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REVIEW 4 major objections 4 minor 73 references

Predicting Thermodynamics of Liquid Water from Time Series Analysis

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the time-resolved counting of hydrogen-bonded ring motifs in liquid water carries enough information to predict density, compressibility, and heat capacity, including at pressures the model never saw during training.

desk verdict A genuinely new ML application to water's hydrogen-bond network, but the extrapolation claim rests on a validation protocol that selects the most flattering window on the held-out isobar, so the main conclusion is not yet supported. read the letter →

arxiv 2506.21821 v1 pith:QECXZGWF submitted 2025-06-26 physics.chem-ph physics.comp-ph

Ma{l}gorzata J. Zimoń , Fausto Martelli This is my paper · ORCID
classification physics.chem-phphysics.comp-ph
keywords hydrogenbondnetworkringstatisticstimeseriesanalysisgatedrecurrentunitliquidwateranomaliesthermodynamicresponsefunctionsmoleculardynamicsextrapolation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that the temporal evolution of hydrogen-bond network topology, specifically the time series of counts of ring-shaped motifs of size 3 through 12, carries enough information to determine macroscopic thermodynamic properties of liquid water. Using classical molecular dynamics of the TIP4P/2005 model, the authors feed these ring-count signals to a bidirectional gated recurrent unit and show it recovers density, isothermal compressibility, and heat capacity at four pressures. The stronger claim is extrapolation: after training on three isobars, the model predicts the fourth, including pressures outside the training range. If true, this gives a way to read thermodynamics from short, un-averaged dynamical signals rather than from statistical-mechanical ensembles.

What carries the argument

The central object is the n-membered ring: a cyclic path of n hydrogen-bonded water molecules, with n running from 3 to 12 and bonds defined by the Luzar-Chandler geometric criterion. At each thermodynamic state point, the simulation produces a 10-dimensional time series of ring counts over 5000 snapshots. A bidirectional multi-layer gated recurrent unit reads fixed-length windows of these signals, and its final hidden states are passed through a two-layer feedforward network with ReLU activation, layer normalization, and a sigmoid output to keep predictions physical. This machine-learning setup is the carrier of the argument because it can, in principle, exploit temporal patterns that conventional running averages throw away.

What would settle it

The claim is falsified if a model trained on ring-count probability distributions with time order destroyed matches the GRU's accuracy, because then no temporal encoding is needed; it is also falsified if applying the Task-2 model to a new simulation at 2500 bar predicts density, compressibility, or heat capacity with errors far exceeding those already reported at 1500 bar.

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Extended reading notes

Core claim

At each simulated state point, the hydrogen bond network is reduced to a 10-dimensional signal counting how many n-membered hydrogen-bonded rings are present over 5000 snapshots. The paper's central claim is that a machine-learning model exposed only to these signals, never to pressure or temperature, can predict density, isothermal compressibility, and heat capacity. In the first task, the model reproduces the isobars it trained on, including the non-monotonic profiles associated with crossing Widom lines. In the second task, training on three isobars and predicting the fourth yields density errors below about 2.2%, compressibility errors from 2.8% to 30.7%, and heat-capacity errors from 0.2% to 8.5%, depending on the target isobar. The authors interpret the qualitative agreement across all twelve unseen state points as evidence that the time series contains thermodynamic information that conventional averaging discards.

Load-bearing premise

The load-bearing premise is that the relation between hydrogen-bond ring time series and thermodynamic properties learned at a few pressures transfers to pressures and temperatures the model never saw; if that mapping is not portable, the extrapolation claim collapses.

