论文标题
基于微麦克罗分解的模型数据渐近传播神经网络方法，用于灰色辐射转移方程
A model-data asymptotic-preserving neural network method based on micro-macro decomposition for gray radiative transfer equations
论文作者
论文摘要
我们提出了一种模型数据渐近保护神经网络（MD-APNN）方法，以求解非线性灰色辐射转移方程（GRTES）。由于多尺度的特征，该系统既可以通过传统的数值方案和香草物理信息的神经网络（PINN）进行模拟具有挑战性。在PINN的框架下，我们采用微型麦克罗分解技术来构建一种新的渐近性抛光（AP）损耗函数，其中包括微型麦克罗耦合形式中管理方程的剩余，初始和边界条件，具有其他扩散限制信息，保护法，保存法和一些标记的数据。为提出的方法进行了收敛分析，并提供了许多数值示例，以说明MD-APNN的效率，尤其是AP特性在神经网络中对于扩散问题的重要性。数值结果表明，在非线性非稳态GRTE的模拟中，MD-APNN与APNN或纯数据驱动网络相比，MD-APNN的性能更好。
We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks(PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving(AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure data-driven networks in the simulation of the nonlinear non-stationary GRTEs.
