominant region in the parameter space.

[0023] The candidate parameter solution sets generated by each algorithm are collaboratively screened. Using a preset fitness evaluation index, the best-performing combination of parameters is selected from the candidate solutions of each algorithm to form a unified candidate parameter solution set.

[0024] Furthermore, in the aforementioned parameter optimization method based on surrogate model and multi-algorithm gradient collaboration, the step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions further includes:

[0025] A genetic algorithm is used to perform a global coarse search of the nuclear facility parameter space. Through selection, crossover, and mutation operations, an iterative evolution is performed to generate a batch of initial candidate parameter solutions covering the main dominant regions of the parameter space.

[0026] The generated initial candidate parameter solutions are used as the initial parent parameters of the evolutionary strategy. Random sampling and offspring selection are performed in their vicinity to further focus on the dominant region and generate candidate parameter solutions.

[0027] The candidate parameter solutions are used as the initial state of the proximal policy optimization algorithm. A Markov decision process is constructed and a parameter adjustment policy is learned. The policy is refined by maximizing the reward function to generate the final multiple sets of candidate parameter solutions.

[0028] Furthermore, in the aforementioned parameter optimization method based on surrogate model and multi-algorithm gradient collaboration, the step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions further includes:

[0029] Initialize the search parameters of the proximal strategy optimization algorithm, genetic algorithm, and evolutionary strategy. Each algorithm takes the differentiable surrogate model as the objective function and minimizes the absolute error between the effective multiplication coefficient Keff value and the objective value as the optimization objective. They conduct the first round of independent exploration of the nuclear facility parameter space in parallel and output the first round of candidate parameter solutions of each algorithm and the corresponding quantitative indicators of algorithm performance.

[0030] A dynamic weight allocation model for algorithms is constructed, and the historical search performance quantification indicators of each algorithm are used as input to the model. Dynamic search weights are assigned to each algorithm according to the preset weight calculation rules.

[0031] Based on dynamic search weights, the core facility parameter space search resources of each algorithm are dynamically allocated. The search resources include the number of parameter sampling times, the number of iteration rounds, and the search area range. At the same time, the number of candidate parameter solutions generated by each algorithm is determined according to the weight ratio.

[0032] A new round of parameter space exploration is carried out to output candidate parameter solutions with corresponding weight ratios. All candidate parameter solutions generated by the algorithm are deduplicated and non-dominated, and duplicate solutions and parameter combinations that are inferior to existing solutions are eliminated to form multiple sets of candidate parameter solutions.

[0033] Furthermore, the above-mentioned parameter optimization method based on surrogate model and multi-algorithm gradient collaboration further includes:

[0034] If the absolute error between the actual effective multiplication coefficient Keff value and the target effective multiplication coefficient Keff value exceeds a preset threshold, the corresponding optimal parameter combination candidate solution and the corresponding effective multiplication coefficient Keff value will be added to the training set, and the differentiable surrogate model will be retrained.

[0035] Another objective of this invention is to provide a parameter optimization system based on a surrogate model and multi-algorithm gradient collaboration, the system comprising:

[0036] The acquisition module is used to acquire the nuclear facility equipment to be analyzed, determine the combination of nuclear facility parameters of the nuclear facility equipment, call the Monte Carlo calculation program to perform high-fidelity calculation on the combination of nuclear facility parameters, and obtain the effective multiplication coefficient Keff value corresponding to the parameter combination to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value;

[0037] The training module is used to train the training set using a feedforward neural network combined with the backpropagation algorithm to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information.

[0038] The search module is used to explore the nuclear facility parameter space globally using a differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective. It generates multiple sets of candidate parameter solutions by using a preset hybrid optimization algorithm.

[0039] The optimization module is used to calculate the gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters based on the differentiable surrogate model, and to use the gradient to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution;

[0040] The calculation module is used to input the candidate solution of the optimal parameter combination into the Monte Carlo calculation program again for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is less than the threshold, the candidate solution of the optimal parameter combination is used as the final parameter combination solution.

[0041] Another object of the present invention is to provide a readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0042] Another object of the present invention is to provide an electronic device including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0043] This invention obtains the combination of nuclear facility parameters of the nuclear facility to be analyzed, calls a Monte Carlo calculation program to perform high-fidelity calculations to obtain the corresponding Keff values ​​and constructs a training set, and uses a feedforward neural network combined with a backpropagation algorithm to train the training set to form a differentiable surrogate model that can predict Keff values ​​and gradient information; using this differentiable surrogate model as the objective function, with the optimization objective of minimizing the absolute error between the predicted Keff value and the target value, a preset hybrid optimization algorithm is used to globally explore the nuclear facility parameter space to generate multiple sets of candidate parameter solutions, and then calculates the gradient of the Keff value with respect to the input parameters based on the differentiable surrogate model, and uses the gradient to perform auxiliary local optimization on the candidate parameter solutions to obtain the optimal parameter combination candidate solution; finally, the candidate solution is input into the Monte Carlo calculation program again for high-fidelity calculation verification, and if the error is lower than a threshold, it is taken as the final parameter combination solution. By replacing most of the repetitive Monte Carlo high-fidelity calculations with a differentiable surrogate model, the number of time-consuming computation calls is significantly reduced. At the same time, by combining the global exploration capability of the hybrid optimization algorithm with the local optimization accuracy of gradient assistance, the computational efficiency of parameter optimization is guaranteed, and the accuracy of the optimization results is ensured through the final verification of the Monte Carlo program. Furthermore, the collaboration of multiple algorithms avoids the problem of a single algorithm being prone to local optima, realizing automated parameter optimization. This effectively solves the problem that existing technologies cannot balance computational efficiency and accuracy in nuclear critical safety parameter optimization. Attached Figure Description

[0044] Figure 1 This is a flowchart of the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in the first embodiment of the present invention;

[0045] Figure 2 This is a block diagram of the parameter optimization system based on surrogate model and multi-algorithm gradient collaboration in the third embodiment of the present invention.

