Two-Scale Localized PCA-Net v0.1.0
First public research release accompanying the two-scale localized PCA-Net study for artifact-reduced elliptic PDE operator learning.
Highlights
- Two-scale coarse-global plus local-residual output representation.
- Block-balanced latent supervision for coarse and residual score blocks.
- Optional interface-aware physical-field fine-tuning with reconstruction, value-trace, and normal-derivative trace losses.
- Differentiable patch assembly and consistent interface, spectral, and PDE-residual diagnostics.
- Config-driven Poisson and Darcy experiment suites, including headline, mechanism, resolution, sample-efficiency, coarse-representation, loss, and SVD-solver studies.
- Manuscript table, figure, schematic, and diagnostic-generation scripts.
- Deterministic splits, randomized-SVD controls, stage-wise timing, and 93 passing tests.
- MIT license, GitHub citation metadata, and Zenodo release metadata.
Reproducibility
Processed datasets and generated paper results are intentionally excluded from this source release. The companion Zenodo dataset record will provide the exact processed Poisson and Darcy archives, checksums, and experiment configurations.
Scope
This is research software accompanying the manuscript. The primary method is two-scale localized PCA-Net; interface-aware fine-tuning is an optional continuity-oriented refinement.