Predicting fluid-structure interaction with graph neural networks

TL;DR

This paper introduces a rotation-equivariant graph neural network framework for reduced-order modeling of fluid-structure interactions, capable of stable long-term predictions and force calculations, advancing digital twin development.

Contribution

It presents a novel quasi-monolithic GNN approach combining hypergraph neural networks and POD for accurate, stable fluid-structure interaction modeling with direct force computation.

Findings

Accurately predicts fluid-structure system states for over 2000 time steps.

Demonstrates stability and some self-correction in long-term rollouts.

Enables direct calculation of lift and drag forces from predicted states.

Abstract

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.