  The exploding research interest for neural networks in modeling nonlinear
dynamical systems is largely explained by the networks' capacity to model
complex input-output relations directly from data. However, they typically need
vast training data before they can be put to any good use. The data generation
process for dynamical systems can be an expensive endeavor both in terms of
time and resources. Active learning addresses this shortcoming by acquiring the
most informative data, thereby reducing the need to collect enormous datasets.
What makes the current work unique is integrating the deep active learning
framework into nonlinear system identification. We formulate a general static
deep active learning acquisition problem for nonlinear system identification.
This is enabled by exploring system dynamics locally in different regions of
the input space to obtain a simulated dataset covering the broader input space.
This simulated dataset can be used in a static deep active learning acquisition
scheme referred to as global explorations. The global exploration acquires a
batch of initial states corresponding to the most informative state-action
trajectories according to a batch acquisition function. The local exploration
solves an optimal control problem, finding the control trajectory that
maximizes some measure of information. After a batch of informative initial
states is acquired, a new round of local explorations from the initial states
in the batch is conducted to obtain a set of corresponding control trajectories
that are to be applied on the system dynamics to get data from the system.
Information measures used in the acquisition scheme are derived from the
predictive variance of an ensemble of neural networks. The novel method
outperforms standard data acquisition methods used for system identification of
nonlinear dynamical systems in the case study performed on simulated data.
