GFocal通过全局与局部特征协同学习,提升任意几何下PDE求解的精度与稳定性。
GFocal: A Global-Focal Neural Operator for Solving PDEs on Arbitrary Geometries
- 设计全局-局部双路径结构,融合长程依赖与局部细节
- 在6个基准上平均相对提升15.2%,工业级气动模拟表现优异
- 适合复杂几何、多尺度物理系统建模,尤其适用于工程仿真
基于Transformer的神经算子已成为求解偏微分方程的有前景替代方法,其利用Transformer捕捉长程依赖和全局相关性的能力,在语言建模中已得到充分验证。然而,现有方法忽略了局部物理细节与全局特征之间协同学习的重要性,这在处理多尺度问题、保持长期推演中的物理一致性与数值稳定性以及精确捕捉过渡动态方面至关重要。本文提出GFocal,一种基于Transformer的神经算子方法,强制实现全局与局部特征的同时学习与融合。通过基于Nyström注意力的全局模块和基于切片的焦点模块,生成具备物理感知的特征表示,并经卷积门控模块调制整合,实现多尺度信息的动态融合。实验表明,GFocal在五个基准任务中平均取得15.2%的相对性能提升,且在汽车与翼型气动仿真等工业级场景中表现卓越。
原文摘要 · Abstract (English)
Transformer-based neural operators have emerged as promising surrogate solvers for partial differential equations, by leveraging the effectiveness of Transformers for capturing long-range dependencies and global correlations, profoundly proven in language modeling. However, existing methodologies overlook the coordinated learning of interdependencies between local physical details and global features, which are essential for tackling multiscale problems, preserving physical consistency and numerical stability in long-term rollouts, and accurately capturing transitional dynamics. In this work, we propose GFocal, a Transformer-based neural operator method that enforces simultaneous global and local feature learning and fusion. Global correlations and local features are harnessed through Nyström attention-based \textbf{g}lobal blocks and slices-based \textbf{focal} blocks to generate physics-aware tokens, subsequently modulated and integrated via convolution-based gating blocks, enabling dynamic fusion of multiscale information. GFocal achieves accurate modeling and prediction of physical features given arbitrary geometries and initial conditions. Experiments show that GFocal achieves state-of-the-art performance with an average 15.2\% relative gain in five out of six benchmarks and also excels in industry-scale simulations such as aerodynamics simulation of automotives and airfoils.
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