{
  "abstract": "Monte Carlo PDE solvers enable mesh-free pointwise queries, but repeatedly traversing heterogeneous media is costly, particularly in scenes with reusable or dynamically changing materials. We introduce Walk on Multiscale Media (WoMM), which compiles fine-scale transport into reusable, editable and composable transport prefabs. A probabilistic interpretation of multiscale finite-element bases and condensed operators yields coarse transitions retaining fine-scale material effects. Each prefab combines port-level operators, entrance-dependent exit distributions, and Poisson-marked trajectory records, enabling incremental updates for overlapping absorption fields, gradient-field steering through path reweighting and transient diffusion. Integrated with conventional Walk-on-Spheres in a hybrid continuous--discrete solver, these prefabs accelerate repeated pointwise PDE queries and support interactive material edits without repeatedly solving the fine-scale problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35952",
  "author_total": 2,
  "authors": [
    {
      "name": "Yunfeng Liao"
    },
    {
      "name": "Xiucheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/742v1t1av78d3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35952",
  "fulltext_url": null,
  "id": "742v1t1av78d3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35952",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.GR"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.35952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/742v1t1av78d3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.35952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Walk on Multiscale Media: Compiling Editable and Composable Transport Medium Prefabs for Monte Carlo PDE Solvers",
  "title_text": "Walk on Multiscale Media: Compiling Editable and Composable Transport Medium Prefabs for Monte Carlo PDE Solvers",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/742v1t1av78d3",
  "venue": "arXiv",
  "versions": []
}