Editorial extensions

If this is right

  • Response functions could be estimated directly from hydrogen bond network dynamics without long averaging, fluctuation formulas, or numerical differentiation of equations of state.
  • A single pressure-agnostic model can serve multiple isobars, so thermodynamic portraits of a liquid could be assembled from sparse simulated state points.
  • The method's qualitative success on unseen pressures suggests it could be used to locate Widom lines and anomaly regions before expensive simulations are run.
  • The same time-series treatment of ring motifs is claimed to extend beyond water to other network-forming materials.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The authors leave implicit that the same encoding might predict transport properties; if ring dynamics carry thermodynamic information, they likely also correlate with relaxation times and diffusion.
  • A decisive test of physical content would be to train on TIP4P/2005 data and transfer to another water model; success would show the ring-to-property mapping is a property of water, not of one force field.
  • The largest errors at 1500 bar and 190 K suggest the transferability assumption may hold only when relaxation dynamics are fast enough relative to the fixed window length, which sets a boundary the paper does not map.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript reports classical molecular dynamics simulations of TIP4P/2005 water at 48 state points (four isobars and twelve temperatures) and analyzes the time evolution of hydrogen-bond network ring statistics (rings of size 3 to 12). A bidirectional multi-layer GRU is trained to map short windows of these 10-dimensional ring-statistics time series to three thermodynamic properties: density, isothermal compressibility, and isobaric heat capacity. Task 1 evaluates the model on held-out time segments at the same thermodynamic state points, while Task 2 trains on three isobars and predicts the thermodynamic properties on the fourth, unseen isobar. The authors report low mean relative errors for most predictions and conclude that the dynamics of microscopic topological motifs encode macroscopic thermodynamic behavior and that the approach enables prediction in regions beyond those directly sampled.

Significance. If the central claim were convincingly established, the paper would be significant: it would show that temporally resolved topological fluctuations of the hydrogen-bond network carry thermodynamic information usable for interpolation and extrapolation across the phase diagram. The tasks are clearly formulated and the descriptor (ring-statistics time series) is physically motivated. However, the significance currently hinges on Task 2, the only evidence for extrapolation to unseen thermodynamic conditions, and that evidence is undermined by the validation protocol and by the absence of baseline comparisons. The paper is therefore not yet publishable in its present form, but the underlying approach is testable and the identified issues are addressable.

major comments (4)
  1. [§4.3, Task 2 validation] The validation protocol for Task 2 is selection-biased and directly compromises the central claim. The text states that "the validation window of size 600 snapshots is not moved along the entire signal, but over the length of 1500 snapshots characterized by the lowest error." Because the error is computed against the true labels of the held-out isobar, this procedure selects the evaluation segment after seeing the test labels. Since the ring-statistics signals are nonstationary, different segments of the same trajectory can yield very different errors, so the reported MREs (e.g., 1.24% for ρ, 9.29% for κT, 0.21% for CP at 1 bar) are optimistic lower bounds rather than honest estimates of extrapolation accuracy. The evaluation should use a window-selection rule fixed without reference to the held-out labels, for example the same relative segment for all isobars or a rule selected on training isobars only. This issue is load-bearing because Task 2 is the only evidence for the abstract's claim of predicting thermodynamics "in regions beyond those directly sampled."
  2. [§2 (Task 2) and §4.3, baselines] No baseline comparison is reported. The manuscript's central claim that the temporal dynamics of ring motifs encode thermodynamics requires showing that the GRU's time-series input adds predictive power beyond (i) time-averaged ring counts or (ii) simple regression on temperature and pressure. Since the model is trained on ring statistics from the same MD trajectories whose thermodynamic labels are the targets, a baseline is needed to rule out the possibility that the model is learning a static correlation between mean ring fractions and thermodynamic state, which would sever the claimed dependence on temporal dynamics. I recommend reporting MREs for an MLP fed with time-averaged ring statistics and for a linear or Gaussian-process regression on T and P using the same train/test split as Task 2.
  3. [§4.3, Eq. (1), sigmoid output and min-max normalization] The output layer uses a sigmoid (Eq. 1) and the labels are min-max normalized before training. In Task 2, the authors correctly note that the held-out isobar's labels can lie outside the range of values seen during training. A sigmoid output cannot produce normalized predictions outside [0,1], so if the true normalized labels lie outside this interval, the model is structurally incapable of predicting them. The manuscript does not describe how predictions are denormalized or how the bounded output is handled in the extrapolation task. This should be clarified, and for extrapolation tasks an unbounded output layer may be necessary.
  4. [Fig. 4 caption and §2 (Task 1)] The caption of Fig. 4 states that "The MREs reported in the plots at 1 bar are shared across isobars." This is ambiguous and suggests that per-isobar errors are not actually reported. If the same MRE value is used for all isobars, the quantitative accuracy at each pressure is not shown. Please report per-isobar MREs separately, together with the standard deviation across the ns = 10 seeds, since the models are described as seed-sensitive.
minor comments (4)
  1. [§4.1] The Methods section mentions a Parrinello-Rahman barostat but then refers to "the time constant for the Berendsen barostat is set to 1 ps." Please correct this inconsistency and specify the barostat used and its parameters.
  2. [Introduction] The statement that the paper "prove[s] that such a link indeed exists" is too strong for an empirical machine-learning study; "provide evidence for" would be more appropriate.
  3. [Introduction] The phrase "fine-elements" in the discussion of RNNs for multiscale simulations appears to be a typo for "finite elements."
  4. [Abstract and Conclusions] The claim of establishing "a new paradigm for understanding material properties beyond the classical confines of statistical mechanics" is not supported by the presented evidence; it should be tempered to reflect that the work is an exploratory demonstration of a time-series-based approach.

