Uncertainty quantification using conformal prediction for mesh-based simulations.

Authors

Samira Mabtoul, Izhar Ali, Shen Shyang Ho

Published in

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. Volume 384. Issue 2327. Aug 27, 2026.

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'.

PMID:
42656158
Bibliographic data and abstract were imported from PubMed on 27 Aug 2026.

Read full publication at:
Please sign in to see all details.

Stats

1-terrible, 9-excellent. How would you rate this publication? Sign in in to submit your rating.

Post a comment

You need to be signed in to post comments. You can sign in here.

Comments

There are no comments yet.