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REVIEW 3 major objections 4 minor 22 references

Two Newton–Raphson steps keep a coarse-grained water cluster thermodynamically consistent with its all-atom reference to within 1 k_B.

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2026-08-05 05:24 UTC pith:MXL442XP

load-bearing objection Solid incremental algorithm with credible accuracy on (H2O)10, but the 'comparable cost' claim needs a wall-clock benchmark and a second system. the 3 major comments →

arxiv 2509.05279 v1 pith:MXL442XP submitted 2025-09-05 physics.chem-ph physics.atm-clusphysics.comp-ph

A computationally efficient subspace harmonic relaxation algorithm for coarse-graining of molecular systems with nearly exact thermodynamic consistency

Jo\~ao V. M. Pimentel , Vladimir A. Mandelshtam This is my paper
classification physics.chem-ph physics.atm-clusphysics.comp-ph
keywords coarse-grainingsubspace harmonic relaxationrigid-body modelblock-diagonal HessianNewton-Raphson iterationminimum energy manifoldthermodynamic consistencywater cluster
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that coarse-graining a molecular system by relaxing fast intramolecular degrees of freedom—rather than freezing them—can reproduce all-atom thermodynamics almost exactly, at a cost comparable to an all-atom simulation. It turns the Subspace Harmonic Relaxation (SHR) method into a practical algorithm: two Newton-Raphson steps using a block-diagonal Hessian pseudoinverse bring the system to the minimum energy manifold, and a harmonic free-energy correction defines the coarse-grained potential. On the (H2O)10 cluster, the resulting heat capacity and structural distributions agree with the all-atom reference within about 1 k_B, while needing roughly ten times fewer Monte Carlo samples. The approach also recovers all-atom bond and angle distributions from the coarse-grained simulation for negligible extra cost.

Core claim

The central claim is that near-exact thermodynamic consistency survives two aggressive approximations: truncating the Hessian to its per-monomer blocks and limiting subspace relaxation to P=2 Newton-Raphson iterations. For each rigid-body configuration, the algorithm relaxes the fast coordinates along the pseudoinverse of the block-diagonal Hessian, landing on a point near the minimum energy manifold, then evaluates the coarse-grained free energy as the all-atom potential plus a harmonic correction from the selected fast-mode frequencies. Demonstrated with the q-TIP4P/F model of (H2O)10, this cheap recipe reproduces the all-atom heat capacity and O–O, O–H, and H–O–H distributions within stat

What carries the argument

The minimum energy manifold R*, defined by \tilde K(r*) M^{-1/2} \nabla V(r*) = 0, where \tilde K is the pseudoinverse of the mass-scaled Hessian restricted to the fast degrees of freedom. The algorithm approximates R* with the iteration r <- r - M^{-1/2} \tilde K M^{-1/2} \nabla V, with \tilde K assembled from the L largest eigenpairs of each block-diagonal Hessian block K_i. The block-diagonal form K = diag{K_1,...,K_I} is the object that cuts the diagonalization cost from (3N)^3 to the sum of per-group cubes, and the final Hessian evaluation at the relaxed point supplies the harmonic frequencies for the free-energy correction.

Load-bearing premise

The method assumes the off-diagonal blocks of the Hessian—the couplings between different rigid groups—can be dropped without shifting the relaxed fast coordinates or the selected fast-mode frequencies enough to change thermodynamic averages; this is validated only on a single small water cluster and not tested on covalently bonded groups such as a protein backbone.

What would settle it

Run the same CG-SHR protocol with P=2 and the block-diagonal Hessian on a small peptide or protein fragment, and compare the heat capacity and pair distributions against an all-atom replica-exchange simulation. If the SHR results deviate by more than the statistical error or the heat-capacity peak shifts by several kelvin, the block-truncation assumption is falsified. A direct check would compare the MEM point and free-energy correction obtained with the block-diagonal pseudoinverse versus the full-Hessian pseudoinverse: a meaningful difference in the gradient projection or in the harmonic fre

