Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

Abstract

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens' embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.

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Cited by in corpus (9)

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• Catch-22s of reservoir computing
• Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case
• Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
• CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation
• CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation
• Reduced-order adaptive synchronization in a chaotic neural network with parameter mismatch: A dynamical system vs. machine learning approach
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Asymptotic behavior of the forecast-assimilation process with unstable dynamics