math.NA · 2026-08-29 · No. 99

Numerical Analysis, 2026-08-29.

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

    Enforcing Dirichlet Boundary Conditions in Operator Learning

    Andrew M. Stuart, Margaret Trautner

    math.NA · cs.LG

    Operator learning in scientific machine learning is concerned with approximation of maps between infinite-dimensional function spaces; such maps frequently arise as the solution operators of partial differential equations (PDEs). Neural operators have demonstrated broad empirical success at approximating such maps from data. However, most existing neural operator architectures enforce boundary conditions indirectly through training from data...

    arxiv.org/abs/2608.27256 · PDF

  2. 02

    Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations

    Yuehao Song, Zhong Chen, Lihui Cen, Liang Wu, Kai Zhang

    math.NA · cs.AI · cs.LG · eess.SY

    While Physics-Informed Neural Networks (PINNs) have emerged as a transformative paradigm for solving complex differential equations, their reliance on backpropagation-based gradient descent and automatic differentiation (AD) imposes significant computational bottlenecks and severe non-convex optimization challenges. To overcome these fundamental limitations, we propose the Physics-Informed Stochastic Configuration Machine (PI-SCM), a novel...

    arxiv.org/abs/2608.26549 · PDF

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