  In this paper, we take a data-driven approach and apply machine learning to
the moment closure problem for 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.
