Physics GNN Symbolic Discovery: A Self-Auditing Graph Neural Network for Classical Mechanics

This paper studies a deliberately closed testbed for scientific relation discovery. Classical mechanics is encoded as a typed graph with 159 quantity nodes, 131 equation nodes, and 15 law nodes, and an operator-conditioned graph attention network is trained to infer hidden quantities from partial observations. The training corpus contains 650,000 scenario-consistent physical worlds. Five input–target combinations are excluded during training; at epoch 40, the archived model obtains R² values from 0.986 to 0.994 on these held-out tests. Counterfactual probes generate candidate power-law relations, and a symbolic audit separates derivable corollaries from prior-sensitive artifacts and cases outside the certifier’s algebra. The work does not claim new physics; it provides a reproducible closed-world benchmark for evaluating whether neural relation-discovery systems can distinguish encoded consequences from distribution-dependent correlations.