  To benefit from the modeling capacity of deep models in system
identification, without worrying about inference time, this study presents a
novel training strategy that uses deep models only at the training stage. For
this purpose two separate models with different structures and goals are
employed. The first one is a deep generative model aiming at modeling the
distribution of system output(s), called the teacher model, and the second one
is a shallow basis function model, named the student model, fed by system
input(s) to predict the system output(s). That means these isolated paths must
reach the same ultimate target. As deep models show a great performance in
modeling of highly nonlinear systems, aligning the representation space learned
by these two models make the student model to inherit the approximation power
of the teacher model. The proposed objective function consists of the objective
of each student and teacher model adding up with a distance penalty between the
learned latent representations. The simulation results on three nonlinear
benchmarks show a comparative performance with examined deep architectures
applied on the same benchmarks. Algorithmic transparency and structure
efficiency are also achieved as byproducts.