Circularity Check

1 steps flagged · score 6.0 of 10

Task 2's extrapolation errors are selected by choosing the lowest-error validation window on the held-out isobar, making the central 'prediction beyond sampled regions' claim fitted rather than predictive.

  1. fitted input called prediction [Methods §4.3 (Machine learning model), second-task validation protocol; reported in Results, Task 2 (Fig. 6)]
    "A similar approach is used in the second case. The model is validated using the time segments from unseen pressure. The validation window of size 600 snapshots is not moved along the entire signal, but over the length of 1500 snapshots characterized by the lowest error, generating Nv = 900 samples."

    The MREs reported for Task 2 (e.g., 1.24% for density, 9.29% for kT, 0.21% for CP at 1 bar) are computed on a 1500-snapshot window selected post hoc by scanning the held-out isobar's signal and choosing the segment with the lowest error against the true labels. Since the ring-statistics signals are nonstationary, different evaluation windows yield different errors, so selecting the best one makes the reported errors minima by construction. The 'prediction' accuracy is therefore a fitted selection from the test data, not an unbiased estimate of extrapolation performance.

full rationale

The paper's Task 1 is a standard supervised interpolation experiment: a GRU is trained on 90% of each trajectory and evaluated on the remaining 10%, and showing that it can recover thermodynamic labels from ring-statistics time series is evidence of a learnable correlation but is not itself circular. The central circularity is in Task 2, the only evidence for extrapolation to unseen pressures. The Methods explicitly state that the validation window on the held-out isobar is not slid over the entire signal but is chosen as the 1500-snapshot segment with the lowest error, which requires access to the true labels of the test set. This post-hoc selection makes the reported MREs optimistic lower bounds rather than honest predictive errors, and it is this selected error that is presented as successful prediction beyond sampled conditions. No load-bearing self-citation or imported uniqueness theorem was found: prior ring-theory work is used as motivation, not as a forced derivation. The main issue is not that supervised learning fits data, but that the headline extrapolation result reduces, by construction, to a minimum over test-set windows. This warrants a score of 6: one 'prediction' reduces by construction, giving partial circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a supervised fit of a neural network to simulation data. Free parameters include the network weights and the post-hoc validation window. The axioms are the validity of the TIP4P/2005 model, the informativeness of ring statistics, the generalizability to unseen pressures, and the specific hydrogen-bond definition. No new physical entities are introduced.

