Open Set Domain Adaptation for Classification of Dynamical States in Nonlinear Fluid Dynamical Systems

Nonlinear fluid dynamical systems, such as thermoacoustic systems, aeroelastic systems are archetypical complex systems involving state transitions upon a change in bifurcation parameter. These state transitions in any certain direction are always undesirable and can radically alter the operational paradigms associated with these systems. Hence, predicting the impending dynamical state is paramount for avoiding such undesirable transitions. The hitherto research so far focused largely on metric-based and model-based indicators to foretell an impending transition and is often fraught with difficulties when deployed in practicable scenarios. In this study, we assuage this end of concern by proposing a model-agnostic data-driven method for automated classification of the dynamical states of nonlinear fluid dynamical systems. By using recurrence plots we transform the time series pertaining to the dynamical states into images and subsequently employ a convolution neural network (CNN) to classify the generated images. This study also proceeds to present cross-domain classifications via a trained deep learning (DL) model and successfully classify the dynamical states of one fluid dynamical system (say, thermoacoustic) with the dynamical states of another fluid dynamical system (say, aeroelastic). The underlying methodology for the above is based on open set (OS) domain adaptation - inherent to transfer learning schemes. Towards enhancing the confidence levels of our proposed methodology, we carry out four cross-domain numerical experiments, wherein we consistently get about 94 - 98% accuracy.