发表机构
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出GeoQ框架，用于科学代理模型的非侵入式误差估计，经多类任务验证，其几何感知条件分位数建模可实现感知有效性的误差估计。
AI 中文摘要
神经网络代理模型正越来越多地用于加速科学模拟，但将其部署到外推和自回归场景中需要依赖输入的预测误差估计。本研究提出GeoQ（Geometry-Aware Conditional Quantile Error Estimation，几何感知条件分位数误差估计），这是一种用于估计单个查询点处代理误差的非侵入式校准框架。GeoQ将查询点处的误差表示为锚点平均校准误差加上一个可学习的非负修正项，该修正项被建模为锚点相对误差增量的上条件分位数，使用编码表示空间位移和局部支持密度的基于几何的特征。交叉拟合过程生成近似的样本外校准元组，而特征空间k近邻支持分数则识别出校准数据支持学习到的误差模型的区域。我们在标量回归、混沌动力学、中期天气预报和Richtmyer-Meshkov不稳定性预测任务上对GeoQ进行评估，结果表明，几何感知条件分位数建模为科学代理模型中感知有效性的误差估计提供了一种实用且非侵入式的方法。
英文摘要
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.
Comments25 pages, 6 figures, 5 tables
