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Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations — arXiv:2608.26549

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.26549
License (as archived): CC0-1.0
Archived: 2026-10-17T14:27:53.504Z
SHA-256 of the archived text: 30feeaf0790cf8c6a348ad13356c2db762e36d6563cea0e09be3755deb2b7003
Stable URL of this page: https://metraipolis.com/documento/dc_b273be335136

How to cite

Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations — arXiv:2608.26549 — arXiv (en), https://arxiv.org/abs/2608.26549 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b273be335136 (Metraipolis archive dc_b273be335136, sha256 30feeaf0790cf8c6a348ad13356c2db762e36d6563cea0e09be3755deb2b7003)

BibTeX

@misc{dcb273be335136,
  title = {Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations — arXiv:2608.26549},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.26549},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b273be335136; sha256 30feeaf0790cf8c6a348ad13356c2db762e36d6563cea0e09be3755deb2b7003},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.26549. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

While Physics-Informed Neural Networks (PINNs) have emerged as a transformative paradigm for solving complex differential equations, their reliance on backpropagation-based gradient descent and automatic differentiation (AD) imposes significant computational bottlenecks and severe non-convex optimization challenges. To overcome these fundamental limitations, we propose the Physics-Informed Stochastic Configuration Machine (PI-SCM), a novel backpropagation-free framework for both forward and inverse problems in differential equations. The core mathematical contribution lies in the analytical evaluation of local Jacobians for nonlinear differential operators, which facilitates a linearized representation of the physical loss and projects it into a unified, linearized algebraic subspace. This reformulation allows for the explicit determination of optimal network weights via a sequence of generalized linear least squares solvers, effectively bypassing the iterative traps of traditional nonlinear optimizers. We develop a progressive algorithmic suite comprising localized construction (PI-SC-I), sliding-window updating (PI-SC-II), and global updating (PI-SC-III), and rigorously establish their universal approximation properties. Extensive experiments demonstrate that PI-SCM achieves high-fidelity predictive accuracy and robust parameter identification while accelerating the training process by orders of magnitude compared to standard PINNs. Our work provides a highly efficient and scalable foundation for next-generation, real-time Scientific Machine Learning applications.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-28 in cs.AI).
Categorie arXiv: Numerical Analysis (math.NA) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2608.26549 — 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 2026-10-17T13:16:53.645Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).