  Nonlinear state-space identification for dynamical systems is most often
performed by minimizing the simulation error to reduce the effect of model
errors. This optimization problem becomes computationally expensive for large
datasets. Moreover, the problem is also strongly non-convex, often leading to
sub-optimal parameter estimates. This paper introduces a method that
approximates the simulation loss by splitting the data set into multiple
independent sections similar to the multiple shooting method. This splitting
operation allows for the use of stochastic gradient optimization methods which
scale well with data set size and has a smoothing effect on the non-convex cost
function. The main contribution of this paper is the introduction of an encoder
function to estimate the initial state at the start of each section. The
encoder function estimates the initial states using a feed-forward neural
network starting from historical input and output samples. The efficiency and
performance of the proposed state-space encoder method is illustrated on two
well-known benchmarks where, for instance, the method achieves the lowest known
simulation error on the Wiener--Hammerstein benchmark.