[0046] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0047] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0048] It should be noted that when a component is said to be "fixed to" another component, it can be directly on the other component or there may be an intervening component. When a component is said to be "connected to" another component, it can be directly connected to the other component or there may be an intervening component. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0050] Example 1

[0051] Please see Figure 1 The figure shows a parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in the first embodiment of the present invention, the method including steps S10 to S14.

[0052] Step S10: Obtain the nuclear facility equipment to be analyzed, determine the combination of nuclear facility parameters for the nuclear facility equipment, call the Monte Carlo calculation program to perform high-fidelity calculation on the combination of nuclear facility parameters, and obtain the effective multiplication coefficient Keff value corresponding to the parameter combination to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value.

[0053] The nuclear facilities and equipment to be analyzed may include all equipment involving fissile materials, such as spent fuel storage racks in nuclear power plants, nuclear fuel transport containers, and various geometrically complex containers in nuclear fuel reprocessing plants. The combination of nuclear facility parameters includes the core parameters for the design and optimization of such equipment. Specific examples include the geometric dimensions, material composition, and internal component arrangement of the equipment. Geometric dimensions can be further exemplified by the inner diameter and height of the container and the spacing of the racks. Material composition can be exemplified by the elemental proportions of the shielding material and the material ratio of the fuel rods.

[0054] Monte Carlo calculation programs are commonly used high-fidelity calculation programs in nuclear criticality safety analysis. Programs such as MCNP, MONK, and RMC can be selected. These programs obtain highly accurate effective multiplication coefficient (Keff) values ​​through multiple neutron transport calculations, accurately reflecting the criticality safety state of nuclear facilities. After determining the combination of nuclear facility parameters, the aforementioned Monte Carlo calculation program is called to perform high-fidelity calculations on each parameter combination, obtaining a unique effective multiplication coefficient (Keff) value for each parameter combination. The nuclear facility parameter combination is then used as input features, and the corresponding effective multiplication coefficient (Keff) value is used as output labels to construct the training set required for model training. Obtaining training data through high-fidelity Monte Carlo calculations ensures the authenticity and accuracy of the training set, laying a data foundation for subsequent training of differentiable surrogate models and ensuring that the model prediction results closely match the actual physical state of the nuclear facility.

[0055] Step S11: The training set is trained using a feedforward neural network combined with the backpropagation algorithm to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information.

[0056] Feedforward neural networks are a simple and efficient deep learning model consisting of an input layer, hidden layers, and an output layer. The neurons in each layer are unidirectionally connected, with no feedback loops, enabling rapid mapping from input features to output results. Backpropagation is a classic algorithm used to train feedforward neural networks. By calculating the error between the model's predicted values ​​and the true values, the error is propagated back from the output layer to the input layer, continuously adjusting the network's weights and biases to achieve iterative optimization of the model. The constructed training set is input into the initialized feedforward neural network, and training is iteratively performed using the backpropagation algorithm as the core until the model's prediction accuracy reaches the preset requirements, ultimately forming a differentiable surrogate model. For example, other machine learning models such as Support Vector Regression (SVR) and Random Forest can also be used for the surrogate model.

[0057] This differentiable surrogate model possesses two core functions: first, it can quickly predict the corresponding effective multiplication coefficient Keff value based on the input combination of nuclear facility parameters; second, it is differentiable, enabling it to calculate the gradient information of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters. The differentiable surrogate model, trained using a feedforward neural network combined with the backpropagation algorithm, can predict the effective multiplication coefficient Keff value at extremely high speed, thousands of times faster than Monte Carlo calculation programs, significantly reducing the number of time-consuming high-fidelity computation calls.

[0058] Step S12: Using the differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective, a preset hybrid optimization algorithm is used to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions.

[0059] The trained differentiable surrogate model is used as the objective function for the entire parameter optimization process. All subsequent optimization algorithms are based on the predictions of this differentiable surrogate model, eliminating the need for real-time Monte Carlo calculations. A target value for the effective multiplication coefficient Keff is pre-set according to the critical safety requirements of the nuclear facility. This target value must meet the nuclear safety guidelines, i.e., Keff + 2Δ < 0.95, where Δ represents the calculation error of the effective multiplication coefficient Keff. Minimizing the absolute error between the predicted effective multiplication coefficient Keff and this target value is the core objective of the entire parameter optimization process, ensuring that the optimization process consistently revolves around this objective.

