Exploring attractor reconstruction derived from encoder-decoder time series prediction

Reconstructing the state space is a generic and basic step for studying nonlinear dynamics with partial observables. Recently, time series forecasting through an encoder-decoder artificial neural network is expected to implicitly realize this procedure. However, existing explanatory and comparative studies are insufficient to strongly support such an argument. This paper analyzes the feasibility of such a reconstruction from the predictive perspective. To produce the topologically equivalent attractor via the encoder, we generalize the conditions about the predictive range, measurement noise and model suitability. Based on these analyses, we explore an adapted reconstruction methodology from time series prediction. Moreover, we found that the inverted transformer network is more appealing for multivariate observations and the penalty function of noise amplification compensates for the deficiency of standard prediction error. We conduct an experimental comparison between the prediction-based reconstruction and typical delay coordinate reconstruction in multiple situations. The comparative outcomes demonstrate that sensible predictive designs can steadily reconstruct the attractor at the best level. Additionally, we recover the underlying dynamics from real meteorological data associated with El Niño-Southern Oscillation.