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • For (H2O)10, the CG-SHR heat capacity stays within about 1 k_B of the all-atom result at all temperatures, while the fixed-shape CG model shifts the heat-capacity peak by roughly 10 K.
  • Because the CG simulation needs about an order of magnitude fewer Monte Carlo steps, the overall cost of the SHR simulation is comparable to the all-atom simulation despite two Hessian evaluations per step.
  • All-atom properties such as OH bond-length and HOH-angle distributions follow from the CG simulation with almost no extra cost, by adding harmonic Gaussian fluctuations along the fast modes.
  • The block-diagonal Hessian makes the SHR evaluation scale per group rather than with the full system, which is the step that opens the method to larger molecules such as proteins.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • We infer that the number of Newton-Raphson iterations P could be tuned per system: P=1 is exact for a harmonic system, and anharmonicity or strong inter-mode coupling would show up as a growing need for P>2, measurable by comparing CG-SHR with AA across temperatures.
  • We infer that the block-diagonal truncation's success on water may not carry over to covalently linked groups (e.g., protein backbone fragments), where inter-block Hessian couplings could be strong; a cheap diagnostic would compare the block-diagonal pseudoinverse with the full-Hessian pseudoinverse on a small peptide.
  • The harmonic reconstruction of AA configurations (Eq. 12) could serve as a fast surrogate for backmapping; one could test whether the reconstructed ensemble reproduces not just static distributions but also correlated two-body properties, which the paper does not report.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper revisits the subspace harmonic relaxation (SHR) method for coarse-graining molecular clusters, originally introduced by the same authors. It proposes two algorithmic improvements: (i) replacing the conjugate-gradient subspace minimization with a fixed small number P of Newton-Raphson iterations and (ii) replacing the full Hessian by its block-diagonal approximation, so that the pseudoinverse and normal-mode calculation factorize over the rigid groups. The resulting CG potential is tested on the (H2O)10 cluster with q-TIP4P/F, comparing against all-atom replica-exchange Monte Carlo. The authors report that CG-SHR reproduces the heat capacity within 1 k_B, matches O-O RDFs essentially exactly, and recovers OH-bond and HOH-angle distributions via cheap harmonic backmapping, while requiring about 20x fewer MC steps than AA. On this basis they conclude that the overall computational cost is comparable to AA simulations and that the approach is applicable to larger systems such as proteins.

Significance. If the efficiency claim is valid, the paper offers a practical route to nearly exact coarse-graining for systems with well-separated fast and slow degrees of freedom, and the block-diagonal Hessian idea could remove the main bottleneck of the original SHR method. The accuracy results on (H2O)10 are credible and substantial: no target observable is fitted, the CG results are benchmarked against independent AA replica-exchange simulations, and the agreement is demonstrated for several complementary observables, including backmapped atomistic distributions. The algorithmic contribution is a natural extension of Paper I and is clearly described. However, the headline computational-efficiency claim is not supported by the data presented, and the extension to large covalently bonded systems is asserted without evidence. These issues are central to the paper's stated purpose and must be addressed.

major comments (3)
  1. [Numerical example; Conclusions] The abstract and Conclusions claim that the CG simulation's 'overall computational cost becomes comparable' to AA because it requires roughly an order of magnitude fewer MC steps. The manuscript reports only MC step counts (4.5e9 vs 2.2e8) and no wall-clock times, per-step cost decomposition, or complexity comparison including Hessian construction/diagonalization. Each CG-SHR step is more expensive: it requires P=2 Newton-Raphson gradient evaluations plus construction and eigendecomposition of the block Hessian at r^(0) and again at r^(P). Even with block-diagonal truncation, each block Hessian K_i depends on all pairwise interactions involving group i, so the step cost has a larger prefactor than a single AA energy evaluation. A 20x reduction in MC steps can be erased if the CG step is more than 20x slower; this is plausible and untested. Please add actual CPU timings or careful flop co
  2. [Eqs. (2)-(6); Introduction] The block-diagonal approximation K = diag{K_1,...,K_I} discards all inter-group second-derivative couplings. The paper presents this as enabling application to large proteins, but the numerical demonstration is limited to (H2O)10, where groups are independent monomers. For a covalently bonded protein, the inter-block Hessian elements between connected groups are not negligible, so the MEM condition (6) and the Newton step (11) are not obviously accurate. No test or error estimate is given for such systems. The broad applicability claim should either be supported by a test on a bonded multi-group system or explicitly narrowed.
  3. [Algorithm, step 2] The algorithm computes the pseudoinverse tilde-K(r^(0)) once and reuses it for all P Newton-Raphson iterations. The text says 'we confirmed that this is the case' but provides no quantitative data on how the projected gradient or the resulting frequencies change if tilde-K is updated. This is a key approximation for large systems. Please report a comparison for (H2O)10 between fixed and updated pseudoinverse, or provide a convergence criterion.
minor comments (4)
  1. [Preliminary Setup] The statement that 'P=2 will maintain the accuracy on the order of 1 cm^-1 for the CG free energy of (H2O)10' is not supported by a figure, table, or error analysis. Please provide evidence or remove the quantitative claim.
  2. [Fig. 1] The y-axis label 'Cv (kb)' should be typeset as C_v/k_B, with units and notation defined in the caption. Currently the label is ambiguous.
  3. [Figs. 2-4] The statement that agreement is 'within the thickness of the lines' is visual. For the RDFs and backmapped distributions, no statistical errors or quantitative deviation (e.g., RMS difference) are reported. Adding a measure of uncertainty or deviation would strengthen the accuracy claim.
  4. [Data Availability Statement] The statement says 'The data that supports the findings of this study are available within the article.' However, the numerical data underlying the figures is not provided. Please deposit raw simulation data or specify a repository.

