aiqbench analysis
This research introduces a novel framework that enhances coarse-grained molecular dynamics by integrating stochastic Hessian-vector product matching to capture second-order curvature information in neural potentials. The method significantly improves the accuracy of slow-mode dynamics and local structural representation for biomolecules compared to traditional force-matching approaches. By enabling higher-order physical supervision without prohibitive computational cost, this advancement offers a practical pathway for simulating complex atomic systems at previously inaccessible timescales.
Hessian Matching for Machine-Learned Coarse-Grained Molecular Dynamics
arXiv:2605.12823v2 Announce Type: replace 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: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.
38 pages (9-page main text, references, and 3 appendices), 22 figures, 5 tables. v2: substantially revised; main experiments now train and evaluate directly on the nine-protein benchmark, the unseen-protein results move to Appendix C, and full per-protein results are added
Machine Learning (cs.LG); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph); Biomolecules (q-bio.BM)
arXiv:2605.12823 [cs.LG]
(or arXiv:2605.12823v2 [cs.LG] for this version)
Full text under the publisher's open licence · 264 words
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