{
  "abstract": "Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. A central limitation of its continuous-time dynamics is premature covariance collapse, which can restrict the directions accessible to the inversion and increase sensitivity to the initial ensemble. We introduce a second-order interacting particle system that combines the Kalman force with inertia, damping, attraction towards the ensemble mean, and short-range repulsion. We establish a generalized subspace property showing that nonzero initial velocities may enlarge the affine space accessible to the dynamics, while a finite-ensemble restriction remains. For linear inverse problems, we derive the mean and fluctuation dynamics, identify a regime in which fully collapsed configurations are linearly unstable, characterize asymptotic optimality on the subspace retained by the limiting covariance, and prove exponential decay for the associated frozen-covariance mean dynamics. Numerical experiments on high-dimensional linear and nonlinear inverse problems investigate subspace enlargement, discrepancy-based regularization, and ensemble collapse.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.06121",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Herty"
    },
    {
      "name": "Pierpaolo Porretta"
    },
    {
      "name": "Giuseppe Visconti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xd6wh4dnbg8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.06121",
  "fulltext_url": null,
  "id": "8xd6wh4dnbg8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.06121",
  "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.NA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7163680519",
  "pdf_url": "https://arxiv.org/pdf/2606.06121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xd6wh4dnbg8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2606.06121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.06121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Ensemble Kalman Inversion as an Inertial Interacting Particle System",
  "title_text": "Ensemble Kalman Inversion as an Inertial Interacting Particle System",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8xd6wh4dnbg8m",
  "venue": "arXiv",
  "versions": []
}