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Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition

arXiv · AI, language, vision and robotics · article · Sep 20, 2026 · UTC

Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment. Existing approaches to out-of-distribution (OOD) generalization in operator learning are largely empirical and black-box: they report aggregate error metrics without explaining why errors arise or when they will grow. We propose a structure-preserving framework that makes OOD generalization predictable and auditable. Our key idea is to parameterize the learned solution operator as a spectral filter $h_θ(

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