{
  "abstract": "Real-time prediction of complex physical systems requires surrogate models that learn from data while representing strong multiphysics coupling. Deep Operator Networks have shown success in single-physics problems, yet their effectiveness in capturing nonlinear interactions in coupled systems (such as thermo-mechanical or electro-thermal coupling) remains underexplored. Here we pose a practical question: should the architecture of a neural operator reflect the strength of physical coupling it aims to model? We compare single-branch and multi-branch designs, in both feedforward and sequential recurrent forms, across three representative systems: a reaction-diffusion problem with heterogeneous sources, a nonlinear thermo-electrical problem with temperature-dependent conductivity and Joule heating, and a viscoplastic thermo-mechanical model of steel solidification. Single-branch networks consistently outperform multi-branch variants in tightly coupled regimes by encouraging shared latent representations, whereas multi-branch designs remain favorable for decoupled or single-physics tasks. Once trained, these surrogates deliver full-field predictions up to 1.8 × 104 times faster than physics-based solvers.",
  "abstract_shown": true,
  "affiliations": [
    "National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL USA",
    "The Grainger College of Engineering, Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL USA",
    "The Grainger College of Engineering, Nuclear, Plasma & Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL USA",
    "Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS USA",
    "Civil and Urban Engineering Department, New York University Abu Dhabi, Abu Dhabi, UAE"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Jaewan Park"
    },
    {
      "affs": [
        2
      ],
      "name": "Kazuma Kobayashi",
      "orcid": "0000-0002-0931-3420"
    },
    {
      "affs": [
        0,
        3
      ],
      "name": "Qibang Liu",
      "orcid": "0000-0001-7935-7907"
    },
    {
      "affs": [
        0,
        4
      ],
      "name": "Diab Abueidda"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Seid Koric"
    },
    {
      "affs": [
        0,
        2
      ],
      "name": "Syed Bahauddin Alam",
      "orcid": "0000-0001-5506-6953"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7r3hbw5yfbke7.bib",
  "cited_by": 0,
  "doi": "10.1038/s44172-026-00714-4",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13696711/",
  "id": "7r3hbw5yfbke7",
  "issns": [
    "2731-3395"
  ],
  "landing_url": "https://doi.org/10.1038/s44172-026-00714-4",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Article"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7167275373",
  "pdf_url": null,
  "pmcid": "PMC13696711",
  "pmid": "42399436",
  "published": "2026-07-03",
  "publisher": "Nature Publishing Group",
  "ris": "https://research.draconitic.com/paper/7r3hbw5yfbke7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "PMC13696711",
      "source": "pmc",
      "url": "https://doi.org/10.1038/s44172-026-00714-4"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Model Reduction and Neural Networks",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Network architecture follows coupling in multiphysics systems: single vs. multiple branches in DeepONet and S-DeepONet",
  "title_text": "Network architecture follows coupling in multiphysics systems: single vs. multiple branches in DeepONet and S-DeepONet",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:34:00Z",
  "url": "https://research.draconitic.com/paper/7r3hbw5yfbke7",
  "venue": "Communications Engineering",
  "versions": []
}