{
  "abstract": "Feature-mapping methods represent structural designs by explicit geometric primitives on fixed analysis grids, an interpretable and parametric alternative to the density fields of density-based topology optimization (SIMP). In contrast to SIMP, however, feature-mapping optimization is sensitive to the initial design. We present a gradient-based approach to align a feature-mapping configuration to a given (pseudo) density field, e.g., to initialize a subsequent feature-mapping optimization. The staged approach is based on a least-squares tracking formulation, preceded by a variant that only rewards alignment and does not penalize mismatch. Without an underlying finite element simulation, iterations are cheap, but isolated features receive little sensitivity information. As a remedy, we propose an asymmetric transition function based on automatically parametrized Bézier curves. We demonstrate the approach for a 2D cantilever and the five-bar design; for the latter, we show optional feature minimization based on the feature scaling variable of the geometry projection method. The approach works well with first-order optimizers. The absence of a state problem and the small number of variables, however, also make a second-order formulation attractive. To the best of the authors' knowledge, we present the first Hessian formulation for feature mapping and report the behavior of first- and second-order optimizers on our benchmark problems. For completeness, we also give the exact Hessian of the state-based compliance, which requires one additional solution of the FEM system per feature variable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39472",
  "author_total": 4,
  "authors": [
    {
      "name": "Fabian Wein"
    },
    {
      "name": "Patrick Jung"
    },
    {
      "name": "Arash Moradian"
    },
    {
      "name": "Michael Stingl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8550wc5mq4qd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39472",
  "fulltext_url": null,
  "id": "f8550wc5mq4qd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39472",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2205|Topology Optimization in Engineering"
    ]
  ],
  "openalex": "W7215079570",
  "pdf_url": "https://arxiv.org/pdf/2609.39472",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8550wc5mq4qd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39472",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39472"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Aligning feature-mapping designs to given density fields, first and second order",
  "title_text": "Aligning feature-mapping designs to given density fields, first and second order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/f8550wc5mq4qd",
  "venue": "arXiv",
  "versions": []
}