  SINDy is a method for learning system of differential equations from data by
solving a sparse linear regression optimization problem [Brunton et al., 2016].
In this article, we propose an extension of the SINDy method that learns
systems of differential equations in cases where some of the variables are not
observed. Our extension is based on regressing a higher order time derivative
of a target variable onto a dictionary of functions that includes lower order
time derivatives of the target variable. We evaluate our method by measuring
the prediction accuracy of the learned dynamical systems on synthetic data and
on a real data-set of temperature time series provided by the R\'eseau de
Transport d'\'Electricit\'e (RTE). Our method provides high quality short-term
forecasts and it is orders of magnitude faster than competing methods for
learning differential equations with latent variables.
