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Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes — arXiv:2609.23105

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.23105
License (as archived): CC0-1.0
Archived: 2026-10-09T23:41:22.359Z
SHA-256 of the archived text: 9e9c00dc8da486d11938af678e51e8e52f5f71abd88cd10a9c356e929b2edb60
Stable URL of this page: https://metraipolis.com/documento/dc_7c8a265122cc

How to cite

Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes — arXiv:2609.23105 — arXiv (en), https://arxiv.org/abs/2609.23105 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7c8a265122cc (Metraipolis archive dc_7c8a265122cc, sha256 9e9c00dc8da486d11938af678e51e8e52f5f71abd88cd10a9c356e929b2edb60)

BibTeX

@misc{dc7c8a265122cc,
  title = {Equivariant Neural Prediction of the Stokes Resistance Tensors for Arbitrary Microparticle Shapes — arXiv:2609.23105},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.23105},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7c8a265122cc; sha256 9e9c00dc8da486d11938af678e51e8e52f5f71abd88cd10a9c356e929b2edb60},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.23105. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-22 in physics.comp-ph).
Categorie arXiv: Fluid Dynamics (physics.flu-dyn) ; Computational Physics (physics.comp-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.23105 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:46:47.373Z dalla pagina https://arxiv.org/catchup/physics.comp-ph/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).