free parameters (3)
  • Neural network weights and biases (GRU and fully connected layers) = Learned during training; specific values not reported
    The model's output is a function of these fitted parameters; the 'prediction' is a fit, not a derivation.
  • Validation window length in Task 2 (600 snapshots over a 1500-snapshot segment selected for lowest error) = Not reported; selected post hoc from validation data
    The window is chosen based on the validation data itself, inflating apparent accuracy.
  • Number of ring motifs (n=3 to 12) and hydrogen-bond definition = n=3..12; HB distance <3.5 A, angle <30 deg
    These are modeling choices that define the input representation and could affect results.
assumptions (4)
  • domain assumption TIP4P/2005 classical MD is a valid model of liquid water
    The entire study is based on this force field; results may not transfer to real water or other water models.
  • ad hoc to paper Ring-statistics time series contain sufficient information to determine the thermodynamic state
    The paper assumes this without proof; it is the central hypothesis being tested.
  • ad hoc to paper The mapping learned from three isobars generalizes to unseen pressures
    This is the extrapolation assumption tested in Task 2; it fails at low temperature and high pressure.
  • domain assumption The Luzar-Chandler hydrogen-bond definition is appropriate for ring statistics
    Ring statistics depend on this operational definition, which may influence the time series features.

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Cite this review

Pith. "Pith review of Predicting Thermodynamics of Liquid Water from Time Series Analysis." pith.science (2026). https://pith.science/paper/QECXZGWF

@misc{pith2026250621821,
  author       = {Pith},
  title        = {Pith review of: Predicting Thermodynamics of Liquid Water from Time Series Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QECXZGWF}},
  note         = {Machine review of arXiv:2506.21821}
}
read the original abstract

Thermodynamics, introduced over two centuries ago, remains foundational to our understanding of physical, chemical, biological, and engineering systems. Its principles are traditionally grounded in the statistical mechanics framework, which explains macroscopic behavior from microscopic states. In this work, we propose an alternative approach that interprets thermodynamic behavior through the lenses of time series analysis, an approach commonly used in other fields, including finance, climate, and signal processing. We perform classical molecular dynamics simulations of liquid water, the most complex, anomalous, and important substance known, over a wide range of its phase diagram. By examining the temporal evolution of the hydrogen bond network (HBN) topology, we demonstrate that the dynamics of microscopic topological motifs populating the HBN encode the system's macroscopic thermodynamic behavior. Furthermore, our approach enables the prediction of thermodynamic properties in regions beyond those directly sampled in our simulations. We achieve this result by leveraging artificial intelligence to uncover patterns in temporally resolved data that are often lost through conventional averaging. This work offers new insights into the fundamental behavior of water and network-forming materials more broadly, establishing a new paradigm for understanding material properties beyond the classical confines of statistical mechanics.

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Reference graph

Works this paper leans on

73 extracted references · 59 canonical work pages

  1. [1]

    The Journal of chemical physics 150(6) (2019)

    Salzmann, C.G.: Advances in the experimental exploration of water’s phase diagram. The Journal of chemical physics 150(6) (2019)

    work page 2019

  2. [2]

    Reviews of Modern Physics 88(1), 011002 (2016)

    Amann-Winkel, K., B¨ ohmer, R., Fujara, F., Gainaru, C., Geil, B., Loerting, T.: Colloquium: Water’s controversial glass transitions. Reviews of Modern Physics 88(1), 011002 (2016)

    work page 2016

  3. [3]

    Science 379(6631), 474–478 (2023)

    Rosu-Finsen, A., Davies, M.B., Amon, A., Wu, H., Sella, A., Michaelides, A., Salzmann, C.G.: Medium-density amorphous ice. Science 379(6631), 474–478 (2023)

    work page 2023

  4. [4]

    Physical review letters 119(13), 136002 (2017)

    Martelli, F., Torquato, S., Giovambattista, N., Car, R.: Large-scale structure and hyperuniformity of amorphous ices. Physical review letters 119(13), 136002 (2017)

    work page 2017

  5. [5]

    PNAS nexus 1(3), 090 (2022)

    Martelli, F.: Steady-like topology of the dynamical hydrogen bond network in supercooled water. PNAS nexus 1(3), 090 (2022)

    work page 2022

  6. [6]

