基于PINN的源迭代法求解及加速算法研究

江勇; 安萍; 刘东; 于洋

doi:10.13832/j.jnpe.2024.090040

基于PINN的源迭代法求解及加速算法研究

doi: 10.13832/j.jnpe.2024.090040

中国核动力研究设计院核反应堆技术全国重点实验室，成都，610213

基金项目: 四川省自然科学基金（2023NSFSC0066、2023NSFSC1321）；四川省揭榜挂帅行业共性技术攻关项目（23jBGOV0001)；国家基础性科研院所基础科研稳定支持专项资助项目（WDZC-2023-05-03-05)

详细信息

作者简介:
江　勇（1998—），男，硕士，助理工程师，现主要从事反应堆智能数值计算与工业软件研究，E-mail: 2229602945@qq.com

通讯作者:
安　萍，E-mail: anpingwork@126.com

中图分类号: TL32
计量
- 文章访问数: 29
- HTML全文浏览量: 11
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2024-09-16
- 修回日期: 2024-12-22
- 网络出版日期: 2025-01-15
- 刊出日期: 2025-04-02

Research on the Solution and Acceleration Algorithm of Source Iteration Method Based on PINN

National Key Laboratory of Nuclear Reactor Technology, Nuclear Power Institute of China, Chengdu, 610213, China

摘要

摘要: 本文将基于物理驱动的人工智能方法和传统源迭代法结合，建立求解少群扩散方程的新型方法流程，并采用Anderson加速方法对迭代源项进行加速。二维多材料、三维单材料等例题的计算结果显示，基于物理驱动的物理信息神经网络（PINN）和传统源迭代法相结合，在保证计算精度的前提下可计算出连续中子注量率分布，采用Anderson加速可减少迭代次数，成功实现了少群中子扩散方程的正向求解，助推了人工智能算法在核领域的应用。
- 物理信息神经网络（PINN） /
- Anderson加速 /
- 源迭代 /
- 中子扩散方程
Abstract: This paper integrates physics-driven artificial intelligence methods with the traditional source iteration method to establish a novel approach for solving the few-group diffusion equations, and employs the Anderson acceleration method to accelerate the iterative source term. The results of numerical examples such as two-dimensional multi material and three-dimensional single material show that the combination of physics-driven Physics-Informed Neural Networks (PINN) and traditional source iteration method can calculate the continuous neutron flux density distribution while ensuring calculation accuracy. The use of Anderson acceleration method can reduce the number of iteration, ssuccessfully achieving the forward solution of the few-group neutron diffusion equations. This advancement promotes the application of artificial intelligence algorithms in the nuclear field.
- PINN /
- Anderson acceleration /
- Source iteration /
- Neutron diffusion equation

HTML全文

图 1 MSIDL方法流程图

Figure 1. Flowchart of the MSIDL Method

下载: 全尺寸图片幻灯片

图 2 材料区域几何描述

Figure 2. Geometric Description of Material Area

下载: 全尺寸图片幻灯片

图 3 源迭代与深度学习结合方法验证结果图

Figure 3. Verification Results of the Combination of Source Iteration and Deep Learning Method

下载: 全尺寸图片幻灯片

图 4 材料区域几何描述　cm

Figure 4. Geometric Description of Material Area

下载: 全尺寸图片幻灯片

图 5 源迭代与深度学习结合方法验证结果图

Figure 5. Verification Results of the Combination of Source Iteration and Deep Learning Method

下载: 全尺寸图片幻灯片

图 6 源迭代与深度学习结合方法验证结果图

Figure 6. Verification Results of the Combination of Source Iteration and Deep Learning Method

下载: 全尺寸图片幻灯片

表 1 计算区域材料特性

Table 1. Material Characteristics of Area

材料号	能群g	D/cm	$ {{\varSigma }}_{\mathrm{a}} $/cm⁻¹	$ \vartheta {{\varSigma }}_{\mathrm{f}} $/cm⁻¹	$ {{\varSigma }}_{1\to 2} $/cm⁻¹
1	1	1.2550	0.008252	0.004602	0.02533
1	2	0.2110	0.100300	0.109100	0.02533
2	1	1.2680	0.007181	0.004609	0.02767
2	2	0.1902	0.070470	0.086750	0.02767
3	1	1.2590	0.008002	0.004663	0.02617
3	2	0.2091	0.083440	0.102100	0.02617
4	1	1.2590	0.008002	0.004663	0.02617
4	2	0.2091	0.073324	0.102100	0.02617

下载: 导出CSV

表 2 二维矩形几何多群两材料计算结果

Table 2. Multi-group Two-material Calculation Results for the 2D Rectangular Geometry

方法	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_net	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_cor	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $相对误差	外迭代次数	MSE₁	MSE₂	Loss1	Loss2
MSIDL	0.8273	0.8378	0.0125	300	7.9462×10⁻⁴	6.1047×10⁻⁴	0.1912	0.0766
MSIDL+AA1	0.8299		0.0094	132	1.1700×10⁻²	2.7256×10⁻³	0.3626	0.0826
MSIDL+AA2	0.8294		0.0100	288	8.2466×10⁻⁴	4.7734×10⁻⁴	0.1376	0.0699

下载: 导出CSV

表 3 二维多材料计算结果

Table 3. Numerical Results of Two-dimensional Examples with Multi-material

方法	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_net	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_cor	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $相对误差	外迭代次数	MSE₁/10⁻³	MSE₂/10⁻³	Loss1	Loss2
MSIDL	0.7854	0.7957	0.0129	29	4.6841	3.3315	0.3140	0.3340
MSIDL+AA1	0.8001		0.0055	16	5.0547	3.5475	0.3270	0.3526
MSIDL+AA2	0.7869		0.0111	18	4.1098	3.4594	0.3236	0.4118

下载: 导出CSV

表 4 三维单材料计算结果

Table 4. Numerical Results of Three-dimensional Examples with Single-material

方法	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_net	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_cor	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $相对误差	外迭代次数	MSE₁	MSE₂	Loss1	Loss2
MSIDL	0.7808	0.8132	0.0398	48	0.0506	0.0100	0.0554	0.0219
MSIDL+AA1	0.7872		0.0320	33	0.0821	0.0159	0.0565	0.0241
MSIDL+AA2	0.7962		0.0209	44	0.0528	0.0107	0.0578	0.0201

下载: 导出CSV

表 5 高精度情况下二维两材料计算结果

Table 5. High-Accuracy Numerical Results of Two-dimensional Examples with Two-material

方法	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_net	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $_cor	$ {k}_{\mathrm{e}\mathrm{f}\mathrm{f}} $相对误差	外迭代次数	MSE₁/10⁻⁴	MSE₂/10⁻⁴	Loss1/10⁻³	Loss2/10⁻⁴
MSIDL	0.8451	0.8378	0.0087	153	9.5664	4.2012	1.3262	3.9391
MSIDL+AA1	0.8434	0.8378	0.0067	127	8.1504	3.4201	0.9824	3.1263

下载: 导出CSV

参考文献(14)

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