Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
This work addresses forecasting challenges in fields like meteorology or engineering, but it is incremental as it builds on existing techniques like random feature maps and data assimilation.
The authors tackled the problem of forecasting dynamical systems from noisy partial observations by combining machine learning with data assimilation, resulting in a method called RAFDA that outperforms standard random feature maps.
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.