Hierarchical Classifier-Regression Ensemble for Multi-phase Non-linear Dynamic System Response Prediction: Application to Climate Analysis

A dynamic physical system often undergoes phase transitions in response to fluctuations induced on system parameters. For example, hurricane activity is the climate system's response initiated by a liquid-vapor phase transition associated with non-linearly coupled fluctuations in the ocean and the atmosphere. Because our quantitative knowledge about highly non-linear dynamic systems is very meager, scientists often resort to linear regression techniques such as Least Absolute Deviation (LAD) to learn the non-linear system's response (e.g., hurricane activity) from observed or simulated system's parameters (e.g., temperature, precipitable water, pressure). While insightful, such models still offer limited predictability, and alternatives intended to capture non-linear behaviors such as Stepwise Regression are often controversial in nature. In this paper, we hypothesize that one of the primary reasons for lack of predictability is the treatment of an inherently multi-phase system as being phase less. To bridge this gap, we propose a hybrid approach that first predicts the phase the system is in, and then estimates the magnitude of the system's response using the regression model optimized for this phase. Our approach is designed for systems that could be characterized by multi-variate spatio-temporal data from observations, simulations, or both.