  The identification of the constrained dynamics of mechanical systems is often
challenging. Learning methods promise to ease an analytical analysis, but
require considerable amounts of data for training. We propose to combine
insights from analytical mechanics with Gaussian process regression to improve
the model's data efficiency and constraint integrity. The result is a Gaussian
process model that incorporates a priori constraint knowledge such that its
predictions adhere to Gauss' principle of least constraint. In return,
predictions of the system's acceleration naturally respect potentially
non-ideal (non-)holonomic equality constraints. As corollary results, our model
enables to infer the acceleration of the unconstrained system from data of the
constrained system and enables knowledge transfer between differing constraint
configurations.