[0060] The pre-defined hybrid optimization algorithm integrates multiple optimization algorithms with different mechanisms, which can give full play to the advantages of each algorithm and make up for the shortcomings of a single algorithm. Based on the above objective function and optimization objective, the hybrid optimization algorithm conducts a comprehensive global exploration of the core facility parameter space. The core facility parameter space is a multi-dimensional space formed by the combination of the value ranges of all core facility parameters. The hybrid optimization algorithm performs parameter search, iteration and screening in this space, and finally generates multiple sets of candidate parameter solutions with optimization potential.

[0061] Step S13: Calculate the gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters based on the differentiable surrogate model, and use the gradient to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution.

[0062] This method leverages the differentiability of the differentiable surrogate model to calculate the gradient of the effective multiplication coefficient Keff with respect to each input core facility parameter for each set of candidate parameter solutions generated by the multi-algorithm global exploration. This gradient accurately reflects the direction and degree of influence of small changes in each core facility parameter on the effective multiplication coefficient Keff. Guided by this gradient information, each set of candidate parameter solutions undergoes fine-tuning and optimization within a local range, allowing the candidate parameter solutions to converge towards the target value within the local region. Through this gradient-assisted local optimization, a better optimal parameter combination candidate solution is selected from multiple sets of candidate parameter solutions. The gradient information provides a precise adjustment direction for local optimization, freeing the local optimization process from blind trial and error, achieving fine-tuned convergence of candidate parameter solutions, effectively improving the accuracy of parameter optimization, and enabling candidate parameter solutions to better fit the target value of the effective multiplication coefficient Keff. Furthermore, gradient-assisted local optimization is performed based on the multi-algorithm global exploration.

[0063] Specifically, the formula for calculating the gradient of the input nuclear facility parameters is as follows:

[0064] ;

[0065] in, For the input nuclear facility parameters, This is the predicted value of the effective multiplication coefficient Keff output by the differentiable surrogate model.

[0066] In the actual calculation process, The parameter represents any input nuclear facility parameter, such as the height of the container, the spacing of the grid, or the proportion of a certain element in the shielding material. Keff is the predicted effective multiplication coefficient Keff value output by the differentiable surrogate model for the combination of input nuclear facility parameters. The predicted value of the effective multiplication factor Keff for nuclear facility parameters The partial derivatives, This is the gradient vector of the effective multiplication coefficient Keff value with respect to all input nuclear facility parameters. Each element in this gradient vector corresponds to a partial derivative of a nuclear facility parameter, which can comprehensively reflect the influence of all nuclear facility parameters on the effective multiplication coefficient Keff value.

[0067] The gradient can be quickly calculated using automatic differentiation techniques based on a differentiable surrogate model trained on a feedforward neural network, without the need for complex manual differentiation calculations.

[0068] More specifically, the formula for calculating the candidate solution with the optimal parameter combination is:

[0069] ;

[0070] in, This represents a candidate solution for the optimal parameter combination after local optimization. For the current candidate parameter solution, The gradient step size is adjusted adaptively.

[0071] Step S14: Input the candidate solution of the optimal parameter combination into the Monte Carlo calculation program again for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is lower than the threshold, then the candidate solution of the optimal parameter combination is taken as the final parameter combination solution.

[0072] The candidate solution of the optimal parameter combination obtained by gradient-assisted local optimization is re-input into the Monte Carlo calculation program for a high-fidelity calculation. This calculation can obtain the true effective multiplication coefficient Keff value corresponding to the parameter combination. This true value can accurately reflect the actual critical safety state of the nuclear facility under the parameter combination.

[0073] An error threshold is pre-set based on the design requirements and safety standards of the nuclear facility. The calculated actual effective multiplication coefficient Keff value is compared with the target effective multiplication coefficient Keff value, and the absolute error between the two is calculated. If the absolute error is lower than the preset error threshold, it indicates that the candidate solution for the optimal parameter combination can meet the critical safety requirements and design objectives of the nuclear facility. At this point, the candidate solution for the optimal parameter combination is determined as the final parameter combination solution, serving as the final basis for the design and optimization of the nuclear facility. A Monte Carlo calculation program is used to perform a final high-fidelity verification of the candidate solution for the optimal parameter combination, effectively ensuring the authenticity and reliability of the final parameter combination solution and avoiding the optimization results not conforming to the actual physical state of the nuclear facility due to prediction errors in the differentiable surrogate model.

[0074] Furthermore, in some optional embodiments of the present invention, if the absolute error between the actual effective multiplication coefficient Keff value obtained by inputting the candidate solution of the optimal parameter combination into the Monte Carlo calculation program and the target effective multiplication coefficient Keff value exceeds a preset error threshold, it indicates that the candidate solution of the optimal parameter combination cannot meet the critical safety requirements and design objectives of the nuclear facility. In this case, the parameter combination is not directly discarded, but the candidate solution of the optimal parameter combination is used as a new input feature, and the corresponding actual effective multiplication coefficient Keff value is used as a new output label, and both are added to the initially constructed training set to expand the training set. The expanded training set is then re-input into the feedforward neural network, and the differentiable surrogate model is retrained using the backpropagation algorithm as the core, updating the model's weights and biases, so that the model can learn the input-output mapping relationship corresponding to the parameter combination, improving the model's prediction accuracy and generalization ability. After retraining, the process returns to the step of global exploration of the parameter space using a hybrid optimization algorithm. Based on the updated differentiable surrogate model, the entire parameter optimization process is repeated until the absolute error between the obtained actual effective multiplication coefficient Keff value and the target value is lower than the threshold.

