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Solving complex fluid-structure interaction (FSI) problems, characterized bynonlinear partial differential equations, is crucial in various scientific andengineering applications. Traditional computational fluid dynamics (CFD)solvers are insufficient to meet the growing requirements for large-scale andlong-period simulations. Fortunately, the rapid advancement in neural networks,especially neural operator learning mappings between function spaces, hasintroduced novel approaches to tackle these challenges via data-drivenmodeling. In this paper, we propose a Fourier neural operator-basedfluid-structure interaction solver (FNO-based FSI solver) for efficientsimulation of FSI problems, where the solid solver based on the finitedifference method is seamlessly integrated with the Fourier neural operator topredict incompressible flow using the immersed boundary method. We analyze theperformance of the FNO-based FSI solver in the following three situations:training data with or without the steady state, training method with one-steplabel or multi-step labels, and prediction in interpolation or extrapolation.We find that the best performance for interpolation is achieved by training theoperator with multi-step labels using steady-state data. Finally, we train theFNO-based FSI solver using this optimal training method and apply it to vesicledynamics. The results show that the FNO-based FSI solver is capable ofcapturing the variations in the fluid and the vesicle.

Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics