Data-driven estimation using an Echo-State Neural Network equipped with an Ensemble Kalman Filter
Debdipta Goswami, Artur Wolek, Derek A. Paley · 2021
This paper considers the problem of data-driven estimation with sparse measurements for a complex nonlinear system. While model-based nonlinear estimation methods are well known, state estimation from partial observations with unmodeled dynamics is less understood. Here we use a method for model-free estimation based on an echo-state network (ESN) where a reasonably accurate set of training data is available during the training period and some sparse measurements are obtained during the testing phase. The measurements are assimilated by an ensemble Kalman filter (EnKF) to improve the predictor's performance when compared to a free-running neural network architecture. The proposed method is applied to three systems: a low-dimensional chaotic system, a high-dimensional chaotic system, and a set of real-time traffic data.