Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data-driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems.

翻译：近年来,数据驱动的预测和物理 -- -- 不可知的机器学习方法吸引了越来越多的兴趣,使预测前景大大超出对混乱动态系统的预期。在另外一组研究数据模拟中,成功地将预测模型及其固有的不确定性与进取的噪音观测最佳地结合起来。我们这里工作的关键思想是通过明智地将机器学习算法和数据同化结合起来,从而提高预测能力。我们把随机地貌图的物理 -- -- 不可知性数据驱动方法作为预测模型,作为共同点卡尔曼过滤数据同化程序的一种预测模型。机器学习模型通过吸收噪音观测相继学习。我们表明,获得的预测模型在经过培训后在计算成本低廉的情况下具有极好的预测技能。我们除了预测任务外,还表明,我们的方法可以用来产生可靠的概率预测组合,并在多尺度系统中学习有效的模型关闭。