PassiveHNet: A Structure-Constrained Port-Hamiltonian Neural Residual for Differentiable High-Dimensional Vehicle Dynamics and Implicit Sensitivity Analysis

This work presents PassiveHNet, a structure-constrained neural residual architecture embedded in a 108-state hybrid multibody vehicle dynamics simulator. The formulation enforces mechanical consistency via a monotone kinetic ICNN over squared momenta, an affine FiLM-conditioned convex potential with exact Bregman tangent subtraction at equilibrium, and a masked positive semi-definite dissipation operator. State transitions are integrated using a two-stage Gauss-Legendre Runge-Kutta method (GLRK-4) coupled with an exact 216-variable Implicit Function Theorem (IFT) sensitivity audit that confirms production gradients to a $6.61 \\times 10^{-10}$ relative error. Empirical evaluation on held-out Tire Test Consortium (TTC) experimental data shows a 13.2% global lateral force RMSE reduction over an analytical Pacejka baseline. Full implementation and reproducibility artifacts are available at https://github.com/calico21/Project-GP.