Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
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DOI：
10.1016/j.jcp.2022.110941
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Juntao Huang;Yingda Cheng;A. Christlieb;L. Roberts
中科院分区：
文献类型：
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作者：
Juntao Huang;Yingda Cheng;A. Christlieb;L. Roberts
在本文中，我们采取数据驱动的方法，并将机器学习应用于板几何中的辐射传输方程的矩封闭问题。我们提出用神经网络直接学习高阶矩的梯度，而不是学习未闭合的高阶矩。这种新方法与我们针对自由流限制推导出的精确闭包一致，并且还提供了自然的输出归一化。各种基准测试，包括变量散射问题，具有周期性和反射边界的高斯源问题，以及两种材料问题，都显示了我们的机器学习闭合模型的良好准确性和可推广性。
In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for the radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. A variety of benchmark tests, including the variable scattering problem, the Gaussian source problem with both periodic and reflecting boundaries, and the two-material problem, show both good accuracy and generalizability of our machine learning closure model.