Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, it is important for the learned model to be discretization-invariant, or resolution-robust, and to reflect PDE-specific structure. It is therefore natural to ask how such structure should be encoded in the model architecture, hypothesis class, or learning procedure. In this paper, we study operator learning for solution operators of nonlinear parabolic PDEs based on Duhamel--Picard iteration. We formulate Picard iteration as an abstract state-transition model and present a theoretical framework for Picard-type op...
| Authors | Koichi Taniguchi, Sho Sonoda |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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