NeuroForge: Self-Auditing Neural CFD Surrogates with Calibrated Physics-Residual Trust

Abstract

Machine-learning surrogates for computational fluid dynamics (CFD) predict steady flow fields far faster than classical solvers, but emit a single field with no built-in way to know whether to trust it -- especially out of distribution. We make the surrogate audit itself against the governing physics: we compute the discretised steady-state Reynolds-averaged (RANS) residual of the prediction and ask what jobs it can do. Our central finding is a clean two-way dissociation: the physics residual is a reliable, backbone-robust trust signal (it tells you where the prediction is wrong) but a poor correction objective (it does not tell you how to fix it). As a trust signal, the residual's per-case rank correlation with field error is consistently positive across three architecturally distinct backbones and a second dataset of laminar bluff bodies; it flags the worst-decile cases with AUROC $\approx 0.9$, and a distribution-free split-conformal layer attains its target coverage. As a correction objective, the residual fails: reducing it does not reduce field error. The monotone-residual acceptance gate built on it, by contrast, does help. Separately, a learned deep-equilibrium corrector trained toward ground truth lowers volume-field error on a state-of-the-art backbone; a controlled ablation that removes the residual input matches this gain, so the improvement comes from the learned correction, not from conditioning on the residual. The contribution is a self-auditing, calibrated trust layer, the residual's two roles (trust signal yes, correction objective no), and the learned correction it accompanies, demonstrated on a competitive surrogate and released as the open-source neuroforge-cfd package.

31 pages, 10 figures, 9 tables. v3 corrects v2's claim that the eddy-viscosity channel is effectively unlearned: measured, it is learned (R^2 0.996 grid backbone, 0.67-0.70 MeshGraphNet) and supplies 84% of nu_eff. Also closes the no-slip-weight objection to the residual-floor result in closed form, and adds a wall-clock cost measurement. Code: https://github.com/ali-kin4/neuroforge-cfd