Optimality of uniform sampling for non-multiscale linear systems

Determine whether uniformly spaced sampling is guaranteed to be the optimal sampling approach for linear dynamical systems that are not necessarily multiscale.

Background

The numerical experiments indicate that uniformly spaced delay-coordinate maps often perform better and converge faster than maps using randomly generated non-uniform delays. However, the paper does not establish whether this observed advantage is universal or whether it depends on the system, observation function, or sampling distribution.

The unresolved issue is particularly relevant for selecting sampling strategies in applications where non-uniform sampling may be operationally convenient but uniform sampling remains a possible baseline.