{
  "abstract": "Machine-learning emulators of chaotic and stochastic systems are usually validated on forecast skill and long-run statistics. Neither certifies that an emulator responds correctly to forcing, the property that projection and attribution studies rely on. Linear response theory makes this testable: the forced response follows from unperturbed correlations through a generalized fluctuation-dissipation relation, and decomposes over the stochastic Ruelle-Pollicott resonances of the Koopman generator. Building on the Koopmanism Response framework, we turn this into a calibrated, mode-resolved test for learned surrogates: each surrogate rollout passes or fails each check, and failure rates are compared with those of independent realizations of the true system. On stochastic Lorenz-63, a three-variable toy model, we evaluate SINDy, an MLP, a reservoir computer, a neural ODE and a neural SDE with learned diffusion, over up to 80 rollouts each. A sparse-regression model with the correct library passes every check at rates consistent with the true system. Invariant-statistics fidelity and response fidelity dissociate in both directions: a quarter of reservoir-computer rollouts pass every invariant-statistics check and match the static susceptibility $χ(0)$, yet misrepresent the slow relaxation modes, while the neural ODE and SDE rarely meet the invariant-statistics floor but recover those modes in three quarters of rollouts. As expected of a time-integrated quantity dominated here by fast relaxation, $χ(0)$ does not separate these cases. For a fixed network, the training formulation (one-step drift, flow map, or multi-step through the integrator) decides which of these properties it gets right.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06798",
  "author_total": 5,
  "authors": [
    {
      "name": "João Böger"
    },
    {
      "name": "Simon Driscoll"
    },
    {
      "name": "Niccolò Zagli"
    },
    {
      "name": "Valerio Lucarini"
    },
    {
      "name": "Francisco Camara Pereira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51qfz1ettknzb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06798",
  "fulltext_url": null,
  "id": "51qfz1ettknzb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06798",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7220714251",
  "pdf_url": "https://arxiv.org/pdf/2610.06798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51qfz1ettknzb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.06798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63",
  "title_text": "A Response Theory Probe for Learned Stochastic AI Simulators, Tested on Lorenz-63",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/51qfz1ettknzb",
  "venue": "arXiv",
  "versions": []
}