{
  "abstract": "Coarse-grained (CG) molecular dynamics enables simulations of atomic systems such as biomolecules at timescales inaccessible to all-atom (AA) methods, but existing CG neural potentials trained via force matching capture only the gradient of the free-energy surface, leaving its curvature unsupervised. We introduce a framework that augments force matching with stochastic Hessian-vector product (HVP) matching, instilling second-order curvature information into CG potentials without constructing the full Hessian. We derive a decomposition of the target CG Hessian into a model-independent projected AA Hessian, precomputed once before training, and a model-dependent covariance correction computed online at negligible cost. We then construct an unbiased stochastic estimator of the Hessian-matching objective by using random probe vectors. We evaluate our method by training on a benchmark set of nine fast-folding proteins and gauging agreement of the learned free-energy landscapes with reference data along the directions of slowest collective motion using time-lagged independent component analysis. HVP matching improves slow-mode accuracy over force matching for all but one of our benchmark proteins. It also sharpens local structure, reducing bond-length error on eight of nine proteins, and in several cases by an order of magnitude. Our results demonstrate that higher-order physical supervision is a practical path to more accurate CG potentials for biomolecular simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12823",
  "author_total": 5,
  "authors": [
    {
      "name": "Sanya Murdeshwar"
    },
    {
      "name": "Sanjit Shashi"
    },
    {
      "name": "Kevin Bachelor"
    },
    {
      "name": "William Noid"
    },
    {
      "name": "Razvan Marinescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc64hr0d324ga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12823",
  "fulltext_url": null,
  "id": "bc64hr0d324ga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12823",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "q-bio.BM"
    ],
    [
      "openalex",
      "1312|Protein Structure and Dynamics"
    ]
  ],
  "openalex": "W7161159128",
  "pdf_url": "https://arxiv.org/pdf/2605.12823",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bc64hr0d324ga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2605.12823",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12823"
    }
  ],
  "subjects": [
    {
      "field": "biochemistry",
      "origin": "arxiv:q-bio.BM",
      "subfield": "biophysics"
    },
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics",
  "title_text": "Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:21Z",
  "url": "https://research.draconitic.com/paper/bc64hr0d324ga",
  "venue": "arXiv",
  "versions": []
}