用图神经网络模拟柔性尾鳍与流体的复杂相互作用，实现快速高精度预测。
AeTHERON: Autoregressive Topology-aware Heterogeneous Graph Operator Network for Fluid-Structure Interaction
- 构建双图结构模型，分离流体与结构域，通过稀疏交叉注意力模拟流固耦合。
- 在4×5参数空间上外推预测，平均误差仅0.168，毫秒级推理速度远超传统计算。
- 适合需要快速仿真流固耦合系统的工程与科研人员，尤其关注非线性动态行为。
对于由运动边界驱动的流体流动，其流固耦合（FSI）涉及结构动力学与混沌非定常流体现象的复杂交互，是计算物理与机器学习中的核心挑战。本文提出AeTHERON，一种异构图神经算子，其架构直接模仿尖锐界面浸入边界法（IBM）的结构：采用双图表示分离流体与结构域，并通过稀疏交叉注意力建模二者耦合，反映IBM插值模板的紧支集特性。该物理启发的归纳偏置使AeTHERON能在共享高维隐空间中学习非线性流固耦合，连续正弦时间嵌入实现跨预测时长的时序泛化。我们在柔性尾鳍摆动的直接数值模拟上评估该方法，涵盖前缘涡生成、膜片大变形及混沌尾迹脱落，参数空间为膜厚h* = 0.01–0.04与斯特劳哈尔数St = 0.30–0.50。作为概念验证，基于代表性案例前150个时间步（70/30训练/验证划分）训练，评估完全未见的外推窗口t=150–200。AeTHERON以定性保真度捕捉大尺度涡结构与尾迹特征，平均外推MAE达0.168，无重训练；误差峰值出现在摆动半周期转换处，此时流场重组最剧烈——这一模式具有明确物理解释，符合非线性流-膜耦合规律。单次时间步推理仅需毫秒级，远快于等效直接数值模拟（需数小时）。本预印本持续更新，后续版本将补充结果与图表。
原文摘要 · Abstract (English)
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.
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