辐射传输的最优预测：矩封闭的新视角
Optimal prediction for radiative transfer: A new perspective on moment closure
AI总结：
本文通过将最优预测方法推广到偏微分方程组，为辐射传输方程的矩封闭问题提供了新视角，并重新推导了P_N、扩散和扩散修正等线性封闭。
摘要：
矩方法是经典方法，通过宏观矩方程组近似介观辐射传输方程。角度变量的展开将原始方程转化为无穷多矩的系统。该无穷系统的截断就是矩封闭问题。文献中已提出多种封闭。本文证明，最优预测——一种最初为近似非线性常微分方程组均值解而开发的方法——可用于推导矩封闭。为此，将该形式推广到偏微分方程组。利用高斯测度，可以重新推导现有的线性封闭，如$P_N$、扩散和扩散修正封闭。这为过程中所做的若干近似提供了新视角，并启发了对现有封闭的修改思路。
英文摘要：
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of infinitely many moments. The truncation of this infinite system is the moment closure problem. Many types of closures have been presented in the literature. In this note, we demonstrate that optimal prediction, an approach originally developed to approximate the mean solution of systems of nonlinear ordinary differential equations, can be used to derive moment closures. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, existing linear closures can be re-derived, such as $P_N$, diffusion, and diffusion correction closures. This provides a new perspective on several approximations done in the process and gives rise to ideas for modifications to existing closures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
