混合PDE参数学习中算子误设的检测与区分：无参考工具
原标题：Detecting and Discriminating Operator Misspecification in Hybrid PDE-Parameter Learning: a Reference-Free Instrument, with Discrimination Bounded In Sample
AI 摘要
该研究针对混合PDE参数学习中的算子误设问题，提出了一种无需参考模型的检验工具，能从单次拟合中区分算子错误与参数不可辨识。实验表明，误设估计器在域内误差低于噪声，但系数偏差大，且容量无关，多种架构收敛到相同的伪真值。该工具在正确设定下保持沉默，在误设下高概率拒绝，为可部署测试提供了分离两种失败的能力。
正文节选
Detecting and Discriminating Operator Misspecification in Hybrid PDE-Parameter Learning: a Reference-Free Instrument, with Discrimination Bounded In Sample Abstract We build an instrument that reads, from a single fit and with no oracle, whether the operator a hybrid PDE-parameter estimator postulates is wrong—and separates that from a merely unidentifiable parameter. On one self-adjoint parabolic inverse problem, an information-matrix statistic with plug-in scale and per-seed parameter has medi