Phase-Space-Guided Deep Learning For Time Series Forecasting

Time series forecasting is crucial, yet the challenge of escalating errors in chaotic data and natural phenomena prediction endures. Existing methods for recursive strategies face difficulties in Multi-Input Multi-Output scenarios. A unified learning framework addressing error growth alongside these models is lacking, despite advanced neural networks. While dynamical system theory has inspired research in time series forecasting, these approaches struggle to estimate and mitigate error growth adequately. To address these gaps, we introduce Phase-Space-Guided Forecasting (PSGF), rooted in dynamical system theory. PSGF transforms data into high-dimensional phase space, quantifies error growth rates, and incorporates them into the neural network via Error Growth Awareness Loss (EGAL). PSGF enhances the utilization of dynamical constraints, reducing the need for additional feature engineering or hyperparameter tuning. Experimental results on chaotic systems and real-world climate data demonstrate PSGF’s significant accuracy improvements on diverse deep learning models.