Circularity Check

0 steps flagged

No circular derivation; efficiency claim is an evidentiary gap, not a circular step.

full rationale

The paper's derivation chain is not circular. The CG free energy F(R;T) in Eqs. (7)–(9) is defined from the AA potential V(r) via harmonic relaxation on a block-diagonal Hessian (Eqs. (2)–(6)); no target observable (heat capacity, O–O RDF, O–H bond/angle distributions) enters the definition, and no parameter is fitted to the AA benchmark. The choice P=2 (Numerical Example) is a fixed iteration count, not a fitted potential parameter; it is validated against AA after the fact, which is in-sample tuning of a convergence setting at worst, not a fitted input renamed as prediction. The self-citations to Paper I (Ref. 9) provide the underlying bijection Eq. (10) and MC protocols, but these are external peer-reviewed results with independent AA benchmarks from Paper I, and the present paper re-derives the central equations (Eqs. (2)–(9)) and tests them against independent replica-exchange AA MC simulations. No uniqueness theorem is imported, and the block-diagonal approximation [12] is openly presented as an approximation rather than an ansatz smuggled through citation. The paper's accuracy claims are therefore supported by an external comparison. The notable weakness is the efficiency claim: "Combined with the fact that the CG simulation requires roughly an order of magnitude fewer Monte Carlo steps to reach similar statistical accuracy for selected observables compared to the AA model, the overall computational cost becomes comparable" (Abstract) and "Due to the reduced number of MC steps required to achieve comparable statistical accuracy, the overall computational cost remains competitive with AA simulations" (Conclusions) are not demonstrated because no wall-clock per-step comparison is given, only MC step counts (4.5e9 AA vs 2.2e8 CG). That is an evidentiary gap in the 'computationally efficient' title, but it is a correctness/evidence concern, not a circularity. Similarly, the method is validated only on (H2O)10, a scope limitation the authors acknowledge in Conclusions: "for large molecular systems, one may still find the improved algorithm for direct evaluation of the SHR potential too expensive." Circularity score: 1 (minor self-citation present but not load-bearing in a circular sense).

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central claim rests on no fitted potential parameters and no invented entities. The only hand-selected numbers are the NR iteration count P=2 and the confining sphere radius R_c=6.0 A. The key approximation assumptions are the harmonic separation, block-diagonal Hessian, frozen pseudoinverse, and the AA model as reference; only the block-diagonal approximation is new to this paper, and the frozen-pseudoinverse assumption is validated on a single system.

