  Type-I X-ray burst light curves encode unique information about the structure
of accreting neutron stars and the nuclear reaction rates of the rp-process
that powers bursts. Using the first model calculations of hydrogen/helium
burning bursts for a large range of astrophysical conditions performed with the
code MESA, this work shows that simultaneous model-observation comparisons for
bursts from several accretion rates $\dot{M}$ are required to remove
degeneracies in astrophysical conditions that otherwise reproduce bursts for a
single $\dot{M}$ and that such consistent multi-epoch modeling could possibly
limit the $^{15}\rm{O}(\alpha,\gamma)^{19}\rm{Ne}$ reaction rate. Comparisons
to the year 1998, 2000, and 2007 bursting epochs of the neutron star GS 1826-24
show that $\dot{M}$ must be larger than previously inferred and that the
shallow heating in this source must be below 0.5 MeV/u, providing a new method
to constrain the shallow heating mechanism in the outer layers of accreting
neutron stars. Features of the light curve rise are used to demonstrate that a
lower-limit could likely be placed on the $^{15}\rm{O}(\alpha,\gamma)$ reaction
rate, demonstrating the possibility of constraining nuclear reaction rates with
X-ray burst light curves.
