Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs

ArXi:2605.10277v1 Announce Type: new 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.