math.NA · 2026-06-16 · No. 25

Numerical Analysis, 2026-06-16.

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

01 — The papers

1 entries
  1. 01

    Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

    Vijay Kumar, Gautam Singh

    math.NA · cs.LG

    This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the...

    arxiv.org/abs/2606.16510 · PDF

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