math.NA · 2026-06-05 · No. 14

Numerical Analysis, 2026-06-05.

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

    DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains

    Anshima Singh, David J. Silvester

    math.NA · cs.LG · stat.ML

    Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains. In this work, a deep adaptive sampling framework for PINNs is extended to the time-dependent setting by treating space and time as a...

    arxiv.org/abs/2606.06314 · PDF

  2. 02

    Learning solution operators of PDEs with sparse approximation methods

    Sebastian Neumayer, Daniel Potts, Fabian Taubert

    math.NA · cs.LG

    We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques. Building on a dimension-incremental framework, we combine product basis expansions with sparse recovery methods, specifically orthogonal matching pursuit (OMP), to substantially reduce the required sample size compared with a previously considered cubature-based approach. We evaluate the resulting method...

    arxiv.org/abs/2606.06046 · PDF

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