{
  "abstract": "Scientific prediction under uncertainty requires more than a single future state: it requires the distribution of possible outcomes. We show that this distribution-valued evolution can be learned directly as a stochastic solution operator between arbitrary source and target times. We introduce Stochastic Latent Twins, which represent the physical state through a deterministic encoder-decoder while placing stochasticity entirely in a probability-valued latent evolution map. This separation makes the stochastic transition law independent of the state representation and enables direct probabilistic prediction without recursive time stepping. We establish an end-to-end Wasserstein approximation theory that separates representation and latent-transition errors, derive stability guarantees, and develop a distributional theory of physics conformity with latent-to-physical transfer bounds and conformity by construction. The resulting framework can be learned directly from observed transitions and supports forward prediction, backward conditional evolution, one-shot generation, and physics-conforming stochastic dynamics within the same formulation. Numerical experiments ranging from linear and non-Gaussian SDEs to stochastic Lorenz dynamics, generative modeling, a stochastic Hamiltonian system, and a two-dimensional stochastic Burgers equation verify the theory, expose the distinct roles of state representation and transition-family expressivity, compare favorably with recent stochastic and one-step generative methods, and demonstrate exact physical conservation by construction. More broadly, Stochastic Latent Twins provide a step toward scientific surrogates that represent not only the evolution of a system, but also its uncertainty and physical structure, opening new opportunities across uncertainty quantification, data assimilation, inverse problems, control, and digital twins.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21084",
  "author_total": 3,
  "authors": [
    {
      "name": "Matthias Chung"
    },
    {
      "name": "Jack Michael Solomon"
    },
    {
      "name": "Deepanshu Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73hacm37xm17q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21084",
  "fulltext_url": null,
  "id": "73hacm37xm17q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21084",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7222503104",
  "pdf_url": "https://arxiv.org/pdf/2610.21084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73hacm37xm17q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Stochastic Latent Twins: Learning Stochastic Solution Operators",
  "title_text": "Stochastic Latent Twins: Learning Stochastic Solution Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/73hacm37xm17q",
  "venue": "arXiv",
  "versions": []
}