  In recent years, several algorithms for system identification with neural
state-space models have been introduced. Most of the proposed approaches are
aimed at reducing the computational complexity of the learning problem, by
splitting the optimization over short sub-sequences extracted from a longer
training dataset. Different sequences are then processed simultaneously within
a minibatch, taking advantage of modern parallel hardware for deep learning. An
issue arising in these methods is the need to assign an initial state for each
of the sub-sequences, which is required to run simulations and thus to evaluate
the fitting loss. In this paper, we provide insights for calibration of neural
state-space training algorithms based on extensive experimentation and analyses
performed on two recognized system identification benchmarks. Particular focus
is given to the choice and the role of the initial state estimation. We
demonstrate that advanced initial state estimation techniques are really
required to achieve high performance on certain classes of dynamical systems,
while for asymptotically stable ones basic procedures such as zero or random
initialization already yield competitive performance.
