Pith Number

pith:C5OAVKAT

pith:2026:C5OAVKATGIQL7Z2AGR3ZFKH3DJ

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Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics

Ashwin Lokapally, Kevin Bachelor, Razvan Marinescu, Sanjit Shashi, Sanya Murdeshwar, William Noid

Adding stochastic Hessian-vector product matching to force matching improves coarse-grained molecular dynamics models by incorporating curvature information.

arxiv:2605.12823 v1 · 2026-05-12 · cs.LG · physics.chem-ph · physics.comp-ph · q-bio.BM

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

HVP matching outperforms plain force matching on 8 of 9 proteins on slow-mode metrics, with reductions of up to 85% in the Kullback--Leibler divergence between the CG and reference distributions along the slowest collective mode of the largest protein.

C2weakest assumption

The decomposition of the target CG Hessian into a model-independent projected AA Hessian plus a model-dependent covariance correction remains valid and the stochastic HVP estimator stays unbiased throughout training.

C3one line summary

Stochastic Hessian-vector product matching augments force matching to instill second-order curvature into coarse-grained molecular dynamics potentials, outperforming force matching on slow-mode metrics for 8 of 9 test proteins.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] David E. Shaw et al. Millisecond-scale molecular dynamics simulations on anton. InProceed- ings of the Conference on High Performance Computing Networking, Storage and Analysis, SC ’09, page 1–11. ACM 2009

[2] David E. Shaw et al. Anton 3: Twenty microseconds of molecular dynamics simulation before lunch. InSC21: International Conference for High Performance Computing, Networking, Storage and Analysis, page 2021

[3] W. G. Noid. Perspective: Coarse-grained models for biomolecular systems.The Journal of Chemical Physics, 139(9), September 2013 2013

[4] Coarse-grained protein models and their applications.Chemical Reviews, 116(14):7898–7936, June 2016 2016

[5] F. Ercolessi and J. B. Adams. Interatomic potentials from first-principles calculations: The force-matching method.Europhysics Letters, 26(8):583–588, 1994 1994

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:12.194820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

175c0aa8133220bfe740347792a8fb1a7f9a19d0866d97850b939c573dfcf494

Aliases

arxiv: 2605.12823 · arxiv_version: 2605.12823v1 · doi: 10.48550/arxiv.2605.12823 · pith_short_12: C5OAVKATGIQL · pith_short_16: C5OAVKATGIQL7Z2A · pith_short_8: C5OAVKAT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C5OAVKATGIQL7Z2AGR3ZFKH3DJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 175c0aa8133220bfe740347792a8fb1a7f9a19d0866d97850b939c573dfcf494

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb975d273f1af5eff956caa1781ce3ce78256fbc89e4e3890d6c7834b14d145d",
    "cross_cats_sorted": [
      "physics.chem-ph",
      "physics.comp-ph",
      "q-bio.BM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-12T23:46:38Z",
    "title_canon_sha256": "32da991e95ad9a3b3262ff36fdaf295cae24357fb9514c1095b649f772e00907"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12823",
    "kind": "arxiv",
    "version": 1
  }
}