free parameters (2)
  • P (number of Newton-Raphson iterations) = 2
    Hand-selected convergence parameter for (H2O)10: P=1 is exact for harmonic systems and P=2 is stated to keep CG free energy accuracy on the order of 1 cm^-1. It is validated against AA results rather than fitted to observables, but it is a user-chosen algorithmic setting.
  • R_c (constraining sphere radius) = 6.0 A
    Simulation constraint used to prevent cluster dissociation. It modifies the sampled ensemble and is chosen by hand; it is not central to the method but affects the numerical example.
axioms (4)
  • domain assumption Fast intramolecular degrees of freedom are low-amplitude and harmonically separable from slow CG coordinates; the local harmonic approximation to the exact CG free energy is accurate (Eqs. (8)-(9)).
    The entire SHR construction and the free-energy correction rely on this time-scale separation, stated in the Introduction and used in Eq. (8). It is reasonable for stiff water monomers but not proven for arbitrary systems.
  • domain assumption Block-diagonal truncation of the Hessian, K = diag{K_1,...,K_I} (Eq. (2)), omitting inter-group blocks, is sufficient for computing MEM directions and harmonic frequencies.
    This is the key approximation introduced in this paper. It is supported by precedent in macromolecular normal-mode analysis (Ref. 12) and by the (H2O)10 test, but not by an error bound.
  • ad hoc to paper The pseudoinverse K~(r(0)) computed at the initial reference configuration remains a good projector throughout the P Newton-Raphson iterations.
    The paper states that 'for well-behaved systems' it often remains good and confirms it only for the single (H2O)10 example. If this fails, the P-step relaxation and the claimed per-step cost savings are compromised.
  • domain assumption The q-TIP4P/F potential and classical mechanics are an adequate all-atom reference for the numerical validation.
    Used as ground truth for the (H2O)10 test (Ref. 13). The conclusions concern consistency with this reference, not with experiment.

pith-pipeline@v1.4.0-alltime-deepseek-medium · 7625 in / 14611 out tokens · 156883 ms · 2026-08-05T05:24:42.721755+00:00 · methodology

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Cite this review

Pith. "Pith review of A computationally efficient subspace harmonic relaxation algorithm for coarse-graining of molecular systems with nearly exact thermodynamic consistency." pith.science (2026). https://pith.science/paper/MXL442XP

@misc{pith2026250905279,
  author       = {Pith},
  title        = {Pith review of: A computationally efficient subspace harmonic relaxation algorithm for coarse-graining of molecular systems with nearly exact thermodynamic consistency},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MXL442XP}},
  note         = {Machine review of arXiv:2509.05279}
}
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read the original abstract

In a recent paper, J. Chem. Phys. 162, 214101 (2025), a novel approach for the rigidification of a molecular cluster was proposed, in which starting with an all-atom (AA) potential, a coarse-grained (CG) potential for the associated cluster of rigid monomers was constructed directly. The method is based on using the harmonic approximation for the fast intramolecular degrees of freedom. While conceptually primitive, the resulting CG model turned out to be surprisingly accurate for selected water and ammonia clusters. However, as originally formulated, a single evaluation of the CG potential turned out to be much more expensive than the evaluation of the AA potential, since the former required a subspace minimization followed by a subspace normal mode calculation. In this communication, we formulate the approach more broadly, making it applicable, e.g., to coarse-graining a large protein. We also introduce key algorithmic improvements, reducing the cost of the subspace minimization and normal mode calculation. Combined with the fact that the CG simulation requires roughly an order of magnitude fewer Monte Carlo steps to reach similar statistical accuracy for selected observables compared to the AA model, the overall computational cost becomes comparable. These improvements are demonstrated on a water cluster.

Figures

Figures reproduced from arXiv: 2509.05279 by Jo\~ao V. M. Pimentel, Vladimir A. Mandelshtam.

Figure 1
Figure 1. Figure 1: FIG. 1. Heat capacity of the (H [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Same as Fig. 1, but for the O-O radial pair distribu [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as Fig. 2 but for the O-H bond length distri [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Same as Fig. 2 but for the H-O-H angle distribution [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

22 extracted references · 16 canonical work pages · 1 internal anchor

  1. [1]

    Jin , author A

    author author J. Jin , author A. J. \ Pak , author A. E. P. \ Durumeric , author T. D. \ Loose ,\ and\ author G. A. \ Voth ,\ title title Bottom-up coarse-graining: Principles and perspectives , \ https://doi.org/10.1021/acs.jctc.2c00643 journal journal Journal of Chemical Theory and Computation \ volume 18 ,\ pages 5759--5791 ( year 2022 ) ,\ note publis...

    work page doi:10.1021/acs.jctc.2c00643 2022

  2. [2]

    author author M. S. \ Shell ,\ title title The relative entropy is fundamental to multiscale and inverse thermodynamic problems , \ https://doi.org/10.1063/1.2992060 journal journal The Journal of Chemical Physics \ volume 129 ,\ pages 144108 ( year 2008 ) ,\ https://arxiv.org/abs/https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.2992060/15419593/144...

    doi:10.1063/1.2992060 2008

  3. [3]

