Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning
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 recons...
| Authors | Mrigank Dhingra, Jordan Stout, Omer San |
|---|---|
| Primary category | cs.LG |
| Published | 7 September 2026 |
| Last updated at source | 7 September 2026 |
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