Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation

Abstract

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.

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• Reservoir Computing as a Tool for Climate Predictability Studies
• State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics
• Supervised machine learning to estimate instabilities in chaotic systems: estimation of local Lyapunov exponents
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
• CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting
• Development of an offline and online hybrid model for the Integrated Forecasting System
• Robust parameter estimation using the ensemble Kalman filter
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
• Fourier Series-Based Approximation of Time-Varying Parameters in Ordinary Differential Equations