AI RESEARCH
Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
arXiv CS.LG
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ArXi:2605.04853v1 Announce Type: new We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close.