On Parameter Decoupling, Conditioning, and Interface Transmission in Multi-Objective Physics-Informed Neural Networks

PREPRINT / MANUSCRIPT UNDER REVIEWVenue: Computer Methods in Applied Mechanics and Engineering (CMAME, Elsevier)Manuscript ID: CMAME-D-26-05120 KEY THEORETICAL & EMPIRICAL HIGHLIGHTS• Algebraic Parameter Decoupling: Exact orthogonal direct-sum parameter splitting (Θ = Θ₀ ⊕ Θ₁, W₀W₁ᵀ = 0) blended via C² Quintic Hermite transition routing.• Representation Rank Invariance: Proof that metric tensor rank is strictly invariant (rank = 2 for all α < 1), acting as an anisotropic optimizer preconditioner.• B-Spline Basis Superiority: Demonstrates that localized cubic B-spline bases resolve boundary stiffness without parameter partitioning, cutting interior error 1.53× with zero parameter splitting.• Cross-Domain Multi-Physics: Rigorously benchmarked across 10 matched-capacity models (P = 9,216) and 6 physical regimes, including 3D Linear Paul Ion Traps (2.0× harmonic purity gain). OPEN-SOURCE CODEBASE & REPRODUCIBILITYOfficial Codebase & Benchmark Suite:https://github.com/KartikeyaGangwar/null-space-pinn