math.NA · 2026-06-17 · No. 26

Numerical Analysis, 2026-06-17.

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

    A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

    Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis

    math.NA · cs.LG · physics.comp-ph

    We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization. The trial space, which we term Linear-in-Learnables (LiL), comprises...

    arxiv.org/abs/2606.18175 · PDF

  2. 02

    INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

    Shayan Dodge, Alessandro Formisano, Sami Barmada

    math.NA · cs.LG · physics.comp-ph

    We propose a new weak-form Physics-Informed Neural Network approach (named INI-VPINN). INI-VPINN naturally incorporates Neumann boundary and interface conditions into the variational formulation. It removes the need for additional loss terms or multiple subdomain networks. This framework employs compact support weighting functions and integration by parts to implicitly impose flux and continuity constraints. In this way, it implicitly ensures...

    arxiv.org/abs/2606.18032 · PDF

This edition is part of The Daily Abstract — math.NA archive. Subscribe to receive these in your inbox each morning, automatically translated to Spanish, with reply-to-PDF: arxivdaily.ignorelist.com.

Colophon Set in Georgia, with system sans for interface chrome and a monospaced stack for code and paper identifiers. Sole accent: amber #D99C5E. Built and served on an always-free VM. The masthead is set 14% letterspaced because newspapers do that and it works.