[0075] In summary, the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in the above embodiments of the present invention obtains the combination of nuclear facility parameters of the nuclear facility to be analyzed, calls the Monte Carlo calculation program to perform high-fidelity calculation to obtain the corresponding Keff value and constructs a training set, and uses a feedforward neural network combined with the backpropagation algorithm to train the training set to form a differentiable surrogate model that can predict Keff value and gradient information; using the differentiable surrogate model as the objective function and minimizing the absolute error between the predicted Keff value and the target value as the optimization objective, a preset hybrid optimization algorithm is used to globally explore the nuclear facility parameter space to generate multiple sets of candidate parameter solutions, and then the gradient of the Keff value with respect to the input parameters is calculated based on the differentiable surrogate model. The gradient is used to perform auxiliary local optimization on the candidate parameter solutions to obtain the optimal parameter combination candidate solution; finally, the candidate solution is input into the Monte Carlo calculation program again for high-fidelity calculation verification, and if the error is lower than the threshold, it is taken as the final parameter combination solution. By replacing most of the repetitive Monte Carlo high-fidelity calculations with a differentiable surrogate model, the number of time-consuming computation calls is significantly reduced. At the same time, by combining the global exploration capability of the hybrid optimization algorithm with the local optimization accuracy of gradient assistance, the computational efficiency of parameter optimization is guaranteed, and the accuracy of the optimization results is ensured through the final verification of the Monte Carlo program. Furthermore, the collaboration of multiple algorithms avoids the problem of a single algorithm being prone to local optima, realizing automated parameter optimization. This effectively solves the problem that existing technologies cannot balance computational efficiency and accuracy in nuclear critical safety parameter optimization.

[0076] Example 2

[0077] This embodiment also proposes a parameter optimization method based on surrogate model and multi-algorithm gradient collaboration. The difference between the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in this embodiment and the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in Embodiment 1 is as follows:

[0078] The step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions includes:

[0079] The nuclear facility parameter optimization problem is constructed as a Markov decision process. The proximal policy optimization algorithm (PPO) is used to learn the parameter adjustment policy. A reward function is set for the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff. The parameter adjustment policy is updated iteratively by maximizing the reward value. In the policy update process, a gradual adjustment method is adopted to limit the magnitude of a single policy update, so as to obtain candidate parameter solutions.

[0080] A Markov Decision Process (MDP) is a mathematical model used to describe sequential decision problems. This model possesses the property of no aftereffect, meaning that the future state depends only on the current state and the actions taken, and is independent of past states. The nuclear facility parameter optimization problem is constructed as a Markov Decision Process, where the parameter state of the nuclear facility is taken as the model's state, parameter adjustment behavior is taken as the model's action, and the optimization effect after parameter adjustment is taken as the model's reward. Based on this Markov Decision Process, a proximal policy optimization algorithm is constructed. A reward function is set, which is related to the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff. The smaller the absolute error, the larger the reward function value, ensuring that the algorithm's optimization objective is consistent with the overall parameter optimization objective. The proximal policy optimization algorithm aims to maximize the reward value through iterative learning of parameter adjustment strategies, continuously optimizing the method and direction of parameter adjustment. During the strategy update process, a gradual adjustment method is adopted, strictly limiting the update magnitude of each strategy to avoid destroying the learned effective strategy due to excessive update magnitude, thus ensuring the stability of strategy learning. Through continuous iterative learning, the candidate parameter solutions explored and generated by the algorithm are finally obtained.

[0081] A genetic algorithm (GA) is employed to simulate the natural selection mechanism. Through selection, crossover, and mutation operations, the combinations of core facility parameters are iteratively evolved to select parameter combinations with high fitness as candidate solutions. The genetic algorithm is a stochastic optimization algorithm that simulates the natural selection and evolutionary process of organisms. Core facility parameter combinations are encoded as chromosomes, with each parameter combination corresponding to an independent chromosome. First, a population containing multiple chromosomes is initialized; this population forms the initial set of core facility parameter combinations. Subsequently, multiple rounds of selection, crossover, and mutation operations are performed on this population. The selection operation involves selecting chromosomes with high fitness from the population based on a preset fitness function. The value of the fitness function is related to the absolute error between the predicted and target values ​​of the effective proliferation coefficient Keff; the smaller the absolute error, the higher the fitness. The crossover operation involves exchanging genes between the selected high-fitness chromosomes to generate new chromosomes. The mutation operation involves randomly modifying some genes on the chromosomes to introduce new parameter combinations. Through multiple rounds of evolutionary iteration, the quality of chromosomes in the population is continuously improved, chromosomes with low fitness are gradually eliminated, and finally chromosomes with high fitness are selected and decoded into combinations of nuclear facility parameters, which serve as candidate parameter solutions explored and generated by the algorithm.

