用于二维中子通量估计的神经算子替代模型
Neural Operator Surrogates for Two-Dimensional Neutron Flux Estimation
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中文总结 AI 辅助
研究将一维单扫描神经算子研究扩展到二维，考虑单群输运，用傅里叶神经算子等近似标量通量，构建三种替代模型，通过离散坐标求解器求解并评估，探讨单扫描输入及通量对数训练对准确性的影响。
中文摘要 AI 辅助
本工作将一维单扫描神经算子研究扩展到二维。考虑具有各向同性散射的单群输运。与一维工作一样，使用傅里叶神经算子（FNO）来近似高保真标量通量，还研究了U形神经算子（UNO）。考虑三种替代模型，前两种将材料和源场直接映射到通量，分别使用FNO和UNO，第三种FNO还将一次源迭代后的标量通量（单扫描近似）作为输入。每种情况都用经过验证的离散坐标求解器求解到高保真度，并用平均相对L_2误差范数表征推断映射的质量。在三个随机种子上训练每个替代模型以评估差异。研究由两个问题指导：单扫描输入是否比直接映射提高准确性，以及在与屏蔽相关的强衰减区域中对通量对数进行训练是否提高准确性。
英文摘要
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.
