Metraipolis › archive › dc_346366c8a388

A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response — arXiv:2608.28683

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28683
License (as archived): CC0-1.0
Archived: 2026-10-17T09:28:20.437Z
SHA-256 of the archived text: 6c492285e3be4f71a9178feb92da96cee97fafebc35a975dedf0ec3cc5ac81b7
Stable URL of this page: https://metraipolis.com/documento/dc_346366c8a388

How to cite

A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response — arXiv:2608.28683 — arXiv (en), https://arxiv.org/abs/2608.28683 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_346366c8a388 (Metraipolis archive dc_346366c8a388, sha256 6c492285e3be4f71a9178feb92da96cee97fafebc35a975dedf0ec3cc5ac81b7)

BibTeX

@misc{dc346366c8a388,
  title = {A Framework Integrating the Dynamic Stiffness Matrix with Physics-Informed Neural Networks for Solving Eigenvalue Problems and Analysing Dynamic Response — arXiv:2608.28683},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28683},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_346366c8a388; sha256 6c492285e3be4f71a9178feb92da96cee97fafebc35a975dedf0ec3cc5ac81b7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28683. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper introduces a framework that integrates the dynamic stiffness matrix (DSM) with physics-informed neural networks (PINN). The DSM-PINN embeds physical constraints within the model and demonstrates robustness, particularly when addressing limited datasets across diverse investigations. In this approach, deep neural network outputs approximate the displacement fields of element nodes. Unlike the finite element method (FEM), the element shape functions are homogeneous solutions to the governing partial differential equation, forming the basis of the exact dynamic stiffness matrix, thereby avoiding high-order derivative terms. This matrix also serves as a frequency-domain spectral element, resulting in a strong-form PINN. The loss function is produced by connecting neural networks with dynamic stiffness matrices. We focus on utilising PINNs to resolve eigenvalue problems by employing the Wittrick-Williams algorithm, which overcomes the challenge of neural networks failing to converge to higher-order eigenvalues. Additionally, the frequency domain-PINN method is used to analyse structural dynamic responses under moving and impulsive loads, addressing the limitation of neural networks in handling complex numbers. Theoretical convergence stability of the suggested approach is also analysed even DSM is an indefinite matrix after implementing the boundary condition. The numerical results validate the practicality and efficacy of the recommended approach.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Computational Physics (physics.comp-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.28683 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:59:54.337Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).