  We present a rotation equivariant, quasi-monolithic graph neural network
framework for the reduced-order modeling of fluid-structure interaction
systems. With the aid of an arbitrary Lagrangian-Eulerian formulation, the
system states are evolved temporally with two sub-networks. The movement of the
mesh is reduced to the evolution of several coefficients via complex-valued
proper orthogonal decomposition, and the prediction of these coefficients over
time is handled by a single multi-layer perceptron. A finite element-inspired
hypergraph neural network is employed to predict the evolution of the fluid
state based on the state of the whole system. The structural state is
implicitly modeled by the movement of the mesh on the solid-fluid interface;
hence it makes the proposed framework quasi-monolithic. The effectiveness of
the proposed framework is assessed on two prototypical fluid-structure systems,
namely the flow around an elastically-mounted cylinder, and the flow around a
hyperelastic plate attached to a fixed cylinder. The proposed framework tracks
the interface description and provides stable and accurate system state
predictions during roll-out for at least 2000 time steps, and even demonstrates
some capability in self-correcting erroneous predictions. The proposed
framework also enables direct calculation of the lift and drag forces using the
predicted fluid and mesh states, in contrast to existing convolution-based
architectures. The proposed reduced-order model via graph neural network has
implications for the development of physics-based digital twins concerning
moving boundaries and fluid-structure interactions.
