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In this work, we present the coupled dynamics and stability predictions of marine vessels in the ocean environment, with particular focus on the synergy of physics-based and data-driven models towards Digital Twin. The ultimate goal is to predict and control the coupled dynamics and stability in normal and extreme conditions via the digital twin of marine vessels and propellers.The first part of this study includes a high-dimensional representation of multiphase fluid-structure interaction via the nonlinear system of partial differential equations. The second part of this study includes the model reduction of flow-induced vibrations (FIV) and the application of the knowledge gained in the previous parts in efficient parametric design optimization and control of marine tugboats. Towards this goal, two advanced physics-based system identification approaches are considered via projection-based and deep-learning-based reduced-order models. The projection-based approach includes a linear reduced-order model (ROM) for stability prediction using the eigensystem realization algorithm (ERA), which provides a low-order approximation of unsteady flow dynamics in the neighbourhood of equilibrium steady state. We perform a systematic ROM-based stability analysis to understand the frequency lock-in mechanism and self-sustained FIV phenomenon by examining eigenvalue trajectories.However, for high Reynolds number flows and near real-time feedback control, this goal can only be achieved through the recent advances in nonlinear model reduction and deep learning (DL) algorithms. To demonstrate this idea, we have developed a data-driven coupling for predicting unsteady forces and vortex-induced vibration (VIV) lock-in by using a long short-term memory network (LSTM) as a DL-based ROM technique. The structure of the LSTM has the format of a nonlinear state-space model (NLSS) and provides a nonlinear mapping of input-output dynamics that can potentially predict the dynamics for a longer horizon utilized for the stability predictions. The simplicity and computational efficiency of the proposed ROMs allow investigation of the FIV mechanism for a variety of geometries and parameters, and open ways for the development of control devices and on-board and in real-time predictions.