pde-learning

This arXiv paper identifies 'geometry–physics confounding' as a unified failure mechanism for learning PDEs across varying domains, and proposes a de-confounding framework using geometry-induced coefficient fields and geometry-complete candidate libraries that dramatically improves operator learning and equation discovery accuracy.

StationPDE is a station-oriented surface PDE learning model for multi-station multivariate weather forecasting that constructs terrain-aware continuous fields and models physical dynamics to outperform state-of-the-art baselines with a 9.6% MSE reduction.

The paper introduces a reference-free instrument to detect and discriminate operator misspecification in hybrid PDE-parameter learning from a single fit, demonstrating its effectiveness on a parabolic inverse problem while separating it from parameter unidentifiability.