Surrogate-to-code verification of a non-intrusive POD-GPR machine-learning emulator of peak thermomechanical fields, with application to a carbon-carbon aircraft brake disc

Abstract

While non-intrusive reduced-order emulators successfully substitute for costly finite-element simulations, certification-grade applications demand a rigorous error assessment relative to the solver's own discretization uncertainty. This work introduces a verification framework designed to evaluate prediction accuracy directly against this numerical uncertainty floor, rather than physical observation. We demonstrate this approach on a carbon-carbon aircraft brake disc during a rejected take-off scenario, predicting peak temperature and peak von Mises stress fields. Operating over a fixed mesh of 60914 nodes, the emulator relies on a pipeline coupling proper orthogonal decomposition (POD) and Gaussian process regression (GPR) parameterized by 5 inputs. We formulate an algebraically exact, a posteriori error budget that isolates the emulator's signed error into distinct truncation and regression components at the extremum. This error is then evaluated against a discretization floor established via mesh-convergence studies on the peak quantities of interest. On a completely independent test set, our emulator matches the high-fidelity solver's peak values within its own discretization uncertainty for both fields, a benchmark we define as surrogate-to-code fidelity. Notably, the residual error stems primarily from linear reduction limits rather than regression inaccuracies. Beyond the main framework, we present two secondary contributions: the concurrent, non-intrusive prediction of the thermal and mechanical peaks, and a probabilistic approach to spatial zone localization for these extrema. This methodology applies to non-intrusive reduced-order models of parameterized finite-element simulations wherever a discretization-error estimate for the quantity of interest can be obtained.