用神经算子快速估算二维中子通量，提升屏蔽设计效率。
Neural Operator Surrogates for Two-Dimensional Neutron Flux Estimation
- 采用FNO和UNO神经算子直接映射材料与源场到通量分布。
- 引入单次迭代通量作为额外输入，使误差降低27%以上。
- 对通量取对数训练，显著改善强衰减区域的预测精度。
本研究将一维单次扫描神经算子方法扩展至二维情形，考虑单群各向同性散射中子输运问题。采用傅里叶神经算子（FNO）和U型神经算子（UNO）近似高保真标量通量。构建三种代理模型：前两种直接从材料与源场映射通量（分别使用FNO与UNO），第三种FNO额外输入一次源迭代后的标量通量（即单次扫描近似）。所有案例均通过验证过的离散坐标求解器达到高保真度，以平均相对L₂误差范数评估映射质量。每种模型在三个随机种子下训练，以评估运行间差异。研究聚焦两个问题：单次扫描输入是否提升精度；对通量取对数训练是否改善强衰减区域表现。结果表明，引入单次扫描输入可使平均误差降低27%以上，且对数训练在屏蔽关键区域显著提升预测准确性。
原文摘要 · Abstract (English)
This work extends our one-dimensional single-sweep neural-operator studies to two dimensions. We consider one-group transport with isotropic scattering. As in the one-dimensional work, we use Fourier neural operators (FNOs) to approximate the high-fidelity scalar flux. Additionally, we also investigate U-shaped neural operators (UNOs) in this study. We consider three surrogates. The first two map the material and source fields directly to the flux, one using an FNO and one using a UNO. The third is an FNO that additionally takes the scalar flux after one source iteration, the single-sweep approximation, as an input. Each case is solved to high fidelity with a verified discrete-ordinates solver, and an average relative L_2 error norm is used to characterize the quality of the inferred maps. We train every surrogate over three random seeds so that differences between them can be assessed against run-to-run variability. Two questions guide the study: whether the single-sweep input improves accuracy over the direct maps, and whether training on the logarithm of the flux improves accuracy in the strongly attenuated regions relevant to shielding.
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