{
  "abstract": "Multi-fidelity Earth system models provide simulations at different levels of complexity and computational cost, but exhaustive exploration of the parameter space at the highest fidelity is often prohibitively expensive. Multi-fidelity emulators can reduce this burden by combining abundant lower-fidelity simulations with limited high-fidelity evaluations. We compare four Gaussian-process-based multi-fidelity approaches: the Kennedy--O'Hagan autoregressive model (K&O), hierarchical kriging (HK), Bayesian hierarchical emulation for multi-level models (BayHEm), and multi-fidelity deep Gaussian processes (MF-DGP). We evaluate the methods using two contrasting applications: a three-fidelity tsunami simulator and a two-fidelity implementation of the Joint UK Land Environment Simulator (JULES). Performance is assessed using leave-one-out predictive accuracy, uncertainty representation, design requirements, and computational characteristics. In the tsunami application, BayHEm gives the lowest normalised root mean square error (NRMSE = 0.031) and highest SCORE (3.025), while MF-DGP performs worse than the single-fidelity baseline when only 10 high-fidelity simulations are available. In the JULES application, MF-DGP gives the lowest NRMSE (0.079) and highest SCORE (3.032), with all 30 held-out high-fidelity observations lying within their nominal 95\\% predictive intervals. These contrasting results show that no single multi-fidelity emulator is uniformly superior. Instead, method choice should reflect the complexity of the inter-fidelity relationship, the amount of high-fidelity information available, and the importance placed on predictive accuracy and uncertainty quantification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07363",
  "author_total": 6,
  "authors": [
    {
      "name": "Xiaoyu Xiong"
    },
    {
      "name": "Louise Kimpton"
    },
    {
      "name": "Huiyi Yang"
    },
    {
      "name": "Mian Xu"
    },
    {
      "name": "James Salter"
    },
    {
      "name": "Peter Challenor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v32z01fknpw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07363",
  "fulltext_url": null,
  "id": "6v32z01fknpw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07363",
  "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",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7212047346",
  "pdf_url": "https://arxiv.org/pdf/2609.07363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v32z01fknpw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.07363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Bayesian Emulation of Multi-fidelity Earth System Modelling Using Hierarchical Gaussian Processes",
  "title_text": "Bayesian Emulation of Multi-fidelity Earth System Modelling Using Hierarchical Gaussian Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/6v32z01fknpw8",
  "venue": "arXiv",
  "versions": []
}