{
  "abstract": "High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a \\textbf{Co}nditional \\textbf{P}osition-induced \\textbf{T}ransformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRANS airfoil fields, including scarce-data and extrapolation regimes, and on three-dimensional BlendedNet++ blended-wing-body surfaces. On the AirfRANS full-data test set, CoPiT reduces surface and volume losses by approximately 54\\% and 24\\% relative to Transolver, respectively, and achieves the lowest overall normalized test MSE among the compared baselines on BlendedNet++. Matched ablations show that FiLM conditioning generally improves upon input concatenation, while the preferred placement is task-dependent. CoPiT thus provides a practical operator-learning surrogate for parametric aerodynamics on unstructured meshes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32299",
  "author_total": 4,
  "authors": [
    {
      "name": "Junfeng Chen"
    },
    {
      "name": "Yongchen Fan"
    },
    {
      "name": "Zhonghua Qiao"
    },
    {
      "name": "Kailiang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7renkq8wpr7c8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32299",
  "fulltext_url": null,
  "id": "7renkq8wpr7c8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32299",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7223692274",
  "pdf_url": "https://arxiv.org/pdf/2610.32299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7renkq8wpr7c8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes",
  "title_text": "CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/7renkq8wpr7c8",
  "venue": "arXiv",
  "versions": []
}