arXiv:2606.23251cs.CEcs.LG2026-06

用注意力机制构建可扩展的流体模拟代理模型,支持动态变形网格。

Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids

论文配图:Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids
图 1 · 摘自论文原文
  • 基于自注意力机制建模节点间复杂交互,保持网格拓扑结构。
  • 在多维自由表面流动中准确预测瞬态与最终状态,计算效率显著提升。
  • 适合工程级流体模拟场景,可直接重建应力场等物理量。

采用拉格朗日方法(如粒子有限元法,PFEM)进行自由表面流高保真模拟时,因域不断更新及控制方程反复求解而计算成本高昂,尤其在非牛顿流变学条件下材料非线性使开销进一步增加。为此,亟需发展高效代理模型以低代价近似PFEM动态行为。尽管数据驱动的深度学习方法前景广阔,但如何在任意且动态变化的几何上构建模型仍是关键挑战。本文提出一种基于自注意力机制的神经代理模型,用于自由表面流的PFEM模拟。该架构利用注意力机制捕捉节点间复杂空间依赖关系,同时保留PFEM网格离散化特性,为重网格化和节点重分布提供几何与拓扑框架,确保滚动预测中保持高质量空间离散,提升长期稳定性,并可通过标准有限元算子重构导出力学量。考虑了两种注意力形式:标准自注意力与线性变体,后者降低计算成本并提升可扩展性。模型在二维与三维自由表面流动基准测试中评估,涵盖动态几何、变化材料参数及非牛顿流体。结果表明,模型能准确预测瞬态动力学与最终构型,显著提升可扩展性。网格基形式还可直接重建应力场等物理量。整体框架为工程规模的PFEM模拟提供了准确且可扩展的代理策略。

原文摘要 · Abstract (English)

High-fidelity simulations of free-surface flows using Lagrangian methods such as the Particle Finite Element Method (PFEM) are computationally demanding due to continuous domain updates and repeated solution of the governing equations. This challenge is further amplified by non-Newtonian rheologies, where material nonlinearities increase computational cost. These limitations motivate the development of efficient surrogate models to approximate PFEM dynamics at reduced cost. While data-driven deep learning approaches are promising, a key challenge is designing models that operate on arbitrary and evolving geometries. We propose a self-attention-based neural surrogate for PFEM simulations of free-surface flows. The architecture leverages attention mechanisms to model node interactions and capture complex spatial dependencies, while preserving the PFEM mesh discretization. This provides a geometric and topological framework for remeshing and node redistribution, maintaining high-quality spatial discretization during rollouts, improving long-term stability, and enabling reconstruction of derived mechanical quantities via standard finite element operators. Two attention formulations are considered: a standard self-attention mechanism and a linear variant that reduces computational cost and improves scalability. The models are evaluated on two- and three-dimensional free-surface flow benchmarks with evolving geometries, varying material parameters, and non-Newtonian fluids. Results show accurate prediction of transient dynamics and final configurations, with significantly improved scalability. The mesh-based formulation also enables direct reconstruction of quantities such as stress fields. Overall, the framework provides an accurate and scalable surrogate strategy for PFEM simulations in engineering-scale applications.

流体模拟注意力机制代理模型网格生成

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