The radiative transfer equation (RTE) is an integro-differential equation and solving it is time-consuming except in a few specific cases. A fast method based on dynamic mode decomposition (DMD) is introduced for solving the RTE in an absorbing-emitting and scattering medium. First, some parameters are considered as independent variables. The RTE is solved for different values of these parameters (known input vectors) using the discrete ordinates method ($S_6$ approximation), and the system responses generate the snapshot matrix. Then using the DMD technique, the dynamic modes are constructed, so the degree of freedom of the system is decreased. The reduced-order model (ROM), called DMD-RBF, is generated by combining the DMD and the radial basis functions. Two cases, radiative equilibrium and medium with known temperature (isothermal and non-isothermal), are considered. The accuracy of the model is investigated using random input vectors. The results show that the DMD-RBF has a good agreement with the numerical solutions. Comparison between the ROM and numerical CPU times shows the high efficiency of the ROM. The results also show that the problem complexity does not affect the computational cost. For all cases, the CPU time of the ROM is of the order of 0.01 seconds.

辐射传递方程 (RTE) 是一个积分微分方程，求解它非常耗时，除了少数特定情况。介绍了一种基于动态模态分解（DMD）的快速方法来求解吸收发射和散射介质中的RTE。首先，一些参数被认为是自变量。RTE 使用离散坐标法求解这些参数（已知输入向量）的不同值（${\mathrm{小号}}_6$近似），系统响应生成快照矩阵。然后利用DMD技术构造动态模态，降低了系统的自由度。通过组合 DMD 和径向基函数生成称为 DMD-RBF 的降阶模型 (ROM)。考虑了两种情况，辐射平衡和已知温度的介质（等温和非等温）。使用随机输入向量来研究模型的准确性。结果表明，DMD-RBF与数值解具有良好的一致性。ROM 和数值 CPU 时间的比较显示了 ROM 的高效率。结果还表明，问题的复杂性不影响计算成本。对于所有情况，ROM 的 CPU 时间大约为 0.01 秒。