{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30328",
  "author_total": 2,
  "authors": [
    {
      "name": "Esha Saha"
    },
    {
      "name": "Hao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ws21ypwr2hwe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30328",
  "fulltext_url": null,
  "id": "5ws21ypwr2hwe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30328",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7204969459",
  "pdf_url": "https://arxiv.org/pdf/2608.30328",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ws21ypwr2hwe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "2608.30328",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30328"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Learning PDE Time-Stepping with Neural Cellular Automata",
  "title_text": "Learning PDE Time-Stepping with Neural Cellular Automata",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/5ws21ypwr2hwe",
  "venue": "arXiv",
  "versions": []
}