PINN 的导数保真度失效模式：函数值训练的基准证据
原标题：A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training
AI 摘要
该论文将「导数保真度」形式化为物理信息神经网络（PINN）的一种失效模式，并用一维基准函数进行验证。作者仅用函数值训练多层感知机拟合 sin(x) 与 exp(x)，再单独评估自动微分得到的二阶导数，结果显示函数值拟合在视觉上准确的同时，二阶导数误差可能显著偏大，尤其在高曲率边界区域附近。研究据此提出一套诊断流程，用于区分函数值精度与物理残差可靠性。
正文节选
[Page 1] J. ADV. SIMULAT. SCI. ENG. A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training [Koji KOYAMADA]1,* 1 Osaka-seikei University * [koyamada@g.osaka-seikei.ac.jp] Abstract. Physics-informed neural networks (PINNs) use automatic differentiation to impose differential-equation residuals, but good a