  In this paper, we present a deep neural network based adaptive learning
(DNN-AL) approach for switched systems. Currently, deep neural network based
methods are actively developed for learning governing equations in unknown
dynamic systems, but their efficiency can degenerate for switching systems,
where structural changes exist at discrete time instants. In this new DNN-AL
strategy, observed datasets are adaptively decomposed into subsets, such that
no structural changes within each subset. During the adaptive procedures, DNNs
are hierarchically constructed, and unknown switching time instants are
gradually identified. Especially, network parameters at previous iteration
steps are reused to initialize networks for the later iteration steps, which
gives efficient training procedures for the DNNs. For the DNNs obtained through
our DNN-AL, bounds of the prediction error are established. Numerical studies
are conducted to demonstrate the efficiency of DNN-AL.
