{
  "abstract": "Matrix-product-state (MPS) and quantized tensor-train (QTT) representations offer a promising framework for computational fluid dynamics, with logarithmic run time and memory scaling in mesh size when bond dimensions remain bounded. Existing MPS-based solvers are Eulerian: they compress velocity fields and enforce immersed-body boundary conditions through static masks or body-fitted coordinates. Moving or flexible bodies complicate this approach: deformation requires updating MPS masks every time step, while filamentary vorticity in high-Reynolds-number flows may resist low-rank compression. We propose a complementary approach: compress the Biot--Savart kernel rather than the flow state, evolve vorticity using Lagrangian vortex particles, and represent immersed bodies by bound vortex sheets on Lagrangian surface points. Our main theoretical result is a lifting theorem: QTT rank $r$ of the kernel implies matrix-product-operator (MPO) rank at most $2^d r$ for the corresponding convolution operator in $d$ dimensions, independent of grid resolution. This bound is sharp for our interleaved ordering. With quantics tensor cross interpolation, the moment-to-local stage of a single-level fast multipole method becomes a precomputed tensor-network contraction with quasi-linear complexity, retaining Lagrangian flexibility for immersed bodies. Our PyTorch implementation (\\texttt{DiffVortex}) is end-to-end differentiable, runs on GPUs, and handles $6.7\\times10^{7}$ particles on a single device. We validate against reference vortex-method results for an impulsively started cylinder and exact and reference solutions for inviscid elliptical vortices. We also demonstrate two-dimensional flows past rigidly moving, multiple, and deforming bodies, including gradients propagated through the full time integration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30012",
  "author_total": 3,
  "authors": [
    {
      "name": "Yu Jun Loo"
    },
    {
      "name": "Silas Alben"
    },
    {
      "name": "Shravan Veerapaneni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amcs9gdt8pn78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30012",
  "fulltext_url": null,
  "id": "amcs9gdt8pn78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30012",
  "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",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7223199286",
  "pdf_url": "https://arxiv.org/pdf/2610.30012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amcs9gdt8pn78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.30012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30012"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "DiffVortex: A quantum-inspired fast solver for incompressible flows",
  "title_text": "DiffVortex: A quantum-inspired fast solver for incompressible flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/amcs9gdt8pn78",
  "venue": "arXiv",
  "versions": []
}