GeoQ: Geometry-Aware Conditional Quantile Error Estimation for Scientific Surrogate Models

Abstract:Neural-network surrogate models are increasingly used to accelerate scientific simulations, but their deployment in extrapolative and autoregressive settings requires input-dependent estimates of prediction error. In this work, we introduce GeoQ (Geometry-Aware Conditional Quantile Error Estimation), a non-intrusive calibration framework for estimating surrogate error at individual query points. GeoQ represents the error at a query point as an anchor-averaged calibration error plus a learned nonnegative correction. This correction is modeled as an upper conditional quantile of the anchor-relative error increment, using geometry-based features that encode representation-space displacement and local support density. A cross-fitting procedure generates approximately out-of-sample calibration tuples, while a feature-space k-nearest-neighbor support score identifies regions \textcolor{black}{where the learned error model is supported by calibration data}. We evaluate GeoQ on scalar regression, chaotic dynamics, medium-range weather forecasting, and Richtmyer-Meshkov instability prediction. The results demonstrate that geometry-aware conditional quantile modeling provides a practical and non-intrusive approach for validity-aware error estimation in scientific surrogate models.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2608.21652 [cs.LG]

(or arXiv:2608.21652v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.21652 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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