Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization

arXiv:2605.23391v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens. We provide a theoretical explanation for this phenomenon through neural tangent kernel (NTK) analysis: for linearly coupled systems, we prove that the standard NTK's spectral radius grows as $\Omega(\gamma^2)$ with coupling strength $\gamma$, shrinking the stable learning rate, while block-diagonal Gauss--Newton (GN) preconditioning yields a preconditioned NTK $K_P = J H^{+} J^\top$ (where $H$ is

Source: arXiv cs.LG — read the full report at the original publisher.

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