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Boosted Physics-Informed Neural Networks for Solving Homogeneous and Non-Homogeneous Lane-Emden Type Equations — arXiv:2611.00701

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00701
License (as archived): CC0-1.0
Archived: 2026-11-03T11:24:54.482Z
SHA-256 of the archived text: a962e27fd884e224fa00de79f4d64e64f84e3e422cba8b2ac6f55723ba6e3522
Stable URL of this page: https://metraipolis.com/documento/dc_da8cd6826558

How to cite

Boosted Physics-Informed Neural Networks for Solving Homogeneous and Non-Homogeneous Lane-Emden Type Equations — arXiv:2611.00701 — arXiv (en), https://arxiv.org/abs/2611.00701 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_da8cd6826558 (Metraipolis archive dc_da8cd6826558, sha256 a962e27fd884e224fa00de79f4d64e64f84e3e422cba8b2ac6f55723ba6e3522)

BibTeX

@misc{dcda8cd6826558,
  title = {Boosted Physics-Informed Neural Networks for Solving Homogeneous and Non-Homogeneous Lane-Emden Type Equations — arXiv:2611.00701},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00701},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_da8cd6826558; sha256 a962e27fd884e224fa00de79f4d64e64f84e3e422cba8b2ac6f55723ba6e3522},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00701. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Lane-Emden Equation is a class of nonlinear differential equations commonly used to model phenomena in astrophysics and mathematical physics, such as stellar structure and thermal behavior in polytropic gas spheres. This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations. Standard PINNs leverage physical laws encoded within the loss function, but their predictive performance can be constrained by optimization challenges and approximation errors. To address this, we introduce a post-processing boosting stage where the residual errors from the PINN prediction are modeled using some regression algorithms - including LightGBM, Random Forest, XGBoost, and Support Vector Regression (SVR). The outputs from these boosted models are aggregated to generate a corrected, high-fidelity prediction. The proposed methodology is systematically validated through quantitative metrics and comparative analysis against the standard PINN baseline. The results demonstrate that the boosted PINN framework significantly reduces prediction error, and improves generalization, offering a powerful and flexible approach for solving scientific and engineering problems governed by differential equations.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Mathematical Physics (math-ph) ; Astrophysics of Galaxies (astro-ph.GA); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE).
Pagina del lavoro: https://arxiv.org/abs/2611.00701 — 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 2026-11-03T11:02:37.783Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).