【摘要】 神经网络可以基于大量数据学习输入输出变量之间的关系，具有强大的拟合能力，在包括核工程计算领域常用作程序的代理模型。中子输运计算作为中子学模拟的核心环节之一，其耗时较长的问题可以利用神经网络模型来解决。然而，神经网络模型具有一系列超参数需要设置，而手动调节这些超参数工作量大，重复繁琐，只能依靠经验进行，而且求解不同问题时这些超参数不可复用。为了解决以上问题，本文提出了一种采用贝叶斯优化（Bayesian Optimization）的算法来调节神经网络超参数，结合了自适应学习率衰减、损失函数优化方法，它可以针对不同问题的数据集，自动搜索超参数的最佳组合，以获得最佳性能，具有很高的灵活性和效率，泛化性强。本文对TAKEDA基准题得到的堆芯关键参数进行拟合，数据集由VITAS程序计算TAKEDA1、2基准题得出，分别为10 000与20 000组，输入为堆芯排布顺序，输出为有效增殖因数k_eff和区域积分通量φ，并将堆芯排布顺序映射为一维向量，以6∶4的比例划分为训练集和验证集。将手动设置的超参数及贝叶斯优化输出的超参数作为神经网络训练参数进行了实验比较，结果表明：贝叶斯优化有效地提升了神经网络的精度，有效增殖因数k_eff的平均误差在1.50×10^-3以内，TAKEDA1数据集上区域积分通量φ的平均误差率为1.72%，最大误差率为7.56%。该研究可为人工智能在堆芯物理计算理论的应用提供一定参考。更多还原

【Abstract】 [Background] Neural networks, with their powerful fitting capabilities, can learn the relationships between input and output variables based on large amounts of data, often serve as proxy models for physical programs in the field of engineering calculations, including nuclear engineering calculations. Neutron transport calculations, as one of the core links in neutronics simulations, are often suffer from lengthy computational times. However, this issue can also be addressed by utilizing neural network models. Nevertheless, neural network models have a series of hyperparameters that need to be set, but manually adjusting these hyperparameters is laborious, repetitive, and reliant only on experience. Moreover, these hyperparameters are not reusable when solving different problems. [Purpose] This study aims to propose a novel algorithm to improve computational efficiency of core neutronic parameter prediction, and provide reference for the application of artificial intelligence in core physics calculation. [Methods] The dataset was derived from the VITAS program’s calculations of the TAKEDA1 and TAKEDA2 benchmark problems, consisting of 10 000 and 20 000 sets respectively. The core layout sequence was taken as input whilst the output included the effective multiplication factor and the regional integral flux. Thereafter, the core layout sequence was mapped into a one-dimensional vector, and the dataset was divided into training and validation sets in a 6: 4 ratio. Then, the Bayesian optimization algorithm was employed to adjust fully connected neural network（FCNN） hyperparameters, and the adaptive learning rate decay and loss function optimization methods were combined to automatically search for the optimal combination of hyperparameters for datasets with different problems. Finally, critical core parameters, i.e., the effective multiplication factor and the regional integrated flux, were fitted to valid the generalization and accuracy of abovementioned algorithm, and a comparative experiment was conducted using manually set hyperparameters and hyperparameters output by Bayesian optimization as neural network training parameters. [Results] The results demonstrate that Bayesian optimization effectively enhances the neural network’s accuracy. Specifically, the average error of the effective multiplication factor is within 1.50×10^-3, while that of the regional integral flux on the TAKEDA1 dataset is 1.72%, with a maximum error rate of 7.56%. [Conclusions] This approach can automatically search for the optimal combination of hyperparameters for different datasets to achieve the best performance, demonstrating high flexibility, efficiency, and strong generalization.更多还原