Multi-Fidelity Physics-Informed Graph Neural Networks for 3D Gear Contact Stress Prediction Under Extreme Gradients

Abstract

Full three-dimensional gear-contact analysis resolves localized tensor fields that simplified models cannot recover, but repeated nonlinear finite element (FE) solutions are costly. This study develops a multi-fidelity physics-informed graph surrogate combining a coarse learning graph, peak-sensitive KDTree projection, gated message passing, and a regularized least-squares finite-difference equilibrium residual. The stress-prior-conditioned benchmark uses a coarse prior derived from the same high-fidelity FE field and therefore is not label-free. Across five random seeds on the 750-case test split, it yields NMSE = (9.1 ± 0.4) × 10−5, R2 = 0.985 ± 0.001, and peak-stress error = 2.5 ± 0.2%. A geometry-only gate provides a preliminary label-free result, with 4.1% peak-stress error for seed 42; its complete multi-seed metrics were not retained. One conditioned forward pass requires 42 ms, excluding preprocessing and prior construction, and peak training memory is 47.6 GB on the reported hardware. Maximum projection outperforms distance-weighted averaging at one fixed graph resolution. All targets are simulated, so the method is presented as a numerical FE surrogate rather than an experimentally validated digital-twin replacement.