AeTHERON: Autoregressive Topology-aware Heterogeneous Graph Operator Network for Fluid-Structure Interaction

2026-04-14

AI Summary

This work addresses the challenge of high-dimensional nonlinear dynamical modeling for chaotic unsteady flows coupled with large-deformation structures under immersed moving boundaries by proposing AeTHERON, a heterogeneous graph neural operator. The method uniquely integrates the physical priors of the immersed boundary method into the design of a graph neural operator, employing a dual-graph architecture to separately represent fluid and structural domains. A sparse cross-attention mechanism captures the local interpolation characteristics inherent in immersed boundary formulations, while continuous sinusoidal time embeddings enable generalization across time steps. Evaluated on a flexible caudal fin benchmark, the model achieves an average MAE of 0.168 during extrapolation (t=150–200), delivers millisecond-level inference on a single GPU, accelerates simulation by several orders of magnitude compared to direct numerical simulation, and accurately reproduces vortex topology and wake structures.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Surrogate modeling of body-driven fluid flows where immersed moving boundaries couple structural dynamics to chaotic, unsteady fluid phenomena remains a fundamental challenge for both computational physics and machine learning. We present AeTHERON, a heterogeneous graph neural operator whose architecture directly mirrors the structure of the sharp-interface immersed boundary method (IBM): a dual-graph representation separating fluid and structural domains, coupled through sparse cross-attention that reflects the compact support of IBM interpolation stencils. This physics-informed inductive bias enables AeTHERON to learn nonlinear fluid-structure coupling in a shared high-dimensional latent space, with continuous sinusoidal time embeddings providing temporal generalization across lead times. We evaluate AeTHERON on direct numerical simulations of a flapping flexible caudal fin, a canonical FSI benchmark featuring leading-edge vortex formation, large membrane deformation, and chaotic wake shedding across a 4x5 parameter grid of membrane thickness (h* = 0.01-0.04) and Strouhal number (St = 0.30-0.50). As a proof-of-concept, we train on the first 150 timesteps of a representative case using a 70/30 train/validation split and evaluate on the fully unseen extrapolation window t=150-200. AeTHERON captures large-scale vortex topology and wake structure with qualitative fidelity, achieving a mean extrapolation MAE of 0.168 without retraining, with error peaking near flapping half-cycle transitions where flow reorganization is most rapid -- a physically interpretable pattern consistent with the nonlinear fluid-membrane coupling. Inference requires milliseconds per timestep on a single GPU versus hours for equivalent DNS computation. This is a continuously developing preprint; results and figures will be updated in subsequent versions.

Problem

• fluid-structure interaction
• surrogate modeling
• immersed boundary
• unsteady flow
• chaotic dynamics

Innovation

• heterogeneous graph neural operator
• fluid-structure interaction
• immersed boundary method
• physics-informed machine learning
• temporal generalization