    Izvekov \ and\ author G

    author author S. Izvekov \ and\ author G. A. \ Voth ,\ title title A multiscale coarse-graining method for biomolecular systems , \ https://doi.org/10.1021/jp044629q journal journal The Journal of Physical Chemistry B \ volume 109 ,\ pages 2469--2473 ( year 2005 ) NoStop

    doi:10.1021/jp044629q 2005

  4. [4]

    author author W. G. \ Noid , author J.-W. \ Chu , author G. S. \ Ayton , author V. Krishna , author S. Izvekov , author G. A. \ Voth , author A. Das ,\ and\ author H. C. \ Andersen ,\ title title The multiscale coarse-graining method. i. a rigorous bridge between atomistic and coarse-grained models , \ https://doi.org/10.1063/1.2938860 journal journal J. ...

    doi:10.1063/1.2938860 2008

  5. [5]

    author author S. J. \ Marrink , author H. J. \ Risselada , author S. Yefimov , author D. P. \ Tieleman ,\ and\ author A. H. \ de Vries ,\ title title The martini force field: Coarse grained model for biomolecular simulations , \ https://doi.org/10.1021/jp071097f journal journal The Journal of Physical Chemistry B \ volume 111 ,\ pages 7812--7824 ( year 20...

    doi:10.1021/jp071097f 2007

  6. [6]

    author author M. M. \ Tirion ,\ title title Large amplitude elastic motions in proteins from a single-parameter, atomic analysis , \ https://doi.org/10.1103/PhysRevLett.77.1905 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 1905--1908 ( year 1996 ) NoStop

    work page doi:10.1103/physrevlett.77.1905 1905

  7. [7]

    Na \ and\ author G

    author author H. Na \ and\ author G. Song ,\ title title Coarse-graining waters: Unveiling the effective hydrophilicity/hydrophobicity of individual protein atoms and the roles of waters’ hydrogens , \ https://doi.org/10.1021/acs.jctc.3c00700 journal journal Journal of Chemical Theory and Computation \ volume 19 ,\ pages 7307--7323 ( year 2023 ) ,\ note p...

    work page doi:10.1021/acs.jctc.3c00700 2023

  8. [8]

    author author K. M. \ Kidder \ and\ author W. G. \ Noid ,\ title title Analysis of mapping atomic models to coarse-grained resolution , \ https://doi.org/10.1063/5.0220989 journal journal The Journal of Chemical Physics \ volume 161 ,\ pages 134113 ( year 2024 ) ,\ https://arxiv.org/abs/https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0220989/201930...

    work page doi:10.1063/5.0220989 2024

  9. [9]

    author author J. V. M. \ Pimentel \ and\ author V. A. \ Mandelshtam ,\ title title From all-atom to rigid monomer treatment of molecular clusters , \ https://doi.org/10.1063/5.0273835 journal journal The Journal of Chemical Physics \ volume 162 ,\ pages 214101 ( year 2025 ) ,\ https://arxiv.org/abs/https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.02...

    work page doi:10.1063/5.0273835 2025

  10. [10]

    author author M. C. \ Muniz , author I. Gartner , Thomas E. , author M. Riera , author C. Knight , author S. Yue , author F. Paesani ,\ and\ author A. Z. \ Panagiotopoulos ,\ title title Vapor–liquid equilibrium of water with the mb-pol many-body potential , \ https://doi.org/10.1063/5.0050068 journal journal The Journal of Chemical Physics \ volume 154 ,...

    work page doi:10.1063/5.0050068 2021

  11. [11]

    R \"u hle , author H

    author author V. R \"u hle , author H. Kusumaatmaja , author D. Chakrabarti ,\ and\ author D. J. \ Wales ,\ title title Exploring energy landscapes: Metrics, pathways, and normal-mode analysis for rigid-body molecules , \ https://doi.org/10.1021/ct400403y journal journal Journal of Chemical Theory and Computation \ volume 9 ,\ pages 4026--4034 ( year 2013...

    work page doi:10.1021/ct400403y 2013

  12. [12]

    Tama , author F

    author author F. Tama , author F. X. \ Gadea , author O. Marques ,\ and\ author Y.-H. \ Sanejouand ,\ title title Building-block approach for determining low-frequency normal modes of macromolecules , \ @noop journal journal Proteins: Structure, Function, and Bioinformatics \ volume 41 ,\ pages 1--7 ( year 2000 ) NoStop

    work page 2000

  13. [13]