[0082] An evolutionary strategy (ES) is employed to randomly sample from the vicinity of the current parameter point, generating offspring parameter combinations. By evaluating the predicted effective proliferation coefficient (Keff) values ​​corresponding to these offspring parameter combinations, superior offspring are selected, and the parent parameters are updated, gradually approximating the dominant region in the parameter space to obtain candidate parameter solutions. The evolutionary strategy is an optimization algorithm based on biological evolution principles. This algorithm uses the current parameter point as the parent parameter, which can be obtained through random initialization or a simple search. Random sampling is performed near the value of the parent parameter, introducing a certain perturbation to generate multiple different offspring parameter combinations. The sampling range can be adjusted according to the progress of parameter optimization. All generated offspring parameter combinations are input into a differentiable surrogate model to obtain the predicted effective proliferation coefficient (Keff) values. The quality of the offspring parameter combinations is evaluated based on the predicted values, and superior offspring whose predicted effective proliferation coefficient (Keff) values ​​are closer to the target value are selected. These superior offspring are used as new parent parameters, and the next round of sampling, evaluation, and selection continues. Through multiple rounds of iteration, the parent parameters continuously move towards the advantageous region in the parameter space where the effective multiplication coefficient Keff value is closer to the target value. Finally, the parent parameters that have been iterated to the advantageous region and the excellent offspring parameters are used as candidate parameter solutions explored and generated by the algorithm.

[0083] The generated candidate parameter solution sets are collaboratively screened. Using a pre-defined fitness evaluation metric, the best-performing parameter combinations are selected from the candidate solutions of each algorithm, forming a unified candidate parameter solution set. After the proximal strategy optimization algorithm, genetic algorithm, and evolutionary strategy independently complete their parameter space exploration, they each generate a set of candidate parameter solutions, forming three independent candidate parameter solution sets. A pre-defined unified fitness evaluation metric is used, which is related to factors such as the absolute error between the predicted and target values ​​of the effective proliferation coefficient Keff, and the engineering feasibility of the parameter combinations, comprehensively evaluating the quality of each candidate parameter solution. Based on this unified fitness evaluation metric, the three candidate parameter solution sets are collaboratively screened, eliminating parameter combinations with low fitness and selecting the best-performing parameter combinations. These parameter combinations are then integrated to form a unified candidate parameter solution set for subsequent gradient-assisted local optimization.

[0084] Furthermore, as another specific implementation step for using a pre-defined hybrid optimization algorithm to globally explore the parameter space of the nuclear facility, the genetic algorithm, evolutionary strategy, and proximal strategy optimization algorithm are iterated sequentially in a chain, with the output of the previous algorithm serving as the input of the next algorithm, thus realizing a progressive exploration from global coarse search to local fine-tuning. The following provides a detailed explanation of each step.

[0085] A genetic algorithm is employed to perform a global coarse search of the nuclear facility parameter space. Through iterative evolution via selection, crossover, and mutation operations, a batch of initial candidate parameter solutions covering the main advantageous regions of the parameter space is generated. By simulating the natural selection mechanism, a comprehensive global coarse search of the nuclear facility parameter space is conducted. Utilizing the randomness and globality of selection, crossover, and mutation operations, a wide range of regions in the parameter space is explored, avoiding getting trapped in local optima.

[0086] The generated initial candidate parameter solutions are used as the initial parent parameters of the evolutionary strategy. Random sampling and offspring selection are performed in their vicinity to further focus on the advantageous region and generate candidate parameter solutions. Alternatively, the initial candidate parameter solutions generated by the genetic algorithm are used as the initial parent parameters of the evolutionary strategy, without further random initialization of the parent parameters. This allows the starting point of the evolutionary strategy to directly fall within the advantageous region of the parameter space locked by the genetic algorithm. Based on these initial parent parameters, the evolutionary strategy performs random sampling in the vicinity of their values ​​to generate offspring parameter combinations. The sampling range is limited to a local region near the initial candidate parameter solutions, without global sampling. Subsequently, by evaluating the predicted values ​​of the effective proliferation coefficient Keff corresponding to the offspring parameter combinations, excellent offspring are selected and the parent parameters are updated. Through multiple iterations, the parent parameters continuously move to better positions within the advantageous region, further focusing on the core advantageous region of the parameter space, ultimately generating the candidate parameter solutions for this step.

[0087] The candidate parameter solutions are used as the initial state of the proximal policy optimization algorithm. A Markov decision process is constructed, and a parameter adjustment strategy is learned. Fine-grained policy iteration is performed by maximizing the reward function to generate multiple sets of candidate parameter solutions. Alternatively, the candidate parameter solutions generated by the evolutionary strategy are used as the initial state of the proximal policy optimization algorithm, allowing the algorithm to start its policy learning from high-quality parameter points within the core advantage region of the parameter space, rather than starting from a random initial state. Based on this initial state, a Markov decision process is constructed, and a reward function is set that is related to the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff. The proximal policy optimization algorithm aims to maximize the reward value and performs fine-grained parameter adjustment strategy iteration. A gradual adjustment method is adopted during policy updates to limit the magnitude of each policy update, ensuring the stability of policy learning. Through multiple rounds of fine-grained iteration, multiple sets of candidate parameter solutions are finally generated.

