Learning Stiffness Dependent Fluid Structure Dynamics from Coarse Flow Representations

We propose an arbitrary Lagrangian-Eulerian (ALE)-consistent machine learning framework for long-term fluid-structure interaction (FSI) prediction on deforming unstructured meshes. Specifically, the fluid dynamics are modeled by a surrogate that combines a graph neural operator (GNO) with a vision Transformer (ViT) for spatiotemporal prediction, while a lightweight long short-term memory (LSTM) network predicts structural kinematics at the interface. The two surrogates are coupled through a standard partitioned procedure. Most importantly, kinematic compatibility at the moving interface is enforced via an ALE-consistent boundary-correction step that updates the fluid-side interface velocity with the predicted structural velocity at each coupling update, thereby improving near-interface accuracy and long-term rollout stability. To mitigate autoregressive error accumulation, a two-stage training strategy is adopted, consisting of single-step supervised pretraining followed by long-term autoregressive fine-tuning. The proposed framework is validated on the benchmark problem of a flexible beam vibration in the wake of a cylinder. Results demonstrate accurate phase-consistent predictions over long rollouts and robust generalization under inlet-profile variations in both interpolation and extrapolation settings. Systematic ablation studies further assess the respective contributions of the ViT module, ALE-consistent boundary correction, and long-term training to predictive accuracy and rollout robustness.

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.

Fluid-solid interaction (FSI) problems are fundamental in many scientific and engineering applications, yet effectively capturing the highly nonlinear two-way interactions remains a significant challenge. Most existing deep learning methods are limited to simplified one-way FSI scenarios, often assuming rigid and static solid to reduce complexity. Even in two-way setups, prevailing approaches struggle to capture dynamic, heterogeneous interactions due to the lack of cross-domain awareness. In this paper, we introduce Fisale, a data-driven framework for handling complex two-way FSI problems. It is inspired by classical numerical methods, namely the Arbitrary Lagrangian-Eulerian (ALE) method and the partitioned coupling algorithm. Fisale explicitly models the coupling interface as a distinct component and leverages multiscale latent ALE grids to provide unified, geometry-aware embeddings across domains. A partitioned coupling module (PCM) further decomposes the problem into structured substeps, enabling progressive modeling of nonlinear interdependencies. Compared to existing models, Fisale introduces a more flexible framework that iteratively handles complex dynamics of solid, fluid and their coupling interface on a unified representation, and enables scalable learning of complex two-way FSI behaviors. Experimentally, Fisale excels in three reality-related challenging FSI scenarios, covering 2D, 3D and various tasks. The code is available at \href{https://github.com/therontau0054/Fisale}.