  Despite the availability of ever more data enabled through modern sensor and
computer technology, it still remains an open problem to learn dynamical
systems in a sample-efficient way. We propose active learning strategies that
leverage information-theoretical properties arising naturally during Gaussian
process regression, while respecting constraints on the sampling process
imposed by the system dynamics. Sample points are selected in regions with high
uncertainty, leading to exploratory behavior and data-efficient training of the
model. All results are finally verified in an extensive numerical benchmark.
