  The discovery of structure from time series data is a key problem in fields
of study working with complex systems. Most identifiability results and
learning algorithms assume the underlying dynamics to be discrete in time.
Comparatively few, in contrast, explicitly define dependencies in infinitesimal
intervals of time, independently of the scale of observation and of the
regularity of sampling. In this paper, we consider score-based structure
learning for the study of dynamical systems. We prove that for vector fields
parameterized in a large class of neural networks, least squares optimization
with adaptive regularization schemes consistently recovers directed graphs of
local independencies in systems of stochastic differential equations. Using
this insight, we propose a score-based learning algorithm based on penalized
Neural Ordinary Differential Equations (modelling the mean process) that we
show to be applicable to the general setting of irregularly-sampled
multivariate time series and to outperform the state of the art across a range
of dynamical systems.
