{
  "abstract": "In spatio-temporal data analysis, estimating covariance parameters for Gaussian random fields via maximum likelihood estimation (MLE) is computationally prohibitive for large datasets. Following recent advances in simulation-based inference techniques, we propose two neural network architectures — Neural Bayes Estimation (NBE) and Neural Ratio Estimation (NRE) — to learn the parameters of Gaussian spatio-temporal Gneiting-Matérn models with advection. The networks are trained on simulations generated directly from the underlying Gaussian random field model. A thorough simulation study demonstrates strong performance across one-dimensional time and both one-dimensional space and two-dimensional space, yielding high accuracy and reliable uncertainty quantification for both NBE and NRE. Through extensive offline training, the framework achieves fully amortized inference, replacing costly optimization with a single forward pass. Finally, we apply our framework to solar radiation prediction and short-term forecasting. By adopting a sliding-window approach, the model accounts for temporal non-stationarity while retaining this key advantage: achieving near-instantaneous parameter inference and forecasting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36855",
  "author_total": 4,
  "authors": [
    {
      "name": "Alexandre Loret"
    },
    {
      "name": "Lucia Clarotto"
    },
    {
      "name": "Nicolas Desassis"
    },
    {
      "name": "Thomas Romary"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mexe5vxn27s7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36855",
  "fulltext_url": null,
  "id": "0mexe5vxn27s7",
  "issns": [],
  "landing_url": "https://hal.science/hal-05646982v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "hal",
      "0.stat"
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      "hal",
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    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
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  "openalex": "W7224108970",
  "pdf_url": "https://hal.science/hal-05646982/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mexe5vxn27s7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05646982",
      "source": "hal",
      "url": "https://hal.science/hal-05646982v1"
    },
    {
      "first_seen": "2026-10-30T12:35:59Z",
      "native_id": "2610.36855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Neural Simulation-Based Inference for space-time Gaussian processes",
  "title_text": "Neural Simulation-Based Inference for space-time Gaussian processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/0mexe5vxn27s7",
  "venue": "HAL",
  "versions": []
}