HGATSolver: A Heterogeneous Graph Attention Solver for Fluid-Structure Interaction

TL;DR

HGATSolver introduces a heterogeneous graph attention framework for surrogate modeling of fluid–structure interaction, explicitly encoding fluid and solid domains and their interface with relation-aware message passing. A Physics-Conditioned Gating Mechanism (PCGM) provides adaptive relaxation to stabilize explicit-time updates, while the Inter-domain Gradient-Balancing Loss (IGBL) automatically weights domain losses according to predictive uncertainty. Across FI-Valve, SI-Vessel, and NS+EW benchmarks, HGATSolver achieves state-of-the-art accuracy, with pronounced gains near interfaces and strong few-shot generalization. By embedding physical heterogeneity as a structural prior and coupling it with uncertainty-aware optimization, the method offers a principled and practical approach to surrogate multi-physics modeling.

Abstract

Fluid-structure interaction (FSI) systems involve distinct physical domains, fluid and solid, governed by different partial differential equations and coupled at a dynamic interface. While learning-based solvers offer a promising alternative to costly numerical simulations, existing methods struggle to capture the heterogeneous dynamics of FSI within a unified framework. This challenge is further exacerbated by inconsistencies in response across domains due to interface coupling and by disparities in learning difficulty across fluid and solid regions, leading to instability during prediction. To address these challenges, we propose the Heterogeneous Graph Attention Solver (HGATSolver). HGATSolver encodes the system as a heterogeneous graph, embedding physical structure directly into the model via distinct node and edge types for fluid, solid, and interface regions. This enables specialized message-passing mechanisms tailored to each physical domain. To stabilize explicit time stepping, we introduce a novel physics-conditioned gating mechanism that serves as a learnable, adaptive relaxation factor. Furthermore, an Inter-domain Gradient-Balancing Loss dynamically balances the optimization objectives across domains based on predictive uncertainty. Extensive experiments on two constructed FSI benchmarks and a public dataset demonstrate that HGATSolver achieves state-of-the-art performance, establishing an effective framework for surrogate modeling of coupled multi-physics systems.

Figures (6)

• Figure 1: Conceptual overview of HGATSolver. (a) The FSI system couples fluid and solid domains with distinct PDEs and a dynamic interface. (b) We encode this structure as a heterogeneous graph, enabling type-aware attention for intra- and inter-domain physics.
• Figure 2: Comparison in the interaction region on FI-Valve. (a) Enlarged error maps show reduced error near the interface. (b) Relative $\ell_2$ errors for fluid and solid domains demonstrate HGATSolver’s superior accuracy compared to a GAT-based baseline.
• Figure 3: Overview of HGATSolver. (a) The FSI mesh is encoded as a heterogeneous graph with fluid and solid nodes and relation-aware edges. (b) PCGM adaptively blends updated and initial states based on physics parameters. (c) IGBL adjusts domain-wise loss weights based on predictive uncertainty.
• Figure 4: Prediction error maps for HGATSolver and AMG across three datasets: (a) FI-Valve, (b) SI-Vessel, and (c) NS+EW.
• Figure 5: Visualization on FI-Valve: (a) GNN output magnitude without gating, (b) learned physics-conditioned gating scalar $g$, and (c) final effective update $g \cdot ||h_{\text{GNN}}||$.