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

An approach based on combining nonparametric Gaussian process (GP) modeling with certain local topological considerations is presented for prediction (one-step look ahead) of complex physical systems that exhibit nonlinear and nonstationary dynamics. The key idea here is to partition system trajectories into multiple near-stationary segments by aligning the boundaries of the partitions with those of the piecewise affine projections of the underlying dynamic system, and deriving nonparametric prediction models within each segment. Such an alignment is achieved through the consideration of recurrence and other local topological properties of the underlying system. This approach was applied for state and performance forecasting in Lorenz system under different levels of induced noise and nonstationarity, synthetic heart-rate signals, and a real-world time-series from an industrial operation known to exhibit highly nonlinear and nonstationary dynamics. The results show that local Gaussian process can significantly outperform not just classical system identification, neural network and nonparametric models, but also the sequential Bayesian Monte Carlo methods in terms of prediction accuracy and computational speed.