  COVID-19 pandemic has had a disruptive and irreversible impact globally, yet
traditional epidemiological modeling approaches such as the
susceptible-infected-recovered (SIR) model have exhibited limited effectiveness
in forecasting of the up-to-date pandemic situation. In this work,
susceptible-vaccinated-exposed-infected-dead-recovered (SVEIDR) model and its
variants -- aged and vaccination-structured SVEIDR models -- are introduced to
encode the effect of social contact for different age groups and vaccination
status. Then, we implement the physics-informed neural network (PiNN) on both
simulated and real-world data. The PiNN model enables robust analysis of the
dynamic spread, prediction, and parameter optimization of the COVID-19
compartmental models. The models exhibit relative root mean square error
(RRMSE) of $<4\%$ for all components and provide incubation, death, and
recovery rates of $\gamma= 0.0130$, $\lambda=0.0001$, and $\rho=0.0037$,
respectively, for the first 310 days of the epidemic in the US with RRMSE of
$<0.35\%$ for all components. To further improve the model performance,
temporally varying parameters can be included, such as vaccination,
transmission, and incubation rates. Our implementation highlights PiNN as a
reliable candidate approach for forecasting real-world data and can be applied
to other compartmental model variants of interest.
