{
  "abstract": "Hybrid physics-machine-learning solvers improve under-resolved simulations by embedding trainable corrections into the time integration. During autoregressive inference, repeated solver-model interactions can amplify small errors, motivating multi-timestep solver-in-the-loop training. However, production solvers rarely expose the derivatives needed to backpropagate through such rollouts. We introduce Diff-NekRS, a scalable differentiable framework that embeds neural corrections directly in the GPU-accelerated NekRS incompressible-flow solver. NekRS computes the authoritative forward trajectory, a manually implemented exact discrete adjoint differentiates the supported fully discrete timestep, and LibTorch supplies neural vector-Jacobian products and parameter gradients. End-to-end Taylor and centered finite-difference tests verify the assembled gradient for two-dimensional cylinder flow (2Dcyl) and the three-dimensional Taylor-Green vortex (3DTGV) across five horizons and 12-1,020 MPI ranks. At 1,020 ranks, optimizer-enabled post-setup training updates retain 54.5%-78.0% and 80.7%-81.9% weak-scaling efficiency for 2Dcyl and 3DTGV, respectively. In 200-step autoregressive inference, the M = 50 model reduces the three-seed median terminal relative L2 velocity error by 59.2% for 2Dcyl and 12.1% for 3DTGV relative to the uncorrected coarse-grid P = 2 baseline, and retains wall-clock speedups of 5.38x and 2.49x, respectively, relative to the corresponding P = 7 configurations for equal simulated-time intervals. These results establish a verified and scalable path for multi-timestep solver-in-the-loop training that improves coarse-grid trajectory accuracy while retaining a speed advantage over the high-order reference",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23208",
  "author_total": 4,
  "authors": [
    {
      "name": "Junoh Jung"
    },
    {
      "name": "Riccardo Balin"
    },
    {
      "name": "Bethany Lusch"
    },
    {
      "name": "Emil Constantinescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/awx9akpqsczqv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23208",
  "fulltext_url": null,
  "id": "awx9akpqsczqv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23208",
  "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": "W7214023516",
  "pdf_url": "https://arxiv.org/pdf/2609.23208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/awx9akpqsczqv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23208"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Diff-NekRS: A Scalable Differentiable Framework for Multi-Timestep Solver-in-the-Loop Training",
  "title_text": "Diff-NekRS: A Scalable Differentiable Framework for Multi-Timestep Solver-in-the-Loop Training",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/awx9akpqsczqv",
  "venue": "arXiv",
  "versions": []
}