{
  "abstract": "Operator learning is an emerging field at the intersection of machine learning and scientific computing. By learning mappings between function spaces, neural operators provide data-driven surrogate models for families of partial differential equations (PDEs). Once trained, these models can evaluate solution operators efficiently, making them suitable for many-query applications such as real-time prediction and parameter sweeps. However, maintaining high approximation accuracy and stable long-term predictions remains challenging for complex forward and inverse problems. To address these challenges, we propose the Starter-Iterator Neural Operator (SINO), which incorporates the initialization and residual-correction structures of classical iterative solvers into neural operator learning. The frequency-domain Starter captures dominant global spectral features and provides an informed initial approximation, while the latent-space Iterator applies successive residual-based corrections to refine local and multiscale solution structures. Experiments on representative time-dependent PDEs, including the Navier-Stokes and acoustic wave equations, together with applications to image super-resolution and weather forecasting, show that SINO achieves competitive accuracy and stable performance across the benchmarks considered in this work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18305",
  "author_total": 7,
  "authors": [
    {
      "name": "Kuilin Qin"
    },
    {
      "name": "Lianfang Wang"
    },
    {
      "name": "Xu Sun"
    },
    {
      "name": "Jiwei Jia"
    },
    {
      "name": "Yu Wang"
    },
    {
      "name": "Yong Wang"
    },
    {
      "name": "Yuping Duan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aj7782evdrv21.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18305",
  "fulltext_url": null,
  "id": "aj7782evdrv21",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18305",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2606.18305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aj7782evdrv21.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2606.18305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems",
  "title_text": "Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/aj7782evdrv21",
  "venue": "arXiv",
  "versions": []
}