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Data-driven nonlinear reduced-order modeling of unsteady fluid–structure interactions

A novel data-driven nonlinear reduced-order modeling framework is proposed for unsteady fluid–structure interactions (FSIs). In the proposed framework, a convolutional variational autoencoder model is developed to determine the coordinate transformation from a high-dimensional physical field into a reduced space. This enables the efficient extraction of nonlinear low-dimensional manifolds from the high-dimensional unsteady flow field of the FSIs. The sparse identification of a nonlinear dynamics (SINDy) algorithm is then used to identify the dynamical governing equations of the reduced space and the vibration responses. To investigate and validate the effectiveness of the proposed framework for modeling and predicting unsteady flow fields in FSI problems, the two-dimensional laminar vortex shedding of a fixed cylinder is considered. Furthermore, the proposed data-driven nonlinear reduced-order modeling framework is applied to the three-dimensional vortex-induced vibration of a flexible cylinder. Using the SINDy model to analyze the vibration responses, the dynamics of the flexible cylinder are found to be correlated with the flow wake patterns, revealing the underlying FSI mechanism. The present work is a significant step toward the establishment of machine learning-based nonlinear reduced-order models for complex flow phenomena, the discovery of underlying unsteady FSI physics, and real-time flow control.