{
  "abstract": "The discrete eigenvalues of the Radiative Transfer Equation (RTE) play a fundamental role in the analysis of radiation transport under anisotropic scattering conditions. For the Henyey–Greenstein phase function, these eigenvalues depend on the single-scattering albedo (ω) and the anisotropy parameter (g). Although the Legendre polynomial (P 9 ) approximation provides accurate reference solutions, each parameter combination requires a separate numerical solution.In this study, a multi-output machine learning framework is developed to predict the five dominant discrete eigenvalues of the RTE directly from the optical parameters. A reference dataset was generated using a Mathematica implementation of the P 9 method and used to train three regression models: Random Forest (RF), Gradient Boosting (GB), and Multi-Layer Perceptron (MLP). Model performance was assessed using standard statistical error metrics and comparisons with the reference P 9 solutions.All three models achieved high predictive accuracy (R 2 > 0.95), with the MLP model providing the best overall performance, particularly for the higher-order eigenvalues. Once trained, the surrogate models estimate the five dominant eigenvalues directly from the optical parameters without repeated execution of the P 9 solution procedure. These results demonstrate that conventional multi-output machine learning models provide an accurate and practical surrogate approach for repeated eigenvalue predictions within the investigated parameter domain.",
  "abstract_shown": true,
  "affiliations": [
    "Vocational School of Health Services, Iğdır University, Iğdır, 76000, Turkey; Corresponding author.",
    "Vocational School of Technical Sciences, Iğdır University, Iğdır, 76000, Turkey"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Halide Köklü"
    },
    {
      "affs": [
        1
      ],
      "name": "Metehan Günde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3rpczpxbc09k.bib",
  "cited_by": 0,
  "doi": "10.1016/j.physo.2026.100502",
  "fulltext_url": "http://www.sciencedirect.com/science/article/pii/S2666032626001353",
  "id": "b3rpczpxbc09k",
  "issns": [
    "2666-0326"
  ],
  "landing_url": "https://doi.org/10.1016/j.physo.2026.100502",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QC1-999"
    ],
    [
      "openalex",
      "2206|Radiative Heat Transfer Studies"
    ]
  ],
  "openalex": "W7222313016",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/b3rpczpxbc09k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:43:45Z",
      "native_id": "fe45ec65a5bf48c590e3151dfa5a3f05",
      "source": "doaj",
      "url": "https://doi.org/10.1016/j.physo.2026.100502"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "lcc:QC1-999",
      "subfield": "general"
    }
  ],
  "title": "Machine learning prediction of discrete eigenvalues for the radiative transfer equation under anisotropic Henyey–Greenstein scattering",
  "title_text": "Machine learning prediction of discrete eigenvalues for the radiative transfer equation under anisotropic Henyey–Greenstein scattering",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:43:45Z",
  "url": "https://research.draconitic.com/paper/b3rpczpxbc09k",
  "venue": "Physics Open",
  "versions": []
}