Data-Free Finite-Volume Convolutional Neural Networks for Steady Compressible Euler Flow around a Circular Cylinder

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 agreement.For 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 3.Ten 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 established.Component interventions remain one-seed conditional responses; Mach 2 uses a separate budget-limited protocol.