摘要：神经代理模型能够显著加速计算机辅助工程（CAE）工作流，但若要将其用于设计，便需要在不同几何形状、空间预测场以及关注的工程量之间仍具实际意义的不确定性估计。我们研究了成熟的不确定性量化（UQ）方法在适配几何条件神经代理模型后的表现。我们比较了一种闭式方法和两种基于采样的方法——基于高斯过程（GP）的方法、concrete Monte Carlo（MC）dropout 和深度集成——并在三个面向工业应用的大型 CAE 数据集上进行了评估，数据集覆盖外部空气动力学和碰撞动力学。

我们考察预测不确定性是否具有可信的量级、能否识别预测误差较大的位置、能否对陌生输入作出响应，以及是否能够为派生工程量提供有效信息。在同时比较三种方法的 DrivAerStar 数据集上，每种方法通常都会为预测误差较大的位置分配更高的不确定性；基于验证集的重缩放可使独立同分布测试集上的区间覆盖率接近标称值。AirFRANS 和汽车碰撞数据集上的结果同样显示出有用的误差排序能力和区间估计效果，但不同方法的相对性能会随数据集和评估标准而变化。因此，应根据预期的下游 CAE 决策选择 UQ 方法和评估指标。

Abstract:Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncertainty quantification (UQ) approaches behave when adapted to geometry-conditioned neural surrogates. We compare one closed-form and two sampling-based approaches-a Gaussian process (GP)-based method, concrete Monte Carlo (MC) dropout, and deep ensembles-and evaluate them on three large, industry-relevant CAE datasets for external aerodynamics and crash dynamics.
We examine whether predicted uncertainties have credible magnitudes, identify locations with larger prediction errors, respond to unfamiliar inputs, and remain informative for derived engineering quantities. On the DrivAerStar dataset, where all three methods are compared, each generally assigns higher uncertainty to locations with larger prediction errors, and validation-based rescaling brings interval coverage close to nominal on a disjoint in-distribution test set. Results on AirFRANS and automotive crash also show useful error ranking and interval estimates, but the relative performance of the methods changes with the dataset and evaluation criterion. UQ methods and evaluation metrics should therefore be selected based on the intended downstream CAE decision.