arXiv cs.AI· Ryosuke Yano·· 13 小时前AI 评分18
无数据有限体积卷积神经网络求解圆柱绕流稳态可压缩 Euler 流
Data-Free Finite-Volume Convolutional Neural Networks for Steady Compressible Euler Flow around a Circular Cylinder
AI 导读
研究提出无数据有限体积卷积神经网络（FV-CNN），在 2–15 共八个马赫数下求解圆柱绕流稳态 Euler 流，训练不使用任何 CFD 或实验场数据。八个流场的密度与压力相对 L₂ 偏差分别为 5.43%–18.69% 和 6.25%–19.70%；在 32/32 自中心与 22–31/32 CFD 中心比较中，闭带缺陷小于 AD-CNN。
正文 · 原文
Abstract:A data-free finite-volume convolutional neural network (FV-CNN) is formulated for steady Euler flow around a cylinder at eight Mach numbers, 2--15. Shared-face fluxes define conservative spatial balances, while automatic differentiation supplies parameter gradients. The derivative mismatch in the earlier automatic-differentiation-based convolutional neural network (AD-CNN) is derived. No computational fluid dynamics (CFD) or experimental field targets enter training; reference-independent selection of coefficients, seeds, and checkpoints is not established. Billig-based upstream fixing conditions shock-location this http URL eight adopted fields, density and pressure relative $L_2$ discrepancies from finite-resolution CFD are $5.43$--$18.69\%$ and $6.25$--$19.70\%$. Closed-band defects are smaller than AD-CNN in 32/32 self-centered and 22--31/32 CFD-centered comparisons over seven half-widths, 0.06--0.12 cylinder diameters. AD-CNN retains smaller enthalpy root-mean-square (RMS) discrepancies in 7/8 cases, shock-position RMS at Mach 11 and 15, and temperature and transverse-velocity discrepancies at Mach this http URL new Mach-15 initializations and adopted seed 42 yield density discrepancies of $12.04$--$43.70\%$ (mean $24.34\%$, sample standard deviation $11.78$ percentage points); the new ten alone give $25.04\%$ and $12.17$ points. Dispersion exceeds the historical adopted-field gap of $3.40$ points; six of eleven outcomes are below AD-CNN. Transition-width ratios of AD-CNN to FV-CNN remain $4.07$--$4.66$, and all 44 self-centered seed--component balances at half-width 0.10 cylinder diameters are smaller for FV-CNN. Local sharpness and this balance metric persist, while initialization-robust accuracy superiority is not this http URL interventions remain one-seed conditional responses; Mach 2 uses a separate budget-limited protocol.
| Subjects: | Fluid Dynamics (physics.flu-dyn); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2603.01001 [physics.flu-dyn] |
| (or arXiv:2603.01001v2 [physics.flu-dyn] for this version) | |
| https://doi.org/10.48550/arXiv.2603.01001 arXiv-issued DOI via DataCite |
Submission history
From: Ryosuke Yano [view email]
[v1]
Sun, 1 Mar 2026 09:04:18 UTC (15,958 KB)
[v2]
Wed, 21 Oct 2026 13:15:59 UTC (36,980 KB)
来源：arXiv cs.AI · arxiv.org