mlsanityData to 7 Oct 2026

DGNN: A Neural PDE Solver Induced by Discontinuous Galerkin Methods

arXiv 2503.10021 ↗First posted 13 Mar 2025cs.LG physics.comp-phcited by 3

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Abstract (arXiv)

We propose a general framework for the Discontinuous Galerkin-induced Neural Network (DGNN), inspired by the Interior Penalty Discontinuous Galerkin Method (IPDGM). In this approach, the trial space consists of piecewise neural network space defined over the computational domain, while the test function space is composed of piecewise polynomials. We demonstrate the advantages of DGNN in terms of accuracy and training efficiency across several numerical examples, including stationary and time-dependent problems. Specifically, DGNN easily handles high perturbations, discontinuous solutions, and complex geometric domains.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 19 of its 34 references that are in the map. First posted on arXiv 13 Mar 2025.

Builds on

19 of 34 references.

References · 19

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7 more
  1. 2020Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structurescited by 52
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  7. 2023ParticleWNN: a Novel Neural Networks Framework for Solving Partial Differential Equationscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025A Variational Physics-Informed Neural Network Framework Using Petrov-Galerkin Method for Solving Singularly Perturbed Boundary Value Problemscited by 1
  2. 2026Discontinuous Galerkin finite element operator network for solving non-smooth PDEscited by 1
  3. 2026Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problemscited by 0