arXiv 2602.158902026-02-07physics.comp-phcs.AIcs.LG

中子输运的替代建模：一种神经算子方法

Surrogate Modeling for Neutron Transport: A Neural Operator Approach

Rensselaer Polytechnic Institute（伦斯勒理工学院）

Md Hossain Sahadath, Qiyun Cheng, Shaowu Pan, Wei Ji

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AI总结：

本研究提出基于神经算子的中子输运替代建模方法，通过DeepONet和FNO两种架构，实现高效且准确的中子输运计算，显著提升计算效率并减少运行时间。

摘要：

本工作介绍了一种基于神经算子的替代建模框架，用于中子输运计算。两种架构，即深度算子网络（DeepONet）和傅里叶神经算子（FNO），被训练用于固定源问题，以学习从各向异性中子源Q(x,μ)到相应角通量ψ(x,μ)的映射，采用一维 slab 几何结构。为每个神经算子训练了三种不同的模型，对应不同的散射比（c=0.1、0.5和1.0），提供了对不同输运领域（吸收主导、中等和散射主导）性能的见解。随后，这些模型在一系列之前未见过的源配置上进行了评估，证明FNO通常在预测准确性方面表现更高，而DeepONet则在计算效率方面更优。两种模型都提供了显著的加速效果，随着散射比的增加，这种加速效果越来越明显，所需运行时间仅为传统S_N求解器的不到0.3%。这些替代模型进一步被纳入S_N k-特征值求解器中，用单次前向传递取代了计算密集型的输运扫描循环。在变化的裂变截面和空间-角网格下，两种神经算子求解器在参考特征值上再现的偏差最高分别为DeepONet 135 pcm和FNO 112 pcm，同时将运行时间减少到传统S_N求解器的不到0.1%（在相对较细的网格上）。这些结果展示了神经算子框架作为准确、高效且通用的替代方案在中子输运中的强大潜力，为实时数字孪生应用和重复评估（如在设计优化中）铺平了道路。

英文摘要：

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source problems to learn the mapping from anisotropic neutron sources, Q(x,μ), to the corresponding angular fluxes, ψ(x,μ), in a one-dimensional slab geometry. Three distinct models were trained for each neural operator, corresponding to different scattering ratios (c = 0.1, 0.5, & 1.0), providing insight into their performance across distinct transport regimes (absorption-dominated, moderate, and scattering-dominated). The models were subsequently evaluated on a wide range of previously unseen source configurations, demonstrating that FNO generally achieves higher predictive accuracy, while DeepONet offers greater computational efficiency. Both models offered significant speedups that become increasingly pronounced as the scattering ratio increases, requiring <0.3% of the runtime of a conventional S_N solver. The surrogate models were further incorporated into the S_N k-eigenvalue solver, replacing the computationally intensive transport sweep loop with a single forward pass. Across varying fission cross sections and spatial-angular grids, both neural operator solvers reproduced reference eigenvalues with deviations up to 135 pcm for DeepONet and 112 pcm for FNO, while reducing runtime to <0.1% of that of the S_N solver on relatively fine grids. These results demonstrate the strong potential of neural operator frameworks as accurate, efficient, and generalizable surrogates for neutron transport, paving the way for real-time digital twin applications and repeated evaluations, such as in design optimization.

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