{
  "abstract": "Neural ordinary differential equations (neural ODE) gained attention in safety critical settings such as continuous-time controllers for cyber-physical systems and classifiers integrated into automated decision pipelines, raising the question whether their behavior can be formally verified. Existing tools dedicated to neural ODE provide only a single reachability call without iterative input-set refinement, limiting the precision of their verdicts to whatever one reachability call can deliver. We present TNODEV, the first formal verifier for neural ODE that integrates a falsification checker, a fast interval-based reachability backend based on continuous-time mixed monotonicity, a verification and refinement loop with three input-set splitting heuristics, and a parallel scheduler in a single end-to-end pipeline. TNODEV supports safe-set inclusion verification on pure neural ODE, neural ODE in closed loop with a neural network controller and general neural ODE (GNODE), with the safe set specified either as an interval or as the half-space intersection induced by a target classification label. We evaluate TNODEV on a range of benchmarks across safe-set inclusion and classification-robustness properties, including a direct reachability comparison against NNV 2.0 and CORA and a verification comparison against NNV 2.0 on MNIST general neural ODE classifiers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16567",
  "author_total": 3,
  "authors": [
    {
      "name": "Abdelrahman Sayed Sayed"
    },
    {
      "name": "Pierre-Jean Meyer"
    },
    {
      "name": "Mohamed Ghazel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmm8y9pbfjw9e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16567",
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  "id": "dmm8y9pbfjw9e",
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  "pdf_url": "https://hal.science/hal-05661783/document",
  "pmcid": null,
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  "published": "2026-10-21",
  "publisher": "[Amherst Massachusetts]: OpenReview.net, 2022",
  "ris": "https://research.draconitic.com/paper/dmm8y9pbfjw9e.ris",
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      "first_seen": "2026-10-30T12:18:00Z",
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      "native_id": "2606.16567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16567"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
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  ],
  "title": "TNODEV: Toolbox for Neural ODE Verification",
  "title_text": "TNODEV: Toolbox for Neural ODE Verification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dmm8y9pbfjw9e",
  "venue": "Transactions on Machine Learning Research",
  "versions": []
}