[0088] Furthermore, as another specific implementation step for using a pre-defined hybrid optimization algorithm to globally explore the parameter space of the nuclear facility, this method is based on the idea of ​​ensemble learning, dynamically allocating weights and search resources according to the historical performance of the algorithms, and realizing adaptive collaborative exploration of each algorithm. The following is a detailed explanation of each step.

[0089] The search parameters for the proximal policy optimization algorithm, genetic algorithm, and evolutionary strategy are initialized. Each algorithm uses the differentiable surrogate model as its objective function and minimizes the absolute error between the predicted effective multiplication coefficient Keff value and the target value as its optimization objective. They then conduct an initial independent exploration of the nuclear facility parameter space in parallel, outputting the first round of candidate parameter solutions and corresponding quantitative indicators of algorithm performance for each algorithm. First, the core search parameters for the proximal policy optimization algorithm, genetic algorithm, and evolutionary strategy are initialized. For the proximal policy optimization algorithm, parameters such as learning rate and policy update step size are initialized; for the genetic algorithm, parameters such as population size, crossover probability, and mutation probability are initialized; and for the evolutionary strategy, parameters such as sampling range and perturbation amplitude are initialized, putting each algorithm in a runnable initial state. Each algorithm uses the differentiable surrogate model as its objective function and minimizes the absolute error between the predicted effective multiplication coefficient Keff value and the target value as its optimization objective, maintaining consistency with the overall parameter optimization objective. Subsequently, each algorithm conducts an initial independent exploration of the nuclear facility parameter space in parallel, generating its own first round of candidate parameter solutions. Meanwhile, multi-dimensional quantitative indicators of algorithm performance are set for each algorithm. These indicators may include the fitness value of candidate parameter solutions, parameter space exploration coverage, solution convergence rate, local optimum avoidance ability, etc. Based on the first round of exploration results of each algorithm, the quantitative indicators of algorithm performance corresponding to each algorithm are calculated and output to provide data basis for subsequent weight allocation.

[0090] A dynamic weight allocation model for algorithms is constructed, using the historical search performance metrics of each algorithm as input. Based on predefined weight calculation rules, dynamic search weights are assigned to each algorithm. This model is a multi-input, single-output mapping model. The inputs are the historical search performance metrics of each algorithm, including data from the first and subsequent rounds of exploration. The output is the dynamic search weight corresponding to each algorithm. Predefined weight calculation rules follow the principle that the better the algorithm's performance, the greater its weight. Specifically, algorithms with higher fitness values ​​for candidate parameter solutions, wider parameter space exploration coverage, faster convergence rates, and stronger local optimum avoidance capabilities will have larger dynamic search weights, while ensuring that the sum of the dynamic search weights of all algorithms is 1. The historical search performance metrics of each algorithm are input into this model. Based on the predefined weight calculation rules, the model assigns corresponding dynamic search weights to proximal strategy optimization algorithms, genetic algorithms, and evolutionary strategies. These weights are continuously updated as the algorithm's exploration progresses.

[0091] Based on dynamic search weights, the search resources in the kernel facility parameter space for each algorithm are dynamically allocated. These resources include the number of parameter sampling iterations, the number of iteration rounds, and the search region. Simultaneously, the number of candidate solutions generated by each algorithm is determined according to its weight proportion. The dynamic search weights of each algorithm are directly correlated with the search resources in the kernel facility parameter space. The search resources for each algorithm are dynamically allocated based on the weight, specifically including the number of parameter sampling iterations, iteration rounds, and search region. Algorithms with higher dynamic search weights are allocated more parameter sampling iterations, more iteration rounds, and a wider search region, allowing better-performing algorithms to obtain more exploration resources and conduct more thorough exploration in the parameter space. Furthermore, the number of candidate solutions generated by each algorithm is determined based on its dynamic search weight proportion; algorithms with higher weight proportions generate more candidate solutions, ensuring that better-performing algorithms occupy a higher proportion in the final candidate solution set.

[0092] A new round of parameter space exploration is initiated, outputting candidate parameter solutions with corresponding weight proportions. All candidate parameter solutions generated by the algorithms are deduplicated and screened for non-dominated solutions, eliminating duplicate solutions and parameter combinations inferior to existing solutions, forming multiple sets of candidate parameter solutions. Each algorithm, based on the allocated search resources and the determined number of candidate parameter solutions generated, conducts a new round of core facility parameter space exploration. During the exploration process, each algorithm remains in parallel and independent, ultimately outputting candidate parameter solutions matching its own weight proportion. The new round of candidate parameter solutions generated by each algorithm are integrated, and two core post-processing operations are performed: first, deduplication, eliminating duplicate parameter combinations to avoid redundant solutions affecting the efficiency of subsequent gradient-assisted local optimization; second, non-dominated solution screening, using preset evaluation criteria to eliminate parameter combinations inferior to existing solutions, retaining only non-dominated solutions. After deduplication and non-dominated solution screening, multiple sets of high-quality candidate parameter solutions are finally formed for subsequent gradient-assisted local optimization.

