Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing.

Area of Science:

• Nonlinear dynamics
• Machine learning
• Time series analysis

Background:

• Time series prediction requires accurate machine learning (ML) model parameter estimation.
• Statistical data assimilation offers techniques applicable to ML tasks.
• Nonlinear time series analysis provides tools for data transformation.

Purpose of the Study:

• To adapt statistical data assimilation techniques for ML time series prediction.
• To enhance the generalization capabilities of ML models for time series forecasting.
• To determine the necessary amount of training data for reliable predictions.

Main Methods:

• Utilizing time-delay embedding to reconstruct a state space from scalar time series data.
• Employing precision annealing to find the global minimum of the action for ML model training.
• Applying feedforward multilayer perceptrons within the reconstructed embedding space.

Main Results:

• Time-delay embedding creates a phase space with no false neighbors, improving data representation.
• Precision annealing effectively identifies the optimal number of training pairs for generalization.
• The developed approach enables accurate prediction of time series segments.

Conclusions:

• The integration of time-delay embedding and precision annealing offers a robust framework for ML-based time series prediction.
• This methodology enhances model performance by optimizing parameter estimation and data representation.
• The findings are applicable to various fields requiring accurate time series forecasting.