{
  "abstract": "Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve local conditioning but require expensive optimizer state, while Kronecker-factored methods such as SOAP scale to larger networks but rely on periodic basis updates. We introduce \\method, which augments SOAP-style preconditioning with a scalar secant-energy correction adapted to Kronecker geometry and an adaptive basis update followed by variance-state downscaling. We characterize the directional secant matching induced by the scalar correction and give a bound on variance-state mismatch across basis changes. Across eight PDE benchmarks, \\method attains the lowest final residual on six, including Burgers and Boussinesq, while SOAP-family baselines perform better on Gray-Scott and Ginzburg-Landau. On Boussinesq, \\method reaches a residual of $10^{-5}$ in 4.1 hours with 9.2 GB peak VRAM, while Adam does not reach this target within 14 hours. Three-seed $L^2$ and $H^1$ errors on four representative PDEs support the link between lower residuals and improved solution accuracy. These results position \\method as a scalable option for stiff, high-accuracy physics-informed training, rather than a uniform replacement for existing optimizers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29448",
  "author_total": 5,
  "authors": [
    {
      "name": "Guangyuan Wang"
    },
    {
      "name": "Mads Toftrup"
    },
    {
      "name": "Sebastian Loeschcke"
    },
    {
      "name": "Yixuan Wang"
    },
    {
      "name": "Anima Anandkumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/av6pf6qkjabg5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29448",
  "fulltext_url": null,
  "id": "av6pf6qkjabg5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29448",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7204926849",
  "pdf_url": "https://arxiv.org/pdf/2608.29448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/av6pf6qkjabg5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning",
  "title_text": "SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/av6pf6qkjabg5",
  "venue": "arXiv",
  "versions": []
}