{
  "abstract": "Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1\\% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1\\% and regional strain energy within 0.35\\% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortical mid-shaft scaffold with porosity 63\\% while satisfying the compliance constraint within 2\\% under walking and stair-climbing loads. It achieves an 84\\% porosity on a proximal cancellous scaffold with strain-energy deviations below 0.25\\% under the same loads. Analysis of the learned representations reveals distinct architectural families in latent space. Further, the attention heads of the rectified-flow transformer specialize for spatial shifts -- learning the analogue of a finite-difference stencil -- and coordinate symmetries, with ablations showing their influence on generated topologies. These results establish a route to printable, mechanically constrained scaffold designs. The framework is general enough for extending to many other multiscale structural design applications including topology-microstructure co-design in metal additive manufacturing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25565",
  "author_total": 2,
  "authors": [
    {
      "name": "Reza T Batley"
    },
    {
      "name": "Sourav Saha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ssge5w33bdt0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25565",
  "fulltext_url": null,
  "id": "9ssge5w33bdt0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25565",
  "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",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2205|Topology Optimization in Engineering"
    ]
  ],
  "openalex": "W7223015016",
  "pdf_url": "https://arxiv.org/pdf/2610.25565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ssge5w33bdt0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25565"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Concurrent two-scale topology optimization of printable bone scaffolds via rectified-flow generation and exact latent-space refinement",
  "title_text": "Concurrent two-scale topology optimization of printable bone scaffolds via rectified-flow generation and exact latent-space refinement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/9ssge5w33bdt0",
  "venue": "arXiv",
  "versions": []
}