{
  "annotation_id": "d8f42bf1-7126-4514-9ed9-16a3a9d4e02d",
  "date_created": "2026-02-17T05:53:23.835000Z",
  "date_modified": "2026-02-17T05:53:23.835000Z",
  "file_hash": "4b8b48deb4f0e4da3fe6a97e9b7f0cd0641f91b59b4e615df16a54dd550c2fab",
  "private": false,
  "record": {
    "abstract": "We consider general parameter to solution maps $\\theta \\mapsto \\mathcal G(\\theta)$ of non-linear partial differential equations and describe an approach based on a Banach space version of the implicit function theorem to verify the gradient stability condition of Nickl\u0026Wang (JEMS 2024) for the underlying non-linear inverse problem, providing also injectivity estimates and corresponding statistical identifiability results. We illustrate our methods in two examples involving a non-linear reaction diffusion system as well as a McKean--Vlasov interacting particle model, both with periodic boundary conditions. We apply our results to prove the polynomial time convergence of a Langevin-type algorithm sampling the posterior measure of the interaction potential arising from a discrete aggregate measurement of the interacting particle system.",
    "arxiv_id": "2601.10326",
    "authors": [
      "Aur\u00e9lien Castre",
      "Richard Nickl"
    ],
    "categories": [
      "math.ST",
      "cs.NA",
      "math.AP",
      "math.NA",
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On gradient stability in nonlinear PDE models and inference in interacting particle systems",
    "url": "https://arxiv.org/abs/2601.10326",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "88625583-891e-4c5d-8e91-9f71d907651c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}