Model adaptive phase space reconstruction.

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Time Series Analysis

Background:

• Traditional phase space reconstruction (PSR) methods have limitations when applied to machine learning (ML) prediction models.
• Integrating dynamical system modeling with ML requires adaptable PSR techniques.

Purpose of the Study:

• To introduce a novel Model Adaptive Phase Space Reconstruction (MAPSR) method.
• To enable ML models for dynamical system prediction by unifying PSR and modeling processes.

Main Methods:

• MAPSR utilizes differentiable time-delay embedding, allowing ML integration.
• Converts discrete-time signals to continuous-time for a differentiable loss function.
• Optimizes embedding delays and model parameters simultaneously to minimize prediction loss, avoiding predefined thresholds.

Main Results:

• MAPSR-trained models achieved superior prediction of chaotic time series (Lorenz system) up to 7-8 Lyapunov time scales compared to AMI-FNN and PECUZAL.
• For turbulent combustor data, MAPSR showed competitive long-term prediction error in chaotic regimes.
• MAPSR outperformed other methods in predicting intermittent regimes of the turbulent combustor time series.

Conclusions:

• MAPSR offers a unified and adaptive approach for phase space reconstruction in ML-based dynamical system modeling.
• The method significantly enhances predictive capabilities for chaotic and intermittent time series.
• MAPSR provides a more robust and data-driven alternative to traditional PSR techniques.