Exploring attractor reconstruction derived from encoder-decoder time series prediction.

Area of Science:

• Nonlinear dynamics
• Time series analysis
• Artificial intelligence

Background:

• State space reconstruction is crucial for studying nonlinear dynamics with limited observations.
• Encoder-decoder neural networks are proposed for implicit state space reconstruction.
• Current research lacks sufficient comparative studies on this approach.

Purpose of the Study:

• To analyze the feasibility of state space reconstruction using time series prediction.
• To develop and validate a prediction-based reconstruction methodology.
• To compare prediction-based methods with traditional delay coordinate reconstruction.

Main Methods:

• Generalizing conditions for topologically equivalent attractor production (predictive range, noise, model suitability).
• Exploring an adapted reconstruction methodology based on time series prediction.
• Utilizing inverted transformer networks for multivariate observations and noise amplification penalty functions.

Main Results:

• Prediction-based reconstruction is feasible and effective.
• Inverted transformers show promise for multivariate data.
• Noise amplification penalty functions improve prediction accuracy.
• Comparative experiments demonstrate superior performance of prediction-based methods over delay coordinate reconstruction.

Conclusions:

• Sensible predictive designs can reliably reconstruct attractors.
• This approach offers a robust alternative for state space reconstruction in nonlinear dynamics.
• The method was successfully applied to reconstruct dynamics from El Niño-Southern Oscillation meteorological data.