  Parameter inference in ordinary differential equations is an important
problem in many applied sciences and in engineering, especially in a
data-scarce setting. In this work, we introduce a novel generative modeling
approach based on constrained Gaussian processes and leverage it to build a
computationally and data efficient algorithm for state and parameter inference.
In an extensive set of experiments, our approach outperforms the current state
of the art for parameter inference both in terms of accuracy and computational
cost. It also shows promising results for the much more challenging problem of
model selection.
