{
  "abstract": "Polynomial manifolds provide nonlinear low-dimensional representations through polynomial decoders. We propose to represent the polynomial terms of the decoder using features that are orthonormal on the training data. This empirical orthogonality enables a greedy algorithm, Greedy-OPM, which jointly selects encoder modes and polynomial features while minimizing the reconstruction error under a prescribed bound on the decoder's Lipschitz constant. Numerical experiments show that this Lipschitz constraint improves generalization away from the training data while retaining high reconstruction accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33784",
  "author_total": 3,
  "authors": [
    {
      "name": "Tomoki Koike"
    },
    {
      "name": "Benjamin Peherstorfer"
    },
    {
      "name": "Elizabeth Qian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a3c124ye0yah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33784",
  "fulltext_url": null,
  "id": "8a3c124ye0yah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33784",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7223890907",
  "pdf_url": "https://arxiv.org/pdf/2610.33784",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a3c124ye0yah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33784",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33784"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling",
  "title_text": "Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8a3c124ye0yah",
  "venue": "arXiv",
  "versions": []
}