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In this paper, we present a deep learning-based reduced-order model (DL-ROM)for the stability prediction of unsteady 3D fluid-structure interactionsystems. The proposed DL-ROM has the format of a nonlinear state-space modeland employs a recurrent neural network with long short-term memory (LSTM). Weconsider a canonical fluid-structure system of an elastically-mounted spherecoupled with incompressible fluid flow in a state-space format. We develop anonlinear data-driven coupling for predicting unsteady forces andvortex-induced vibration (VIV) lock-in of the freely vibrating sphere in atransverse direction. We design an input-output relationship as a temporalsequence of force and displacement datasets for a low-dimensional approximationof the fluid-structure system. Based on the prior knowledge of the VIV lock-inprocess, the input function contains a range of frequencies and amplitudes,which enables an efficient DL-ROM without the need for a massive trainingdataset for the low-dimensional modeling. Once trained, the network provides anonlinear mapping of input-output dynamics that can predict the coupledfluid-structure dynamics for a longer horizon via the feedback process. Byintegrating the LSTM network with the eigensystem realization algorithm (ERA),we construct a data-driven state-space model for the reduced-order stabilityanalysis. We investigate the underlying mechanism and stability characteristicsof VIV via an eigenvalue selection process. To understand the frequency lock-inmechanism, we study the eigenvalue trajectories for a range of the reducedoscillation frequencies and the mass ratios. Consistent with the full-ordersimulations, the frequency lock-in branches are accurately captured by thecombined LSTM-ERA procedure. The proposed DL-ROM aligns with the development ofphysics-based digital twin of engineering systems involving fluid-structureinteractions.

Deep Learning for Stability Analysis of a Freely Vibrating Sphere at Moderate Reynolds Number