AI 中文总结
该研究针对辐射传输方程，提出数据驱动的降阶模型框架，分别处理各向同性与各向异性散射介质的情况，通过数值模拟验证了模型的有效性。
AI 中文摘要
我们提出一种针对辐射传输方程（RTE）解的零阶角矩而非全相空间解的数据驱动降阶建模（ROM）框架。该构建基于角平均密度的Peierls积分形式，对于各向同性散射介质，密度满足带全局衰减弱奇异核的第二类Fredholm封闭方程，我们直接投影此方程；对于各向异性散射介质，我们利用平均-波动分解推导基于投影的ROM封闭系统。数值模拟验证了所实现ROM的有效性。
英文摘要
We present a data-driven reduced-order modeling (ROM) framework for the zeroth angular moment of the solution to the radiative transfer equation (RTE) rather than the full phase-space solution. Our construction is based on the Peierls integral formulation of the angularly averaged density. For media with isotropic scattering, the density satisfies a closed second-kind Fredholm equation with a globally attenuated, weakly singular kernel. We project this equation directly. For media with anisotropic scattering, we utilize the average-fluctuation decomposition to derive a closed system for a projection-based ROM. Numerical simulations are presented to illustrate the effectiveness of the ROMs we implemented.
