Multi-Granularity Conformal Prediction for Reliable Neural-Operator Automotive Aerodynamic Surrogates

Abstract

High-fidelity computational fluid dynamics (CFD) provides detailed aerodynamic data for vehicle design, but its cost limits design iteration. Neural-operator surrogates reduce this cost, yet their deterministic predictions do not indicate when a geometry or surface region is reliable. This study develops a conformal-prediction framework for reliability-aware automotive aerodynamic surrogate modeling on the DrivAerML dataset. GeoTransolver is the main backbone, while Transolver assesses transfer across neural-operator architectures. For drag coefficient prediction, conformalized quantile regression constructs calibrated case-level intervals. For surface pressure and wall shear stress (WSS), point prediction is combined with residual-scale estimation and residual-normalized conformal calibration to obtain spatially adaptive intervals. Global absolute, point-adaptive normalized, and case-wise normalized calibration are compared under split and cross-validation-assisted out-of-fold protocols. All experiments target 90% nominal coverage. Conformal calibration corrects the under-coverage of raw drag-coefficient quantile intervals, while out-of-fold score aggregation reduces the Monte Carlo coverage standard deviation from 10.41 to 3.10 percentage points. For surface fields, point-adaptive normalized calibration yields the narrowest near-nominal intervals, reducing mean width by 22.68% for pressure and 25.35%--27.09% for WSS under the out-of-fold protocol. Case-wise normalized calibration is more conservative but improves vehicle-level reliability. Smoothness regularization reduces the residual-scale local-variation score by 74.29% and lowers interval widths without material coverage loss. The framework converts deterministic neural-operator outputs into calibrated reliability indicators for prioritizing uncertain vehicle geometries and surface regions in follow-up CFD verification.