Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
arXiv:2605.12823 (cs)
[Submitted on 12 May 2026]
Title:Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics
Authors:Sanya Murdeshwar, Sanjit Shashi, Kevin Bachelor, William Noid, Ashwin Lokapally, Razvan Marinescu
View a PDF of the paper titled Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics, by Sanya Murdeshwar and 5 other authors
View PDF
HTML (experimental)
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 unconstrained. 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 construct an unbiased stochastic estimator of the Hessian-matching objective by using random probe vectors. We evaluate our method by comparing against force matching on a benchmark of nine fast-folding proteins unseen during training. 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. Our results demonstrate that higher-order physical supervision is a practical path to more accurate and transferable CG potentials for biomolecular simulation.
| Comments: | 15 pages, 4 figures, 1 table |
| Subjects: | Machine Learning (cs.LG); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph); Biomolecules (q-bio.BM) |
| Cite as: | arXiv:2605.12823 [cs.LG] |
| (or arXiv:2605.12823v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.12823
arXiv-issued DOI via DataCite (pending registration)
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics, by Sanya Murdeshwar and 5 other authors
Current browse context:
cs.LG
Change to browse by:
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Learning When to Act: Communication-Efficient Reinforcement Learning via Run-Time Assurance
May 14
-
CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks
May 14
-
Towards Robust Federated Multimodal Graph Learning under Modality Heterogeneity
May 14
-
OceanCBM: A Concept Bottleneck Model for Mechanistic Interpretability in Ocean Forecasting
May 14
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.