A combined machine learning and data assimilation framework to model geophysical flows

The non-intrusive surrogate models, built on data acquired from sensors and satellites, are computationally inexpensive to model atmospheric and oceanic flows in comparison with numerical simulations, which makes them attractive for online deployments. Despite the recent success of data-driven prediction, online deployment of data-driven forecasting models might result in inaccurate predictions due to their biases regarding initializations, model architectures, and hyperparameters. The purpose of this study is to combine equation-free machine learning models responsible for predicting future states in the proper orthogonal decomposition (POD) latent space with the deterministic ensemble Kalman filter (DEnKF) to remove the biases and instabilities of the machine learning models. To this end, POD identifies dominant structures, and a long short-term memory (LSTM) technology predicts the dynamics of the system. The DEnKF algorithm corrects the prediction of the LSTM ensemble models in the latent space by incorporating noisy and sparse observations obtained from sensors that are optimally located with the QR pivoting method. The benefits of the proposed framework are successfully demonstrated by applying it to the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 dataset.