NeuroForge: A Self-Correcting, Geometry-Native Neural CFD Engine with Calibrated Physics-Residual Trust

Abstract

Machine-learning surrogates for computational fluid dynamics (CFD) predict steady flow fields orders of magnitude 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 close the loop with the governing physics: we compute the discretised steady-RANS residual of the prediction and ask what jobs it can do. Our central finding is a 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 (Transolver 0.625+-0.019; grid Geo-FNO ~0.40, lifted to 0.83 by a learned corrector; MeshGraphNet 0.851+-0.058) and generalizes to a second dataset and flow regime (DeepCFD laminar bluff bodies, rho=0.77+-0.12). A split-conformal layer attains target coverage (0.902+-0.008 at the 0.90 target) and, paired with a deep-ensemble sigma, yields an input-adaptive band (ECE 0.074). As a correction objective or acceptance gate the residual fails: iteration sweeps raise the PDE residual while lowering field error. Alongside the trust layer we deploy a supervised deep-equilibrium corrector trained toward ground truth that reduces volume-field MSE on all three seeds (mse_u -9%, mse_v -21%, mse_p -25%) on the SOTA backbone; a controlled ablation zeroing the corrector's residual input matches it, so the gain is attributable to the learned correction, not residual-conditioning. We report caveats plainly: correction quality is backbone-dependent, and the coverage guarantee holds under exchangeability. The contribution is a self-auditing trust layer, the residual's two roles, and the learned self-correction it accompanies.