{
  "abstract": "Tree-Adjoining Grammars (TAGs) have recently been introduced to Nonlinear System Identification (NLSI) as a means of encoding an entire model class as a finite set of grammatical rules, from which candidate models are assembled as trees. Existing TAG-based identifiers rely on evolutionary optimisation and return point estimates of the model structure. This paper instead proposes the TAG framework within a Bayesian setting. A generative prior is defined over tree structures and their parameters, and a Reversible-Jump MCMC sampler with structure-preserving tree moves is used to infer the joint posterior over model structure, parameters and predictions. Two training objectives are considered; that is, a one-step-ahead objective with conjugate parameter proposals, and a simulation-based objective handled by likelihood-free inference. The approach is validated on a simulated polynomial NARX system, the Silverbox benchmark, and wave-loading data from the Christchurch Bay Tower, where embedding Morison's equation as a fixed initial tree yields a grey-box model that outperforms the physics-driven baseline. The results demonstrate that Bayesian TAGs are well suited to quantifying uncertainty in equation discovery for dynamical systems and to fitting physics-informed models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31368",
  "author_total": 3,
  "authors": [
    {
      "name": "Christopher A. Lindley"
    },
    {
      "name": "Nikolaos Dervilis"
    },
    {
      "name": "Keith Worden"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab8pssvrb6e7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31368",
  "fulltext_url": null,
  "id": "ab8pssvrb6e7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31368",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
    ]
  ],
  "openalex": "W7214635787",
  "pdf_url": "https://arxiv.org/pdf/2609.31368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab8pssvrb6e7z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:03Z",
      "native_id": "2609.31368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Equation discovery with Bayesian tree-adjoining grammars",
  "title_text": "Equation discovery with Bayesian tree-adjoining grammars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/ab8pssvrb6e7z",
  "venue": "arXiv",
  "versions": []
}