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TITLE: Local Gaussian Process Models for Real-time Performance Prediction in Nonlinear Nonstationary Systems
SPEAKER: Dr. Satish Bukkapatnam
ABSTRACT:
Prediction of dynamic states and performance of real-world complex systems, both engineered and natural, has been recognized as a major modern scientific challenge. Accurate and timely prediction is vital for control and operation of modern manufacturing, as well as several engineering, biological and physical systems. Although significant data sources in the form of multi-dimensional time series are becoming available, nonlinear (often chaotic) and nonstationary dynamics of these complex systems pose formidable challenge for prediction. Oftentimes, quantitative relationships between the measured signals and states remain unknown or indeterminable. Nonparametric approaches can be attractive in such cases. Among the nonparametric approaches, Gaussian process (GP) models use Gaussian properties to simplify the modeling efforts. While GP models are known to perform well under stationary conditions, highly nonstationary dynamics of real-world complex systems severely impedes their applicability.
A novel local Gaussian process (LGP) modeling approach is presented to improve prediction under highly nonlinear and nonstationary conditions. The key idea is to use local topological properties of complex systems, including recurrence and local affine approximations are used to partition state space into near-stationary segments. Theoretical studies indicate significant reductions in prediction errors and computational complexity with LGP compared to global GP under certain nonstationary conditions. Experimental investigations involving multiple synthetic and real-world time series from four different physical domains consistently show a 40% (on an average) improvement in prediction accuracies and 20-60% reduction in computation time with LGP compared to GP and others approaches tested, rendering these more suitable for complex system prediction applications.