    Formanek, M., Torquato, S., Car, R., Martelli, F.: Molecular rotations, multi- scale order, hyperuniformity, and signatures of metastability during the com- pression/decompression cycles of amorphous ices. J. Phys. Chem. B 127(17), 3946–3957 (2023)

    work page 2023

  7. [7]

    Nature 314(6006), 76–78 (1985) 12

    Mishima, O., Calvert, L., Whalley, E.: An apparently first-order transition between two amorphous phases of ice induced by pressure. Nature 314(6006), 76–78 (1985) 12

    work page 1985

  8. [8]

    The Journal of chemical physics 100(8), 5910–5912 (1994)

    Mishima, O.: Reversible first-order transition between two h2o amorphs at ∼0.2 gpa and ∼135 k. The Journal of chemical physics 100(8), 5910–5912 (1994)

    work page 1994

Show all 73 references
  1. [9]

    The Journal of Chemical Physics 145(22) (2016)

    Giovambattista, N., Sciortino, F., Starr, F.W., Poole, P.H.: Potential energy landscape of the apparent first-order phase transition between low-density and high-density amorphous ice. The Journal of Chemical Physics 145(22) (2016)

    2016

  2. [10]

    Physical Review Materials 2(7), 075601 (2018)

    Martelli, F., Giovambattista, N., Torquato, S., Car, R.: Searching for crystal-ice domains in amorphous ices. Physical Review Materials 2(7), 075601 (2018)

    2018

  3. [11]

    Journal of Non-Crystalline Solids: X 13, 100081 (2022)

    Mollica, E.M., Russo, J., Stanley, H.E., Sciortino, F.: Decompression dynamics of high density amorphous ice above and below the liquid-liquid critical point. Journal of Non-Crystalline Solids: X 13, 100081 (2022)

    2022

  4. [12]

    Physical Review Letters 133(26), 266102 (2024)

    Guti´ errez Fosado, Y.A., Michieletto, D., Martelli, F.: Link to densify: topological transitions and origin of hysteresis during the compression and decompression of amorphous ices. Physical Review Letters 133(26), 266102 (2024)

    2024

  5. [13]

    Nature, 1–3 (2025)

    Rescigno, M., Toffano, A., Ranieri, U., Andriambariarijaona, L., Gaal, R., Klotz, S., Koza, M.M., Ollivier, J., Martelli, F., Russo, J., Sciortino, F., Teixeira, J., Bove, L.E.: Observation of plastic ice vii by quasi-elastic neutron scattering. Nature, 1–3 (2025)

    2025

  6. [14]

    The Journal of Chemical Physics 157(9) (2022)

    Toffano, A., Russo, J., Rescigno, M., Ranieri, U., Bove, L.E., Martelli, F.: Temperature-and pressure-dependence of the hydrogen bond network in plastic ice vii. The Journal of Chemical Physics 157(9) (2022)

    2022

  7. [15]

    The Journal of Physical Chemistry B 127(30), 6734–6742 (2023)

    Martelli, F.: Electrolyte permeability in plastic ice vii. The Journal of Physical Chemistry B 127(30), 6734–6742 (2023)

    2023

  8. [16]

    Chemical reviews 116(13), 7463–7500 (2016)

    Gallo, P., Amann-Winkel, K., Angell, C.A., Anisimov, M.A., Caupin, F., Chakravarty, C., Lascaris, E., Loerting, T., Panagiotopoulos, A.Z., Russo, J., Sell- berg, J.A., Stanley, H.E., Tanaka, H., Vega, C., Xu, L., Pettersson, G.M.: Water: A tale of two liquids. Chemical reviews...

