Uncertainty quantification using conformal prediction for mesh-based simulations

Abstract

Machine learning surrogates for computational fluid dynamics (CFD) achieve substantial speedups but lack uncertainty quantification (UQ). We develop a post hoc conformal prediction (CP) framework that wraps any trained graph neural network (GNN) surrogate to produce prediction sets with coverage near-nominal levels. Using MeshGraphNet on two benchmark datasets-CylinderFlow (2D velocity) and Flag (3D position), we compare five prediction-set geometries. Our componentwise adaptive (CW-Adaptive) method emerges as the robust universal choice, achieving 28%-55% smaller prediction sets versus ℓ2 balls across both datasets at 95% confidence while maintaining near-nominal coverage. By learning per-component scales from domain-aware features, CW-Adaptive captures both spatial heterogeneity and anisotropic error structure-outperforming Mahalanobis ellipsoids that provide only modest gains (approx. 14%) when residuals are anisotropic and inflate sets otherwise. All methods achieve coverage within 2%-3% of nominal despite distribution drift in mesh-based simulations that violates exchangeability assumption. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.