[0093] In summary, the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration in the above embodiments of the present invention obtains the combination of nuclear facility parameters of the nuclear facility to be analyzed, calls the Monte Carlo calculation program to perform high-fidelity calculation to obtain the corresponding Keff value and constructs a training set, and uses a feedforward neural network combined with the backpropagation algorithm to train the training set to form a differentiable surrogate model that can predict Keff value and gradient information; using the differentiable surrogate model as the objective function and minimizing the absolute error between the predicted Keff value and the target value as the optimization objective, a preset hybrid optimization algorithm is used to globally explore the nuclear facility parameter space to generate multiple sets of candidate parameter solutions, and then the gradient of the Keff value with respect to the input parameters is calculated based on the differentiable surrogate model. The gradient is used to perform auxiliary local optimization on the candidate parameter solutions to obtain the optimal parameter combination candidate solution; finally, the candidate solution is input into the Monte Carlo calculation program again for high-fidelity calculation verification, and if the error is lower than the threshold, it is taken as the final parameter combination solution. By replacing most of the repetitive Monte Carlo high-fidelity calculations with a differentiable surrogate model, the number of time-consuming computation calls is significantly reduced. At the same time, by combining the global exploration capability of the hybrid optimization algorithm with the local optimization accuracy of gradient assistance, the computational efficiency of parameter optimization is guaranteed, and the accuracy of the optimization results is ensured through the final verification of the Monte Carlo program. Furthermore, the collaboration of multiple algorithms avoids the problem of a single algorithm being prone to local optima, realizing automated parameter optimization. This effectively solves the problem that existing technologies cannot balance computational efficiency and accuracy in nuclear critical safety parameter optimization.

[0094] Example 3

[0095] Please see Figure 2 The figure shows a parameter optimization system based on a surrogate model and multi-algorithm gradient collaboration proposed in the third embodiment of the present invention. The system includes:

[0096] The acquisition module 100 is used to acquire the nuclear facility equipment to be analyzed, determine the combination of nuclear facility parameters of the nuclear facility equipment, call the Monte Carlo calculation program to perform high-fidelity calculation on the combination of nuclear facility parameters, and obtain the effective multiplication coefficient Keff value corresponding to the parameter combination to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value.

[0097] The training module 200 is used to train the training set using a feedforward neural network combined with a backpropagation algorithm to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information.

[0098] The search module 300 is used to perform a global exploration of the nuclear facility parameter space using a differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective. It generates multiple sets of candidate parameter solutions by using a preset hybrid optimization algorithm.

[0099] The optimization module 400 is used to calculate the gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters based on the differentiable surrogate model, and to use the gradient to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution;

[0100] The calculation module 500 is used to input the candidate solution of the optimal parameter combination into the Monte Carlo calculation program again for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is less than the threshold, the candidate solution of the optimal parameter combination is used as the final parameter combination solution.

[0101] The functions or operation steps implemented by the above modules are largely the same as those in the above method embodiments, and will not be repeated here.

[0102] Example 4

[0103] In another aspect, the present invention provides a readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps of the method described in any one of Embodiments 1 to 2 above.

[0104] Example 5

[0105] In another aspect, the present invention provides an electronic device, the electronic device including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of any one of the methods described in Embodiments 1 to 2 above.

[0106] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0107] Those skilled in the art will understand that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequential list of executable instructions for implementing logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable storage medium" can mean any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0108] More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable storage media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0109] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0110] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0111] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A parameter optimization method based on a proxy model and a multi-algorithm gradient collaboration, characterized in that, The method includes: The nuclear facility equipment to be analyzed is obtained, and the combination of nuclear facility parameters of the nuclear facility equipment is determined. The Monte Carlo calculation program is called to perform high-fidelity calculation on the combination of nuclear facility parameters to obtain the effective multiplication coefficient Keff value corresponding to the parameter combination in order to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value. A feedforward neural network combined with a backpropagation algorithm is used to train the training set to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information. Using a differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective, a pre-defined hybrid optimization algorithm is used to globally explore the parameter space of the nuclear facility and generate multiple sets of candidate parameter solutions. The gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters is calculated based on the differentiable surrogate model. The gradient is then used to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution. The candidate solution of the optimal parameter combination is input into the Monte Carlo calculation program again for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is less than the threshold, the candidate solution of the optimal parameter combination is taken as the final parameter combination solution. The step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions further includes: Initialize the search parameters of the proximal strategy optimization algorithm, genetic algorithm, and evolutionary strategy. Each algorithm takes the differentiable surrogate model as the objective function and minimizes the absolute error between the effective multiplication coefficient Keff value and the objective value as the optimization objective. They conduct the first round of independent exploration of the nuclear facility parameter space in parallel and output the first round of candidate parameter solutions of each algorithm and the corresponding quantitative indicators of algorithm performance. A dynamic weight allocation model for algorithms is constructed, and the historical search performance quantification indicators of each algorithm are used as input to the model. Dynamic search weights are assigned to each algorithm according to the preset weight calculation rules. Based on dynamic search weights, the core facility parameter space search resources of each algorithm are dynamically allocated. The search resources include the number of parameter sampling times, the number of iteration rounds, and the search area range. At the same time, the number of candidate parameter solutions generated by each algorithm is determined according to the weight ratio. A new round of parameter space exploration is carried out to output candidate parameter solutions with corresponding weight ratios. All candidate parameter solutions generated by the algorithm are deduplicated and non-dominated, and duplicate solutions and parameter combinations that are inferior to existing solutions are eliminated to form multiple sets of candidate parameter solutions.