    Habershon , author T

    author author S. Habershon , author T. E. \ Markland ,\ and\ author D. E. \ Manolopoulos ,\ title title Competing quantum effects in the dynamics of a flexible water model , \ https://doi.org/10.1063/1.3167790 journal journal J. Comp. Phys. \ volume 131 ,\ eid 024501 ( year 2009 ) NoStop

    doi:10.1063/1.3167790 2009

  14. [14]

    author author J. C. \ Maier \ and\ author N. E. \ Jackson ,\ title title Bypassing backmapping: Coarse-grained electronic property distributions using heteroscedastic gaussian processes , \ https://doi.org/10.1063/5.0101038 journal journal The Journal of Chemical Physics \ volume 157 ,\ pages 174102 ( year 2022 ) ,\ https://arxiv.org/abs/https://pubs.aip....

    work page doi:10.1063/5.0101038 2022

  15. [15]

    Stieffenhofer , author M

    author author M. Stieffenhofer , author M. Wand ,\ and\ author T. Bereau ,\ title title Adversarial reverse mapping of equilibrated condensed-phase molecular structures , \ https://doi.org/10.1088/2632-2153/abb6d4 journal journal Machine Learning: Science and Technology \ volume 1 ,\ pages 045014 ( year 2020 ) NoStop

    work page doi:10.1088/2632-2153/abb6d4 2020

  16. [16]

    Generative Coarse-Graining of Molecular Conformations

    author author W. Wang , author M. Xu , author C. Cai , author B. K. \ Miller , author T. Smidt , author Y. Wang , author J. Tang ,\ and\ author R. Gómez-Bombarelli ,\ https://arxiv.org/abs/2201.12176 title Generative coarse-graining of molecular conformations , \ ( year 2022 ),\ https://arxiv.org/abs/2201.12176 arXiv:2201.12176 [cs.LG] NoStop

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  17. [17]

    Li , author C

    author author W. Li , author C. Burkhart , author P. Polińska , author V. Harmandaris ,\ and\ author M. Doxastakis ,\ title title Backmapping coarse-grained macromolecules: An efficient and versatile machine learning approach , \ https://doi.org/10.1063/5.0012320 journal journal The Journal of Chemical Physics \ volume 153 ,\ pages 041101 ( year 2020 ) ,\...

    work page doi:10.1063/5.0012320 2020

  18. [18]

    Shmilovich , author M

    author author K. Shmilovich , author M. Stieffenhofer , author N. E. \ Charron ,\ and\ author M. Hoffmann ,\ title title Temporally coherent backmapping of molecular trajectories from coarse-grained to atomistic resolution , \ https://doi.org/10.1021/acs.jpca.2c07716 journal journal The Journal of Physical Chemistry A \ volume 126 ,\ pages 9124--9139 ( ye...

    work page doi:10.1021/acs.jpca.2c07716 2022

  19. [19]

    Waltmann , author Y

    author author C. Waltmann , author Y. Wang , author C. Yang , author S. Kim ,\ and\ author G. A. \ Voth ,\ title title Msback: Multiscale backmapping of highly coarse-grained proteins using constrained diffusion , \ https://doi.org/10.1021/acs.jctc.5c00459 journal journal Journal of Chemical Theory and Computation \ volume 21 ,\ pages 6184--6193 ( year 20...

    doi:10.1021/acs.jctc.5c00459 2025

  20. [20]

    author author R. H. \ Swendsen \ and\ author J.-S. \ Wang ,\ title title Replica monte carlo simulation of spin-glasses , \ @noop journal journal Physical review letters \ volume 57 ,\ pages 2607 ( year 1986 ) NoStop

    work page 1986

  21. [21]

    author author C. J. \ Geyer et al. ,\ title title Computing science and statistics: Proceedings of the 23rd symposium on the interface , \ @noop journal journal American Statistical Association, New York \ volume 156 ( year 1991 ) NoStop

    work page 1991

  22. [22]

    Campos-Villalobos , author R

    author author G. Campos-Villalobos , author R. Subert , author G. Giunta , et al. ,\ title title Machine-learned coarse-grained potentials for particles with anisotropic shapes and interactions , \ https://doi.org/10.1038/s41524-024-01405-4 journal journal npj Computational Materials \ volume 10 ,\ pages 228 ( year 2024 ) NoStop

    work page doi:10.1038/s41524-024-01405-4 2024