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

2026-08-21

AI Summary

本文提出GeoQ方法，通过几何感知的条件分位数误差估计解决神经网络代理模型在科学仿真中的预测误差估计问题。

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.

Problem

• neural-network surrogate models
• prediction error
• extrapolative and autoregressive settings
• input-dependent estimates

Innovation

• Geometry-Aware
• Conditional Quantile
• Error Estimation
• Surrogate Models