  Snapshot back-ended reduced basis methods for dynamical systems commonly rely
on the singular value decomposition of a matrix whose columns are high-fidelity
solution vectors. An alternative basis generation framework is developed here.
The advocated maximum entropy snapshot sampling (MESS) identifies the snapshots
that encode essential information regarding the system's evolution, by
exploiting quantities that are suitable for quantifying a notion of dynamical
stability. The maximum entropy snapshot sampling enables a direct reduction of
the number of snapshots. A reduced basis is then obtained with any
orthonormalization process on the resulting reduced sample of snapshots. The
maximum entropy sampling strategy is supported by rigid mathematical
foundations, it is computationally efficient, and it is inherently automated
and easy to implement.
