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.

翻译：在数据驱动模型日益普及以表征动态系统的背景下，近期涌现出大量基于机器学习的Koopman算子实现方法。然而，这些研究绝大多数局限于确定性预测，而对于气象学与气候学等关键领域而言，不确定性认知至关重要。本研究探讨了通过集成模型训练生成随机输出的方法。通过对真实遥感影像时间序列的实验，我们证明独立训练的模型集成存在高度过度自信问题，而采用明确鼓励成员产生高模型间方差预测的训练准则，可显著提升集成的不确定性量化能力。