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) |
Submission history
From: Sanya Murdeshwar [view email]
[v1]
Tue, 12 May 2026 23:46:38 UTC (808 KB)