Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning

תקציר מקורי באנגליתarXiv:2609.08034v1 Announce Type: new Abstract: Localized dimensionality reduction improves the scalability of operator learning for high-dimensional partial differential equations (PDEs), but independently decoded local patches can introduce block offsets, interface mismatches, and spurious high-wavenumber content. We introduce Two-Scale Localized PCA-Net, which decomposes the solution into a coarse-global component and local residual corrections. A compact global PCA basis captures domain-scale structure, while nonoverlapping local PCA bases represent the remaining fine-scale residual. A block-balanced latent objective couples the two representations, and optional interface-aware fine-tuning further promotes continuity through reconstruction and trace losses. On Poisson benchmarks, the t