Machine Learning For Predicting Non-Stationary Dynamical Systems, and Global Subseasonal-to-Seasonal Weather Phenomena

Abstract

In this thesis, we are interested in modeling (1) the long-term statistical behavior of non-stationary dynamical systems, and (2) global weather patterns on the Subseasonal-to-Seasonal (S2S) time scale (2 weeks - 6 months). The first part of this thesis is primarily concerned with the situation where we have available to us measured time series data of the past states of the system of interest, and in some cases, a (perhaps inaccurate) scientific-knowledge-based model of the system. The central problem here lies in predicting a future behavior of the system that may be fundamentally different than that observed in the measured time series of its past. We develop machine learning -based methods for accomplishing this task and test it in various challenging scenarios (e.g., predicting future abrupt changes in dynamics mediated by bifurcations encountered that were not included in the training data). We also investigate the effects of dynamical noise in the training data on the predictability of such systems. For the second part of this thesis, we modify a machine learning -based global climate model to predict various weather phenomena on the S2S time scale. The model is a hybrid between a purely data-driven machine learning component and an atmospheric general circulation model. We begin by formulating a purely machine learning approach that utilizes the measured time series of the past states of the target non-stationary system, as well as knowledge of the time-dependence of the non-stationarity inducing time-dependent system parameter. We demonstrate that this method can enable the prediction of the future behavior of the non-stationary system even in situations where the future behavior is qualitatively and quantitatively different from the behavior in the training data. For situations where the training data contains dynamical noise, we develop a scheme to enable the trained machine learning model to predict trajectories which mimic the effects of dynamical noise on typical trajectories of the target system. We test our methods on the discrete time logistic map, the continuous time Lorenz system, and the spatiotemporal Kuramoto-Sivashinsky system, and for a variety of non-stationary scenarios. Next, we study the ability of our approach to not only extrapolate to previously unseen dynamics, but also to regions previously unexplored by the training data of the target system's state space. We find that while machine learning models can exhibit some capabilities to extrapolate in state space, they fail quickly as the amount of extrapolation required increases (as expected of any purely data-driven extrapolation method). We explore ways in which such failures can be mitigated. For instance, we show that a hybrid model which combines machine learning with a knowledge-based component can provide substantial improvements in extrapolation. We test our methods on the Ikeda map, the Lorenz system, and the Kuramoto-Sivashinsky system, under challenging scenarios (e.g., predicting future hysteretic transitions in dynamical behavior). Finally, we modify a machine learning -based hybrid global climate model to forecast global weather patterns on the S2S time scale. Predicting on this time scale is crucial for many domains (e.g., land, water, and energy management), yet it remains a difficult period to obtain useful predictions for. We demonstrate that our model has useful skill in predicting a number of phenomena including global precipitation anomalies, the El Nino Southern Oscillation and its related teleconnections, and various equatorial waves.