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To benefit from the modeling capacity of deep models in systemidentification, without worrying about inference time, this study presents anovel training strategy that uses deep models only at the training stage. Forthis purpose two separate models with different structures and goals areemployed. The first one is a deep generative model aiming at modeling thedistribution of system output(s), called the teacher model, and the second oneis a shallow basis function model, named the student model, fed by systeminput(s) to predict the system output(s). That means these isolated paths mustreach the same ultimate target. As deep models show a great performance inmodeling of highly nonlinear systems, aligning the representation space learnedby these two models make the student model to inherit the approximation powerof the teacher model. The proposed objective function consists of the objectiveof each student and teacher model adding up with a distance penalty between thelearned latent representations. The simulation results on three nonlinearbenchmarks show a comparative performance with examined deep architecturesapplied on the same benchmarks. Algorithmic transparency and structureefficiency are also achieved as byproducts.

Exploiting the capacity of deep networks only at training stage for nonlinear black-box system identification