  In the context of an increasing popularity of data-driven models to represent
dynamical systems, many machine learning-based implementations of the Koopman
operator have recently been proposed. However, the vast majority of those works
are limited to deterministic predictions, while the knowledge of uncertainty is
critical in fields like meteorology and climatology. In this work, we
investigate the training of ensembles of models to produce stochastic outputs.
We show through experiments on real remote sensing image time series that
ensembles of independently trained models are highly overconfident and that
using a training criterion that explicitly encourages the members to produce
predictions with high inter-model variances greatly improves the uncertainty
quantification of the ensembles.
