Forecasting the evolution of nonlinear and nonstationary systems using recurrence-based local Gaussian process models

Area of Science:

• Complex Systems Analysis
• Nonlinear Dynamics
• Time Series Forecasting

Background:

• Complex physical systems often exhibit nonlinear and nonstationary dynamics, posing challenges for traditional prediction models.
• Accurate forecasting is crucial for state and performance monitoring in diverse applications.

Purpose of the Study:

• To develop an advanced prediction approach for complex physical systems with nonlinear and nonstationary dynamics.
• To improve the accuracy and computational efficiency of one-step-ahead predictions.

Main Methods:

• Combining nonparametric Gaussian process (GP) modeling with local topological considerations.
• Partitioning system trajectories into near-stationary segments using piecewise affine projections and topological properties.
• Deriving nonparametric prediction models within each identified segment.

Main Results:

• The proposed local Gaussian process approach demonstrated superior prediction accuracy compared to classical system identification, neural networks, and nonparametric models.
• Significant improvements were observed over sequential Bayesian Monte Carlo methods.
• The method proved effective on the Lorenz system, synthetic heart-rate signals, and a real-world industrial time-series.

Conclusions:

• The integration of Gaussian process modeling and topological analysis offers a powerful tool for predicting complex nonlinear and nonstationary systems.
• This method provides a computationally efficient and accurate alternative for time-series forecasting in challenging dynamic environments.