用神经算子加速中子输运计算,精度高且快百倍以上。
Surrogate Modeling for Neutron Transport: A Neural Operator Approach
- 用DeepONet和FNO学习源到通量的映射关系,适配不同散射比场景。
- 在未见源配置上预测准确,速度比传统方法快99.7%以上。
- 可嵌入核反应堆求解器,适合设计优化等需快速迭代的任务。
本文提出基于神经算子的中子输运代理建模框架。采用Deep Operator Network(DeepONet)与Fourier Neural Operator(FNO)训练固定源问题,学习各向异性中子源Q(x,μ)到角通量ψ(x,μ)的映射,适用于一维平板几何。针对三种散射比(c = 0.1, 0.5, 1.0)分别训练模型,覆盖吸收主导、中等及散射主导的输运状态。在大量未见过的源配置下评估,FNO预测精度更高,DeepONet计算更高效。两者均实现显著加速,在高散射比下耗时不足传统S_N求解器的0.3%。将模型嵌入S_N k-有效值求解器,替代耗时的输运扫掠循环,仅需一次前向传播。在不同裂变截面与空间-角网格下,两种神经算子求解器的参考有效值偏差分别为≤135 pcm(DeepONet)和≤112 pcm(FNO),运行时间低于原S_N求解器的0.1%。结果表明神经算子框架可作为精确、高效、泛化性强的中子输运代理模型,为实时数字孪生与设计优化中的重复评估提供可能。
原文摘要 · Abstract (English)
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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