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蒙特卡罗方法是求解粒子输运问题的有力工具之一, 其局限性在于为达到精度要求需模拟大量粒子, 计算耗时长, 这阻碍了该方法的进一步应用, 尤其在需快速响应的情形. 本文结合神经网络和若干蒙特卡罗方法基本原理发展了一种计算方法, 能够实现源分布可变, 几何、材料和目标计数不变的中子输运问题的快速准确求解. 首先, 为高效生成用于神经网络训练的数据, 利用重要性原理实现在同样模拟次数基础上有效扩充训练数据集容量, 在一定程度上克服了使用蒙特卡罗计算获取训练数据耗时长的缺点. 进而, 基于目标计数是源分布与重要性函数乘积积分的事实, 设计了利用神经网络实现快速输运计算的策略. 该网络的输入是中子源项, 输出是目标计数, 在几何、材料和目标计数固定的情况下, 该神经网络可重复使用, 根据新的源项快速准确得到目标计数. 本文所提出方法的原理和框架同样适用于其他种类粒子的同类型输运问题. 基于若干基准模型的验证表明, 训练得到的神经网络能在不到1 s的时间内得到目标计数, 且与蒙特卡罗大样本模拟得到基准结果的平均相对偏差均低于5%.Monte Carlo (MC) method is a powerful tool for solving particle transport problems. However, it is extremely time-consuming to obtain results that meet the specified statistical error requirements, especially for large-scale refined models. This paper focuses on improving the computational efficiency of neutron transport simulations. Specifically, this study presents a novel method of efficiently calculating neutron fixed source problems, which has many applications. This type of particle transport problem aims at obtaining a fixed target tally corresponding to different source distributions for fixed geometry and material. First, an efficient simulation is achieved by treating the source distribution as the input to a neural network, with the estimated target tally as the output. This neural network is trained with data from MC simulations of diverse source distributions, ensuring its reusability. Second, since the data acquisition is time consuming, the importance principle of MC method is utilized to efficiently generate training data. This method has been tested on several benchmark models. The relative errors resulting from neural networks are less than 5% and the times needed to obtain these results are negligible compared with those for original Monte Carlo simulations. In conclusion, in this work we propose a method to train neural networks, with MC simulation results containing importance data and we also use this network to accelerate the computation of neutron fixed source problems.
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变量 范围 网格尺寸 网格数目 X/Y/Z –3—3 cm 0.2 cm 30 E 9—10 MeV 0.2 MeV 10 U 1.04—2.05 rad 0.2 rad 5 W 1.04—2.05 rad 0.2 rad 5 注:X/Y/Z为相空间网格空间维度在X/Y/Z方向坐标;E为相空间网格能量维度坐标;U/W为相空间网格角度维度在极角和方位角的坐标 
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变量 范围 网格尺寸 网格数目 X/Y/Z –10.1—10.1 cm 0.2 cm 100 E — — — U 0—1.57 rad 0.79 rad 11 W 0—1.57 rad 0.79 rad 11 下载:
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基准题 探测器
位置/cm训练偏差 验证偏差 测试偏差 Kobayashi-1-i (15, 15, 15) 0.0424 0.0458 0.0408 (25, 25, 25) 0.0426 0.0431 0.0442 (35, 35, 35) 0.0473 0.0478 0.0458 (45, 45, 45) 0.0473 0.0483 0.0452 Kobayashi-1-ii (15, 15, 15) 0.0392 0.0401 0.0387 (25, 25, 25) 0.0394 0.0404 0.0364 (35, 35, 35) 0.0402 0.0456 0.0443 (45, 45, 45) 0.0413 0.0455 0.0425 下载:
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基准题 探测器位置/cm 测试偏差 均值 最大值 标准差 < 0.05比例*/% Kobayashi-1-i (15, 15, 15) 0.0408 0.152 0.0078 95.5 (25, 25, 25) 0.0442 0.178 0.0116 94.2 (35, 35, 35) 0.0458 0.214 0.0256 92.6 (45, 45, 45) 0.0452 0.220 0.0250 92.2 Kobayashi-1-ii (15, 15, 15) 0.0387 0.126 0.0106 96.2 (25, 25, 25) 0.0364 0.211 0.0230 95.7 (35, 35, 35) 0.0443 0.245 0.0288 93.4 (45, 45, 45) 0.0425 0.253 0.0298 93.3 注: *预测结果与真值相对偏差小于5%的样本占总测试样本量的比例 下载:
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探测器 测试偏差 均值 最大值 标准差 < 0.05比例* ① 0.0398 0.0826 0.0096 92.3% ② 0.0442 0.0965 0.0132 90.2% *预测结果与真值相对偏差小于5%的样本占总测试样本量的比例 下载:
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