  In this article, we demonstrate the novel use of Proper Generalized
Decomposition (PGD) to separate the axial and, optionally, polar dimensions of
neutron transport. Doing so, the resulting Reduced-Order Models (ROMs) can
exploit the fact that nuclear reactors tend to be tall, but geometrically
simple, in the axial direction $z$, and so the 3D neutron flux distribution
often admits a low-rank "2D/1D" approximation. Through PGD, this approximation
is computed by alternately solving 2D and 1D sub-models, like in existing 2D/1D
models of reactor physics. However, the present methodology is more general in
that the decomposition is arbitrary-rank, rather than rank-one, and no
simplifying approximations of the transverse leakage are made. To begin, we
derive two original models: that of axial PGD -- which separates only $z$ and
the axial streaming direction $\vartheta\in\{-1,+1\}$ -- and axial-polar PGD --
which separates both $z$ and polar angle $\mu$ from the radial domain.
Additionally, we grant that the energy dependence $E$ may be ascribed to either
radial or axial modes, or both, bringing the total number of candidate 2D/1D
ROMs to six. To assess performance, these PGD ROMs are applied to two few-group
benchmarks characteristic of Light Water Reactors. Therein, we find both the
axial and axial-polar ROMs are convergent and that the latter are often more
economical than the former. Ultimately, given the popularity of 2D/1D methods
in reactor physics, we expect a PGD ROM which achieves a similar effect, but
perhaps with superior accuracy, a quicker runtime, and/or broader
applicability, would be eminently useful, especially for full-core problems.
