math.NA · 2026-10-06 · No. 135

Numerical Analysis, 2026-10-06.

2 new papers in math.NA. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Singular parameters and missing limits in neural PDE solvers

    Daniel Fernández

    math.NA · cs.LG

    Neural solvers for partial differential equations (PDEs) can approach an accurate solution while their parameters grow without bound. In such cases, the limiting solution may have no finite representation in the chosen model, leaving the best loss unattained. Our analysis connects missing limits in deep neural tanh- networks to unbounded hidden parameters or increasingly redundant neurons. For a class of models built from translated kernels,...

    arxiv.org/abs/2610.06770 · PDF

  2. 02

    IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs

    Sima Naraghi, Kourosh Parand, Amirhossein Sadr, Dara Rahmati

    math.NA · cs.LG

    Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every...

    arxiv.org/abs/2610.06348 · PDF

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