  Spurred by tremendous success in pattern matching and prediction tasks,
researchers increasingly resort to machine learning to aid original scientific
discovery. Given large amounts of observational data about a system, can we
uncover the rules that govern its evolution? Solving this task holds the great
promise of fully understanding the causal interactions and being able to make
reliable predictions about the system's behavior under interventions. We take a
step towards answering this question for time-series data generated from
systems of ordinary differential equations (ODEs). While the governing ODEs
might not be identifiable from data alone, we show that combining simple
regularization schemes with flexible neural ODEs can robustly recover the
dynamics and causal structures from time-series data. Our results on a variety
of (non)-linear first and second order systems as well as real data validate
our method. We conclude by showing that we can also make accurate predictions
under interventions on variables or the system itself.
