Metraipolis › archive › dc_bfaddfaa2d8b

Solving the Nonlinear Westervelt Equation in Ultrasound Propagation Using Physics-Informed Neural Networks — arXiv:2611.05130

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.05130
License (as archived): CC0-1.0
Archived: 2026-11-04T21:53:29.277Z
SHA-256 of the archived text: 413eb65e3db32218b980b8c096df27a67d4750a20dfd0a865fecb3518b354f92
Stable URL of this page: https://metraipolis.com/documento/dc_bfaddfaa2d8b

How to cite

Solving the Nonlinear Westervelt Equation in Ultrasound Propagation Using Physics-Informed Neural Networks — arXiv:2611.05130 — arXiv (en), https://arxiv.org/abs/2611.05130 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bfaddfaa2d8b (Metraipolis archive dc_bfaddfaa2d8b, sha256 413eb65e3db32218b980b8c096df27a67d4750a20dfd0a865fecb3518b354f92)

BibTeX

@misc{dcbfaddfaa2d8b,
  title = {Solving the Nonlinear Westervelt Equation in Ultrasound Propagation Using Physics-Informed Neural Networks — arXiv:2611.05130},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.05130},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bfaddfaa2d8b; sha256 413eb65e3db32218b980b8c096df27a67d4750a20dfd0a865fecb3518b354f92},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.05130. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Modeling the nonlinear acoustic wave propagation in biological tissues needs accuracy, especially in ultrasound imaging and therapeutic applications. The 1D Westervelt equation, \( p_{xx} - p_{tt} + \gamma\, p_{ttt} + \eta\,(p^{2})_{tt}=0, \) could be used to describe a finite-amplitude ultrasound propagation in these tissues. This equation accounts for nonlinearity, \(\eta\), and attenuation, \(\gamma\). To solve this equation, we observe that traditional solvers may struggle to do so correctly. This is due to the difficulties arising from the nonlinear nature of the equation. We solve the equation by defining three synthetic cases - linear (\(\eta=0.001\), \(\gamma=10^{-6}\)), shock-dominated (\(\eta=0.02\), \(\gamma=10^{-6}\)), and dissipation-dominated (\(\eta=0.01\), \(\gamma=5\times10^{-4}\)) - and using Physics-Informed Neural Networks (PINNs) to showcase the solution. A sinusoidal activation function is used to capture the oscillatory behavior of the problem. The results of our study, with PDE residual converging to at least \(10^{-6}\), boundary condition loss to \(10^{-5}\), and the PINN loss converging to \(10^{-5}\) for each case at \(30,000\) epochs, show that \(\gamma\) scales the rate of amplitude decay, while \(\eta\) governs frequency-dependent phase speeds.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Analysis of PDEs (math.AP) ; Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE).
Pagina del lavoro: https://arxiv.org/abs/2611.05130 — 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 2026-11-04T21:38:49.831Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).