English

Physics Informed Neural Networks for Nonlinear Delay Differential Equations

Numerical Analysis 2026-07-01 v1

Abstract

In this paper we propose a novel physics-informed neural network framework for solving general first-order delay differential equations. Our approach combines a differentiable history switch, a trial-solution formulation that explicitly enforces history constraints, and a segmented collocation strategy to stabilize gradient propagation across large temporal domains. The method enables a scalable and physics-consistent approximation of delay differential equation solutions while maintaining continuity across subintervals. Numerical experiments demonstrate the effectiveness of the proposed method.

Cite

@article{arxiv.2607.00380,
  title  = {Physics Informed Neural Networks for Nonlinear Delay Differential Equations},
  author = {Stone Yao and Vipin Kumar and Roberto Guglielmi},
  journal= {arXiv preprint arXiv:2607.00380},
  year   = {2026}
}

Comments

6-page, double-column, 8 figures, accepted to IFAC World Congress 2026