A Graph-Based Inspection and Intervention Tool for Assessing Mechanistic Learning in PINNs

Adwait Patkhedkar, Alifaraz Lakhani, Prathmesh Mohite, Abhijeet Salunke

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…