  Deriving analytical solutions of ordinary differential equations is usually
restricted to a small subset of problems and numerical techniques are
considered. Inevitably, a numerical simulation of a differential equation will
then always be distinct from a true analytical solution. An efficient
integration scheme shall further not only provide a trajectory throughout a
given state, but also be derived to ensure the generated simulation to be close
to the analytical one. Consequently, several integration schemes were developed
for different classes of differential equations. Unfortunately, when
considering the integration of complex non-linear systems, as well as the
identification of non-linear equations from data, this choice of the
integration scheme is often far from being trivial. In this paper, we propose a
novel framework to learn integration schemes that minimize an
integration-related cost function. We demonstrate the relevance of the proposed
learning-based approach for non-linear equations and include a quantitative
analysis w.r.t. classical state-of-the-art integration techniques, especially
where the latter may not apply.
