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

• URL: http://arxiv.org/abs/2608.21652v1
• Date: Fri, 21 Aug 2026 21:47:16 GMT
• Title: GeoQ: Geometry-Aware Conditional Quantile Error Estimation for Scientific Surrogate Models
• Abstract summary: We introduce GeoQ, a non-intrusive framework for estimating surrogate error at individual query points.<n>GeoQ represents the error at a query point as an anchor-averaged calibration error plus a learned nonnegative correction.<n>We evaluate GeoQ on scalar regression, chaotic dynamics, medium-range weather forecasting, and Richtmyer-Meshkov instability prediction.
• Score: 0.4870652964208548
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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