{
  "abstract": "The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23105",
  "author_total": 4,
  "authors": [
    {
      "name": "Sanjay Pradeep"
    },
    {
      "name": "David Dandy"
    },
    {
      "name": "Candace S. J. Tsai"
    },
    {
      "name": "Jeff D. Eldredge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd9gxvtram068.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23105",
  "fulltext_url": null,
  "id": "fd9gxvtram068",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23105",
  "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",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3104|Micro and Nano Robotics"
    ]
  ],
  "openalex": "W7214045588",
  "pdf_url": "https://arxiv.org/pdf/2609.23105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd9gxvtram068.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23105"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes",
  "title_text": "Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/fd9gxvtram068",
  "venue": "arXiv",
  "versions": []
}