{
  "abstract": "Dimensionless descriptions of complex physical systems can sometimes be reduced further when multiple input groups combine into a single composite scaling coordinate. Identifying such structure from noisy response evaluations is difficult because apparent departures may reflect either genuine response structure or evaluation noise. Here we develop equal-response probing with replicate calibration to assess whether two dimensionless inputs support a one-group representation under prescribed directional and collapse tolerances. Equal-response geometry provides a candidate coordinate without direct numerical differentiation, while a second stage evaluates the accuracy of the resulting one-dimensional collapse. Replicate evaluations estimate the noise contribution to both stages, enabling reducible, not-red and unresolved outcomes. We evaluate the framework across eight model-based benchmark regimes spanning rough-pipe flow, cell-monolayer wound closure, microfluidic droplet generation and column buckling. Six regimes satisfy both criteria and two fail both, while known reduced coordinates are recovered in exact-reduction benchmarks. Controlled synthetic tests assess false-alarm behaviour, sensitivity to structural departures and noise calibration. These results show how replicate-calibrated equal-response probing distinguishes regime-specific scaling structure from variation attributable to evaluation noise while retaining an unresolved outcome when evaluation noise precludes a definitive verdict at the prescribed tolerances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35154",
  "author_total": 3,
  "authors": [
    {
      "name": "Dingbang Yan"
    },
    {
      "name": "Zhaoyue Xu"
    },
    {
      "name": "Hua-Dong Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6yzstbhp7kv8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35154",
  "fulltext_url": null,
  "id": "a6yzstbhp7kv8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35154",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7214794011",
  "pdf_url": "https://arxiv.org/pdf/2609.35154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6yzstbhp7kv8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.35154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35154"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Equal-response probing with replicate calibration identifies scaling relations from noisy observations of complex systems",
  "title_text": "Equal-response probing with replicate calibration identifies scaling relations from noisy observations of complex systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/a6yzstbhp7kv8",
  "venue": "arXiv",
  "versions": []
}