  A well-specified parametrization for single-input/single-output (SISO) linear
port-Hamiltonian systems amenable to structure-preserving supervised learning
is provided. The construction is based on controllable and observable normal
form Hamiltonian representations for those systems, which reveal fundamental
relationships between classical notions in control theory and crucial
properties in the machine learning context, like structure-preservation and
expressive power. The results in the paper suggest parametrizations of the
estimation problem associated with these systems that amount, at least in the
canonical case, to unique identification and prove that the parameter
complexity necessary for the replication of the dynamics is only O(n) and not
O(n^2), as suggested by the standard parametrization of these systems.
