{
  "abstract": "Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz--63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33112",
  "author_total": 5,
  "authors": [
    {
      "name": "Zhidi Lin"
    },
    {
      "name": "Yuhao Liu"
    },
    {
      "name": "Ying Li"
    },
    {
      "name": "Edwin Fong"
    },
    {
      "name": "Petar Djurić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ahfpdje7bvrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33112",
  "fulltext_url": null,
  "id": "6ahfpdje7bvrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33112",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214705272",
  "pdf_url": "https://arxiv.org/pdf/2609.33112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ahfpdje7bvrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.33112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33112"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Simulation-Free Learning of GP-SDEs from Irregular Observations",
  "title_text": "Simulation-Free Learning of GP-SDEs from Irregular Observations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/6ahfpdje7bvrq",
  "venue": "arXiv",
  "versions": []
}