  The SUBNET neural network architecture has been developed to identify
nonlinear state-space models from input-output data. To achieve this, it
combines the rolled-out nonlinear state-space equations and a state encoder
function, both parameterised as neural networks The encoder function is
introduced to reconstruct the current state from past input-output data. Hence,
it enables the forward simulation of the rolled-out state-space model. While
this approach has shown to provide high-accuracy and consistent model
estimation, its convergence can be significantly improved by efficient
initialization of the training process. This paper focuses on such an
initialisation of the subspace encoder approach using the Best Linear
Approximation (BLA). Using the BLA provided state-space matrices and its
associated reconstructability map, both the state-transition part of the
network and the encoder are initialized. The performance of the improved
initialisation scheme is evaluated on a Wiener-Hammerstein simulation example
and a benchmark dataset. The results show that for a weakly nonlinear system,
the proposed initialisation based on the linear reconstructability map results
in a faster convergence and a better model quality.
