Variability of echo state network prediction horizon for partially observed dynamical systems
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Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by proposing an echo state network (ESN) framework with partial state input with partial or full state output. The Lorenz system and Chua's oscillator (both numerically simulated and experimental systems) are used to check the effectiveness of our method. We demonstrate that the ESN, as an autonomous dynamical system, is capable of making short-term predictions up to a few Lyapunov times. However, the prediction horizon has high variability depending on the initial condition – an aspect that we explore in detail. Further, using a variety of statistical metrics to compare the long-term dynamics of the ESN predictions with numerically simulated or experimental dynamics and observed similar results, we show that the ESN can effectively learn the system's dynamics even when trained with noisy numerical or experimental datasets. Thus, we demonstrate the potential of ESNs to serve as a cheap surrogate model for predicting the dynamics of systems where complete observations are unavailable.
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