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：随着数据驱动模型在动力系统表示中的日益普及，近年来涌现出大量基于机器学习的Koopman算子实现方法。然而，这些工作绝大多数局限于确定性预测，而在气象学与气候学等关键领域中，对不确定性的认知至关重要。本研究探讨了通过集成模型训练来生成随机输出。基于真实遥感图像时间序列的实验表明，独立训练的模型集成存在严重的过度自信问题，而采用显式鼓励各成员产生高模型间方差预测的训练准则，能显著提升集成模型的不确定性量化能力。