LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Prediction

תקציר מקורי באנגליתarXiv:2609.14977v1 Announce Type: new Abstract: Finite element stress fields often exhibit strong local non-smoothness, where stress concentrations near holes, notches, and loading regions induce sharp spatial gradients and high-frequency graph components. Although graph neural networks naturally operate on irregular finite element meshes, conventional message passing is inherently smoothing and progressively attenuates such high-frequency information. Unitary propagation alleviates this problem by preserving spectral magnitudes, but typically relies on matrix functions and high-order approximations with $O(Ked)$ propagation complexity. We propose LiftGCN, an efficient spectrally stable graph network based on Joukowski spectral lifting. LiftGCN maps the real spectrum of a normalized graph