📄 中文摘要
神经算子（NOs）为输入场与 PDE 解场之间提供快速且分辨率不变的代理映射，但由于有限数据、不完美优化和分布偏移，其预测可能表现出显著的认知不确定性。在科学计算的实际应用中，不确定性量化（UQ）必须具备计算效率和空间忠实性，即不确定性带应与下游风险管理中重要的局部残差结构对齐。提出了一种结构感知的认知 UQ 方案，利用现代 NOs 的模块化结构（提升-传播-恢复）。该方案避免在整个网络中应用无结构的权重扰动（如简单的 dropout），而是针对特定结构进行优化。
结构感知的认知不确定性量化用于神经算子 PDE 代理
📄 English Summary
Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates
Neural operators (NOs) serve as fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, yet their predictions can exhibit significant epistemic uncertainty due to finite data, imperfect optimization, and distribution shifts. For practical deployment in scientific computing, uncertainty quantification (UQ) must be computationally efficient and spatially faithful, meaning uncertainty bands should align with localized residual structures that are critical for downstream risk management. A structure-aware epistemic UQ scheme is proposed, leveraging the modular anatomy common to modern NOs (lifting-propagation-recovering). Instead of applying unstructured weight perturbations (e.g., naive dropout) across the entire network, this approach optimizes perturbations targeting specific structures.