  A novel methodology is developed to extract accurate skeletal reaction models
for nuclear combustion. Local sensitivities of isotope mass fractions with
respect to reaction rates are modeled based on the forced optimally
time-dependent (f-OTD) scheme. These sensitivities are then analyzed temporally
to generate skeletal models. The methodology is demonstrated by conducting
skeletal reduction of constant density and temperature burning of carbon and
oxygen relevant to SNe Ia. The 495-isotopes Torch model is chosen as the
detailed reaction network. A map of maximum production of $^{56}\text{Ni}$ in
SNe Ia is produced for different temperatures, densities, and proton to neutron
ratios. The f-OTD simulations and the sensitivity analyses are then performed
with initial conditions from this map. A series of skeletal models are derived
and their performances are assessed by comparison against currently existing
skeletal models. Previous models have been constructed intuitively by assuming
the dominance of $\alpha$-chain reactions. The comparison of the newly
generated skeletal models against previous models is based on the predicted
energy release and $^{44}\text{Ti}$ and $^{56}\text{Ni}$ abundances by each
model. The consequences of $\mathtt{y}_e \neq 0.5$ in the initial composition
are also explored where $\mathtt{y}_e$ is the electron fraction. The simulated
results show that $^{56}\text{Ni}$ production decreases by decreasing
$\mathtt{y}_e$ as expected, and that the $^{43}\text{Sc}$ is a key isotope in
proton and neutron channels toward $^{56}\text{Ni}$ production. It is shown
that an f-OTD skeletal model with 150 isotopes can accurately predict the
$^{56}\text{Ni}$ abundance in SNe Ia for $\mathtt{y}_e \lesssim 0.5$ initial
conditions.
