{
  "abstract": "Dimensional homogeneity is a fundamental constraint on physically meaningful models, requiring invariance under changes of units. We present a data-driven method for constructing surrogate models that satisfy this constraint at the level of the hypothesis class. Starting from a dimension matrix of measured variables, the method derives Buckingham $Π$-groups, constructs admissible dimensional prefactors, and approximates the remaining dimensionless dependence using truncated harmonic expansions on normalized invariant domains. Once the prefactor and dictionary are fixed, the coefficients are obtained from a regularized linear regression problem. We test the approach on the simple pendulum, Planck's black-body law, the double-pendulum Lyapunov field, and an experimental COBE/FIRAS black-body spectrum dataset. The results show that dimensional constraints improve conditioning, robustness to noise, and sample efficiency relative to unconstrained baselines, while the choice of dictionary becomes important in non-periodic or multi-invariant settings. The learned expressions are explicit and inexpensive to evaluate, which makes them useful as surrogate models for structured physical problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Sci. Rep. (2026)",
  "arxiv": "2609.38094",
  "author_total": 2,
  "authors": [
    {
      "name": "Ernest Tarrus"
    },
    {
      "name": "Hector Gisbert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czeepah89gbay.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38094",
  "fulltext_url": null,
  "id": "czeepah89gbay",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38094",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "hep-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.38094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czeepah89gbay.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.38094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38094"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions",
  "title_text": "Dimensionally consistent surrogate modelling through dimensional analysis and harmonic expansions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/czeepah89gbay",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1038/s41598-026-63672-z",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}