Reproduce “Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning” on OpenResearch

About this paper

Mrigank Dhingra, Jordan Stout, Omer San

Two-Scale Localized PCA-Net reduces the seam artifacts of nonoverlapping localized reduced-order models by representing PDE solutions as a shared coarse global field plus patchwise residuals. On Poisson problems, it cuts relative error roughly in half compared with overlapping localized PCA-Net while requiring about half the PCA-fitting time; interface-aware fine-tuning further improves trace consistency, whereas gains on heterogeneous Darcy flow are mainly reflected in reduced flux jumps and PDE residuals.

Key insights

• Many localized seam artifacts arise because each patch must independently reproduce domain-scale structure; assigning low-frequency behavior to a single global branch reduces this duplicated and inconsistent prediction burden.
• The PCA representation can be substantially more accurate than the learned operator: on Poisson-128², the two-scale PCA oracle reaches about 0.501% error while predicted scores yield about 1.149%, identifying latent-code prediction as a key remaining bottleneck.
• Interface losses are most useful for continuity and residual diagnostics, not necessarily for the largest global reconstruction improvement; overlap remains competitive when direct seam error is the primary criterion.

Summary by alphaXiv.