math.NA · 2026-07-20 · No. 59

Numerical Analysis, 2026-07-20.

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 zero-one law for one-shot system identification

    Nicolas Boullé, Diana Halikias, Samuel E. Otto, Alex Townsend

    math.NA · cs.LG · math.DS

    Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differential operators and dynamical systems. For a single input-response pair, recovery is possible exactly when the evaluated dictionary terms are linearly independent. We prove a sharp zero-one law: either no input uniquely determines the coefficients, or almost every...

    arxiv.org/abs/2607.15832 · PDF

  2. 02

    A Statistical Formulation Gap for Nonlinear Multiscale Physics-Informed Learning

    Ronald Katende

    math.NA · cs.LG · math.AP

    We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations. For a uniformly monotone divergence-form class with coefficients oscillating at scale $ε$, we derive a finite-width, finite-sample, and finite-iteration error bound for a boundary-compatible variational neural solver. Its stability, sampling, and optimization constants are independent of $ε$, while all unresolved scale dependence...

    arxiv.org/abs/2607.15702 · PDF

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