arXiv cs.AI· Yatin Kumar, Shivani Saini, Ramesh Kumar Vats·· 12 小时前AI 评分22
GeoDiv KAN：面向复杂域时间分数阶 Navier-Stokes 方程的求解器与真实 CFD 重建
GeoDiv KAN Solver for Time Fractional Navier Stokes Equations on Complex Domains to Realistic CFD Reconstruction
AI 导读
研究者提出 GeoDiv KAN——一种几何门控、无散度的 Gaussian 径向基函数 Kolmogorov Arnold 网络，用于求解复杂域上的时间分数阶不可压缩 Navier-Stokes 方程。在方形、圆形和星形域基准上，其预测精度高于 PINN、PIKAN、RBF KAN 和 DF RBFKAN。该方法还应用于圆柱绕流与复杂 U 型弯管湍流 RANS 两个数据驱动 CFD 案例。
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