GeoDiv KAN 求解复杂域上时间分数阶 Navier-Stokes 方程以实现真实 CFD 重建
GeoDiv KAN Solver for Time Fractional Navier Stokes Equations on Complex Domains to Realistic CFD Reconstruction
AI 导读
论文提出几何门控、无散度的高斯径向基函数 Kolmogorov Arnold 网络 GeoDiv KAN，通过几何依赖特征门控和流函数表述在构造上保持不可压缩性，用于求解复杂域上的时间分数阶不可压缩 Navier-Stokes 方程。
正文 · 原文
Abstract:Scientific machine learning provides a promising framework for solving complex problems in science and engineering. Notably, physics informed neural networks (PINNs) have shown considerable potential for solving differential equations and modelling engineering systems. Solving time fractional Navier Stokes equations (TFNSEs) on complex domains is challenging due to temporal nonlocality, nonlinear flow dynamics, geometric complexity, and incompressibility constraints. To address these challenges, we propose a geometry gated, divergence-free Gaussian radial basis function Kolmogorov Arnold network (GeoDiv KAN). The proposed architecture uses geometry dependent feature gating and a streamfunction formulation to preserve incompressibility by construction. GeoDiv KAN is evaluated for the time fractional incompressible Navier-Stokes equations on square, circular, and star-shaped domains. Numerical experiments show that GeoDiv KAN achieves higher predictive accuracy than PINN, PIKAN, RBF KAN, and DF RBFKAN across the considered benchmark problems. To establish practical relevance, GeoDiv KAN is applied to two data driven CFD cases: unsteady flow past a circular cylinder using the \href{this https URL}{Zenodo dataset} and turbulent RANS flow through a complex U bend using the \href{this https URL}{U-bend dataset}.
| Subjects: | Fluid Dynamics (physics.flu-dyn); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.30179 [physics.flu-dyn] |
| (or arXiv:2610.30179v2 [physics.flu-dyn] for this version) | |
| https://doi.org/10.48550/arXiv.2610.30179 arXiv-issued DOI via DataCite |
Submission history
From: Yatin Kumar [view email]
[v1]
Mon, 19 Oct 2026 14:15:49 UTC (37,472 KB)
[v2]
Fri, 23 Oct 2026 15:32:40 UTC (37,472 KB)
来源：arXiv cs.AI · arxiv.org