Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation
This work addresses the challenge of enhancing prediction accuracy and reliability in chaotic systems for fields like meteorology or climate science, representing an incremental advancement by integrating existing techniques.
The paper tackles the problem of improving forecast capabilities for chaotic dynamical systems by combining random feature maps as a machine-learning forecast model with an ensemble Kalman filter for data assimilation, resulting in remarkably good forecast skill and computational efficiency once trained.
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.