  Gradient matching is a promising tool for learning parameters and state
dynamics of ordinary differential equations. It is a grid free inference
approach, which, for fully observable systems is at times competitive with
numerical integration. However, for many real-world applications, only sparse
observations are available or even unobserved variables are included in the
model description. In these cases most gradient matching methods are difficult
to apply or simply do not provide satisfactory results. That is why, despite
the high computational cost, numerical integration is still the gold standard
in many applications. Using an existing gradient matching approach, we propose
a scalable variational inference framework which can infer states and
parameters simultaneously, offers computational speedups, improved accuracy and
works well even under model misspecifications in a partially observable system.