2. The parameter optimization method based on agent model and multi-algorithm gradient cooperation according to claim 1, characterized in that, The formula for calculating the gradient of the input nuclear facility parameters is: ； wherein, is the input nuclear facility parameter, is the predicted value of the effective multiplication factor Keff value output by the differentiable agent model.

3. The parameter optimization method based on agent model and multi-algorithm gradient cooperation according to claim 2, characterized in that, The formula for calculating the optimal parameter combination candidate solution by using gradient to perform auxiliary local optimization on multiple sets of candidate parameter solutions is as follows: ； wherein, is the locally optimized optimal parameter combination candidate solution, is the current candidate parameter solution, is the adaptively adjusted gradient step.

4. The parameter optimization method based on agent model and multi-algorithm gradient cooperation according to claim 1, characterized in that, The step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions includes: The nuclear facility parameter optimization problem is constructed as a Markov decision process. A proximal policy optimization algorithm is used to learn the parameter adjustment strategy. A reward function is set for the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff. The parameter adjustment strategy is updated iteratively by maximizing the reward value. A gradual adjustment method is adopted in the policy update process to limit the magnitude of a single policy update, and candidate parameter solutions are obtained. A genetic algorithm is used to simulate the natural selection mechanism. Through selection, crossover, and mutation operations, the combination of nuclear facility parameters is iterated to screen candidate parameter solutions. An evolutionary strategy is adopted to randomly sample near the current parameter point to generate offspring parameter combinations. By evaluating the predicted value of the effective proliferation coefficient Keff value corresponding to the offspring parameter combinations, excellent offspring are selected and the parent parameters are updated. The candidate parameter solutions are obtained by gradually approaching the dominant region in the parameter space. The candidate parameter solution sets generated by each algorithm are collaboratively screened. Using a preset fitness evaluation index, the best-performing combination of parameters is selected from the candidate solutions of each algorithm to form a unified candidate parameter solution set.

5. The parameter optimization method based on surrogate model and multi-algorithm gradient collaboration according to claim 1, characterized in that, The step of using a preset hybrid optimization algorithm to globally explore the nuclear facility parameter space and generate multiple sets of candidate parameter solutions further includes: A genetic algorithm is used to perform a global coarse search of the nuclear facility parameter space. Through selection, crossover, and mutation operations, an iterative evolution is performed to generate a batch of initial candidate parameter solutions covering the main dominant regions of the parameter space. The generated initial candidate parameter solutions are used as the initial parent parameters of the evolutionary strategy. Random sampling and offspring selection are performed in their vicinity to focus on the dominant region and generate candidate parameter solutions. The candidate parameter solutions are used as the initial state of the proximal policy optimization algorithm. A Markov decision process is constructed and a parameter adjustment policy is learned. The policy is refined by maximizing the reward function to generate the final multiple sets of candidate parameter solutions.

6. The parameter optimization method based on surrogate model and multi-algorithm gradient collaboration according to claim 1, characterized in that, The method further includes: If the absolute error between the actual effective multiplication coefficient Keff value and the target effective multiplication coefficient Keff value exceeds a preset threshold, the corresponding optimal parameter combination candidate solution and the corresponding effective multiplication coefficient Keff value will be added to the training set, and the differentiable surrogate model will be retrained.

7. A parameter optimization system based on a surrogate model and multi-algorithm gradient collaboration, characterized in that, The system is used to implement the parameter optimization method based on surrogate model and multi-algorithm gradient collaboration as described in any one of claims 1 to 6, the system comprising: The acquisition module is used to acquire the nuclear facility equipment to be analyzed, determine the combination of nuclear facility parameters of the nuclear facility equipment, call the Monte Carlo calculation program to perform high-fidelity calculation on the combination of nuclear facility parameters, and obtain the effective multiplication coefficient Keff value corresponding to the parameter combination to construct a training set composed of the combination of nuclear facility parameters and the corresponding effective multiplication coefficient Keff value; The training module is used to train the training set using a feedforward neural network combined with the backpropagation algorithm to form a differentiable surrogate model that predicts the effective multiplication coefficient Keff value and gradient information. The search module is used to explore the nuclear facility parameter space globally using a differentiable surrogate model as the objective function and minimizing the absolute error between the predicted value and the target value of the effective multiplication coefficient Keff as the optimization objective. It generates multiple sets of candidate parameter solutions by using a preset hybrid optimization algorithm. The optimization module is used to calculate the gradient of the effective multiplication coefficient Keff value with respect to the input nuclear facility parameters based on the differentiable surrogate model, and to use the gradient to perform auxiliary local optimization on the generated multiple sets of candidate parameter solutions to obtain the optimal parameter combination candidate solution; The calculation module is used to input the candidate solution of the optimal parameter combination into the Monte Carlo calculation program again for high-fidelity calculation to obtain the true effective proliferation coefficient Keff value. If the absolute error between the true effective proliferation coefficient Keff value and the target effective proliferation coefficient Keff value is less than the threshold, the candidate solution of the optimal parameter combination is used as the final parameter combination solution.

8. A readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor, when executing the program, implements the steps of the method as described in any one of claims 1 to 6.

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