DATA-DRIVEN STUDIES OF TRANSIENT EVENTS AND APERIODIC MOTIONS

Abstract

The era of big data, high-performance computing, and machine learning has witnessed a paradigm shift from physics-based modeling to data-driven modeling across many scientific fields. In this dissertation work, transient events and aperiodic motions of complex nonlinear dynamical system are studied with the aid of a data- driven modeling approach. The goal of the work has been to further the ability for future behavior prediction, state estimation, and control of related behaviors. It is shown that data on extreme waves can be used to carry out stability analysis and ascertain the nature of the transient phenomenon. In addition, it is demonstrated that a low number of soliton elements can be used to realize a rogue wave on the basis of nonlinear interactions amongst the basic elements. The pro- posed nonlinear phase interference model provides an appealing explanation for the formation of ocean extreme wave and related statistics, and a superior reconstruction of the Draupner wave event than that obtained on the basis of linear superposition. Chaotic data, another manifestation of aperiodic motions, which are obtained from prototypical ordinary differential and partial differential systems are considered and a neural machine is realized to predict the corresponding responses based on a limited training set as well to forecast the system behavior. A specific neural architecture, called the inhibitor mechanism, has been designed to enable chaotic time series forecasting. Without this mechanism, even the short-term predictions would be intractable. Both autonomous and non-autonomous dynamical systems have been studied to demonstrate the long-term forecasting possibilities with the de- veloped neural machine. For each dynamical system considered in this dissertation, a long forecasting horizon is achieved with a short historical data set. Furthermore, with the developed neural machine, one can relax the requirement of continuous historical data measurements, thus, providing for a more pragmatic approach than the previous approaches available in the literature. It is expected that the efforts of this dissertation work will lead to a better understanding of the underlying mechanism of transient and aperiodic events in complex systems and useful techniques for forecasting their future occurrences.