  Linear evolution PDE $\partial_t u(x,t) = -\mathcal{L} u$, where
$\mathcal{L}$ is a strongly elliptic operator independent of time, is studied
as an example to show if one can superpose snapshots of a single (or a finite
number of) solution(s) to construct an arbitrary solution. Our study shows that
it depends on the growth rate of the eigenvalues, $\mu_n$, of $\mathcal{L}$ in
terms of $n$. When the statement is true, a simple data-driven approach for
model reduction and approximation of an arbitrary solution of a PDE without
knowing the underlying PDE is designed. Numerical experiments are presented to
corroborate our analysis.
