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.

翻译：我们提出了一种旋转等变、准单块图神经网络框架，用于流固耦合系统的降阶建模。借助任意拉格朗日-欧拉方法，系统状态通过两个子网络进行时间演化。网格运动通过复值本征正交分解简化为若干系数的演化，并通过单层多层感知器预测这些系数随时间的变化。采用基于有限元思想的超图神经网络，根据整个系统状态预测流体状态的演化。结构状态由固-流界面的网格运动隐式建模，从而使所提框架具有准单块特性。我们通过两个典型的流固耦合系统评估该框架的有效性，即弹性安装圆柱绕流，以及固定圆柱后方附着的超弹性板绕流。所提框架在至少2000个时间步的推演中能精准追踪界面描述并提供稳定准确的系统状态预测，甚至展现出一定的自我纠正错误预测能力。与现有基于卷积的架构不同，该框架还可通过预测的流体与网格状态直接计算升力和阻力。该基于图神经网络的降阶模型为开发涉及移动边界与流固耦合的物理信息数字孪生系统提供了新思路。