{
  "abstract": "Latent dynamics learning has emerged as a prominent approach for Model Order Reduction (MOR) of time-dependent, parameterized Partial Differential Equations (PDEs). Traditional autoencoder-based approaches are intrinsically tied to fixed spatial discretizations during both training and inference, motivating the development of meshless methodologies. In this context, conditioning provides a natural mechanism for representing temporal evolution through spatially continuous functions, enabling mesh-agnostic Latent Dynamics Models (LDMs). In this work, we introduce a unified mathematical framework for mesh-agnostic LDMs based on conditioning in Neural Fields (NeFs). Leveraging a taxonomy of conditioning mechanisms (weak, strong, and pure), we formulate meshless LDMs as NeFs conditioned on a latent state. We establish a Universal Approximation Theorem (UAT) for this class of models and analyze their stability by deriving Lipschitz bounds for different conditioning mechanisms. Our analysis reveals an expressivity--stability trade-off, providing insight into why more expressive conditioning, despite its higher representational capacity, can potentially degrade performance during temporal extrapolation. Finally, we provide a comprehensive comparison of meshless and mesh-based architectures in the continuous limit of the spatial discretization, showing that meshless models guarantee grid-independent Lipschitz bounds, unlike mesh-based counterparts. Our experiments across Burgers' equation, Navier--Stokes flow past a cylinder, and linear advection show that meshless LDMs can achieve predictive accuracy comparable to or better than their mesh-based counterparts while using only 2% of the trainable parameters and exhibiting nearly constant error across spatial discretizations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41043",
  "author_total": 3,
  "authors": [
    {
      "name": "Lorenzo Tomada"
    },
    {
      "name": "Federico Pichi"
    },
    {
      "name": "Gianluigi Rozza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8tgmzm34mydk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41043",
  "fulltext_url": null,
  "id": "c8tgmzm34mydk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41043",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8tgmzm34mydk.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Meshless Latent Dynamics Models for Model Order Reduction of time-dependent Partial Differential Equations",
  "title_text": "Meshless Latent Dynamics Models for Model Order Reduction of time-dependent Partial Differential Equations",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/c8tgmzm34mydk",
  "venue": "arXiv",
  "versions": []
}