{
  "abstract": "Inferring effective equations from observations of nonlinear stochastic processes is challenging because individual trajectories are noisy realizations, while the relevant physical information is encoded in ensemble statistics. We introduce a data-driven framework that learns a change of variables in which nonlinear stochastic dynamics become linear. The model combines a neural change of representation with a linear stochastic latent evolution and is trained through a short-time moment-matching objective, thereby avoiding trajectory \\rev{simulation} during optimization. This construction yields an interpretable generative model: both the learned transformation and the latent evolution operators can be directly inspected. We validate the method on the one-dimensional Kardar--Parisi--Zhang (KPZ) equation, a paradigmatic model of stochastic growth for which the Cole--Hopf transformation maps the nonlinear dynamics to the stochastic heat equation. From simulated height trajectories alone, the model recovers the local exponential Cole--Hopf map and the associated linear stochastic operator. Generated trajectories reproduce the main statistical signatures of the KPZ universality class, including the growth law $\\mathrm{Var}(h^{t})\\sim t^{2β}$ with $β=1/3$ and the GOE Tracy--Widom height distribution for flat initial conditions. These results show that interpretable stochastic equations can be inferred from data by learning representations in which the dynamics closes in a simple form. Furthermore the development of the physical informed learning permits to get insights on the physics of the dynamical process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30919",
  "author_total": 6,
  "authors": [
    {
      "name": "Lorenzo Mensi"
    },
    {
      "name": "Simone Cuonzo"
    },
    {
      "name": "Maria Chiara Angelini"
    },
    {
      "name": "Sergio Chibbaro"
    },
    {
      "name": "Cyril Furtlehner"
    },
    {
      "name": "Alberto Rosso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb7zj7mn1q279.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30919",
  "fulltext_url": null,
  "id": "cb7zj7mn1q279",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30919",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7223306030",
  "pdf_url": "https://arxiv.org/pdf/2610.30919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb7zj7mn1q279.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30919"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Learning Cole-Hopf Coordinates for Stochastic Growth Dynamics: the KPZ class",
  "title_text": "Learning Cole-Hopf Coordinates for Stochastic Growth Dynamics: the KPZ class",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/cb7zj7mn1q279",
  "venue": "arXiv",
  "versions": []
}