Library-based Corrector Network

PDEs with boundary, corner, or interior layers exhibit localized multiscale behavior that is hard to capture with standard neural architectures. Classical asymptotic analysis decomposes such solutions into a smooth component and a problem-specific analytical corrector, but designing correctors requires case-by-case analysis and does not transfer across problems. We propose the Library-based Corrector Network (LibCorrNet), which replaces the problem-specific corrector with a shared, family-level structural prior. LibCorrNet combines a Fourier neural operator for the smooth component with a corrector branch that evaluates a fixed candidate-function library on a learned stretched coordinate, combined via adaptive, input-conditioned weights. The same library and architecture are reused across different PDE classes without redesigning a corrector module for each problem. Across several representative classes of singularly perturbed and multiscale PDEs, LibCorrNet consistently outperforms strong neural operator baselines, with the largest gains observed under limited training data. Ablation studies show complementary contributions from coordinate learning, candidate transformation, and adaptive weighting, and the method remains effective even when the exact analytical corrector is excluded from the library, supporting its use as a reusable structural prior rather than a problem-specific design.