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Learning PDE Time-Stepping with Neural Cellular Automata — arXiv:2608.30328

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.30328
License (as archived): CC0-1.0
Archived: 2026-10-17T08:37:08.160Z
SHA-256 of the archived text: 11af4073187ce86dd61dcd3729dd7d7da3bb2d258a58600735c2f046a8018101
Stable URL of this page: https://metraipolis.com/documento/dc_ecb8cb5388fb

How to cite

Learning PDE Time-Stepping with Neural Cellular Automata — arXiv:2608.30328 — arXiv (en), https://arxiv.org/abs/2608.30328 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ecb8cb5388fb (Metraipolis archive dc_ecb8cb5388fb, sha256 11af4073187ce86dd61dcd3729dd7d7da3bb2d258a58600735c2f046a8018101)

BibTeX

@misc{dcecb8cb5388fb,
  title = {Learning PDE Time-Stepping with Neural Cellular Automata — arXiv:2608.30328},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.30328},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ecb8cb5388fb; sha256 11af4073187ce86dd61dcd3729dd7d7da3bb2d258a58600735c2f046a8018101},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.30328. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditions, motivating the need for learned surrogates. In this paper, we propose a trainable Neural Cellular Automata (NCA) based surrogate model for learning long time PDE dynamics. Rather than mapping an entire initial field to a full trajectory in one shot, our proposed model learns a small, local, homogeneous update rule that is applied identically and repeatedly at every grid cell, mirroring the locality of differential operators. We benchmark this framework against three baselines: PDE - Net, a modified physics-informed neural network (PINN), and a Fourier Neural Operator (FNO), on five canonical PDEs (heat, advection, Burgers, Allen - Cahn, and Fisher - KPP), evaluated at temporal domain two times beyond the training temporal domain. The proposed model achieves the lowest long-horizon relative errors on the majority of the experiments.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2608.30328 — 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 2026-10-17T08:13:26.806Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).