发表机构
Sardar Patel Institute of Technology（萨达尔·帕特尔理工学院）
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GIIT工具，通过图映射与干预测试评估PINN中物理对应关系的稳定性，发现时域外推导致层映射漂移，功能对应性在输出指标退化前已改变。
AI 中文摘要
我们探究在训练好的科学模型内部发现的物理上有意义的对应关系，在发现这些关系的条件之外是否仍然有意义。我们引入了GIIT（基于图的检查与干预工具），它将控制物理表示为计算物理依赖图，通过基于敏感性和趋势的发现方法将图节点映射到内部网络组件，并在有针对性的干预下测试所得映射。在日益严重的时域外推分布外（OOD）场景下进行评估，我们发现时域外推与逐层对应漂移和功能对应性降低相关。具体而言，虽然模型在分布内（ID）实现了低物理残差（完整ID上为1.915 x 10-4，ID子窗口t在[0.5, 0.8]上为1.01 x 10-4），但功能映射在离开训练域之前就已发生变化，并且随着评估窗口扩展到训练域之外，这种变化持续：残差误差从跨越边界窗口（t在[0.5, 1.5]）的2.81 x 10-2增加到严重OOD（t在[1, 2]）的3.30 x 10-1，同时内部层映射出现系统性左移，平均获胜层索引从5.71（ID）降至3.00（ID子窗口），再降至2.29（严重OOD）。在跨越边界窗口中，7个物理节点中只有2个保持稳定的层分配，在严重外推下只有1个，这揭示了在传统输出指标严重退化之前可能存在的内部功能对应性变化。线性振荡系统的额外结果在附录中进一步详述。
英文摘要
We ask whether physically meaningful correspondences discovered inside a trained scientific model remain meaningful outside the conditions under which they were discovered. We introduce GIIT (Graph-based Inspection and Intervention Tool), which represents governing physics as a computational physics dependency graph, maps graph nodes to internal network components via sensitivity- and trend-based discovery, and tests the resulting mapping under targeted intervention. Evaluating on temporal extrapolation out-of-distribution (OOD) regimes of increasing severity, we find that temporal extrapolation is associated with layer-wise correspondence drift and reduced functional correspondence. Specifically, while the model achieves low physics residual in-distribution (1.915 x 10-4 on full ID and 1.01 x 10-4 on an ID sub-window t in [0.5, 0.8]), the functional mapping changes even before leaving the training domain, and the shift continues as the evaluation window extends beyond the training domain: residual error increases from 2.81 x 10-2 on the boundary-crossing window (t in [0.5, 1.5]) to 3.30 x 10-1 on severe OOD (t in [1, 2]), accompanied by a systematic leftward shift of internal layer mappings, where the average winner layer index drops from 5.71 (ID) to 3.00 (ID sub-window) down to 2.29 (severe OOD). Only 2 of 7 physical nodes maintain stable layer assignments across the boundary-crossing window, and only 1 of 7 under severe extrapolation, revealing potential internal functional correspondence changes before severe degradation in conventional output metrics. Additional results for linear oscillatory systems are further detailed in the appendix.
CommentsThis is a developmental work which was submitted to NeurIPS workshops. Useful feedback was obtained and an improved version is being developed
