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In this paper, we present a generic approach of a dynamical data-driven model order reduction technique for three-dimensional fluid-structure interaction problems. A low-order continuous linear differential system is identified from snapshot solutions of a high-fidelity solver. The reduced order model (ROM) uses different ingredients like proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and Tikhonov-based robust identification techniques. An interpolation method is used to predict the capsule dynamics for any value of the governing non-dimensional parameters that are not in the training database. Then a dynamical system is built from the predicted solution. Numerical evidence shows the ability of the reduced model to predict the time-evolution of the capsule deformation from its initial state, whatever the parameter values. Accuracy and stability properties of the resulting low-order dynamical system are analyzed numerically. The numerical experiments show a very good agreement, measured in terms of modified Hausdorff distance between capsule solutions of the full-order and low-order models both in the case of confined and unconfined flows. This work is a first milestone to move towards real time simulation of fluid-structure problems, which can be extended to non-linear low-order systems to account for strong material and flow non-linearities. It is a valuable innovation tool for rapid design and for the development of innovative devices.