    2016

  9. [17]

    Proceedings of the National Academy of Sciences 104(23), 9570–9574 (2007)

    Liu, D., Zhang, Y., Chen, C.-C., Mou, C.-Y., Poole, P.H., Chen, S.-H.: Observa- tion of the density minimum in deeply supercooled confined water. Proceedings of the National Academy of Sciences 104(23), 9570–9574 (2007)

    2007

  10. [18]

    Science 358(6370), 1589–1593 (2017)

    Kim, K.H., Sp¨ ah, A., Pathak, H., Perakis, F., Mariedahl, D., Amann-Winkel, K., Sellberg, J.A., Lee, J.H., Kim, S., Park, J., et al.: Maxima in the thermo- dynamic response and correlation functions of deeply supercooled water. Science 358(6370), 1589–1593 (2017)

    2017

  11. [19]

    Nature communications 5(1), 3556 (2014) 13

    Russo, J., Tanaka, H.: Understanding water’s anomalies with locally favoured structures. Nature communications 5(1), 3556 (2014) 13

    2014

  12. [20]

    The Journal of chemical physics 150(9) (2019)

    Martelli, F.: Unravelling the contribution of local structures to the anomalies of water: The synergistic action of several factors. The Journal of chemical physics 150(9) (2019)

    2019

  13. [21]

    AIP Advances 10(5) (2020)

    Formanek, M., Martelli, F.: Probing the network topology in network-forming materials: The case of water. AIP Advances 10(5) (2020)

    2020

  14. [22]

    The Journal of Physical Chemistry B 127(25), 5693–5701 (2023)

    Goswami, Y., Martelli, F., Sastry, S.: Analysis of structural change across the liquid–liquid transition and the widom line in supercooled stillinger-weber silicon. The Journal of Physical Chemistry B 127(25), 5693–5701 (2023)

    2023

  15. [23]

    Nature materials 2(11), 739–743 (2003)

    Sastry, S., Austen Angell, C.: Liquid–liquid phase transition in supercooled silicon. Nature materials 2(11), 739–743 (2003)

    2003

  16. [24]

    Physical review letters 102(7), 075701 (2009)

    Ganesh, P., Widom, M.: Liquid-liquid transition in supercooled silicon determined by first-principles simulation. Physical review letters 102(7), 075701 (2009)

    2009

  17. [25]

    Proceedings of the National Academy of Sciences 107(39), 16772–16776 (2010)

    Beye, M., Sorgenfrei, F., Schlotter, W.F., Wurth, W., F¨ ohlisch, A.: The liquid- liquid phase transition in silicon revealed by snapshots of valence electrons. Proceedings of the National Academy of Sciences 107(39), 16772–16776 (2010)

    2010

  18. [26]

    Nature Physics 7(7), 549–553 (2011)

    Vasisht, V.V., Saw, S., Sastry, S.: Liquid–liquid critical point in supercooled silicon. Nature Physics 7(7), 549–553 (2011)

    2011

  19. [27]

    Physical Review Letters 127(17), 175502 (2021)

    Foffi, R., Sciortino, F.: Structure of high-pressure supercooled and glassy water. Physical Review Letters 127(17), 175502 (2021)

    2021

  20. [28]

    The Journal of Chemical Physics154(18) (2021)

    Foffi, R., Russo, J., Sciortino, F.: Structural and topological changes across the liquid–liquid transition in water. The Journal of Chemical Physics154(18) (2021)

    2021

  21. [29]

    Nature Physics 18(10), 1248–1253 (2022)

    Neophytou, A., Chakrabarti, D., Sciortino, F.: Topological nature of the liquid– liquid phase transition in tetrahedral liquids. Nature Physics 18(10), 1248–1253 (2022)

    2022

  22. [30]

    Proceedings of the National Academy of Sciences 121(36), 2406890121 (2024)

    Neophytou, A., Starr, F.W., Chakrabarti, D., Sciortino, F.: Hierarchy of topo- logical transitions in a network liquid. Proceedings of the National Academy of Sciences 121(36), 2406890121 (2024)

    2024

  23. [31]

    Nature Materials, 1–8 (2025)

    Palombo, G., Weir, S., Michieletto, D., Guti´ errez Fosado, Y.A.: Topological linking determines elasticity in limited valence networks. Nature Materials, 1–8 (2025)

    2025

  24. [32]

    The Journal of chemical physics 123(23) (2005)

    Abascal, J.L., Vega, C.: A general purpose model for the condensed phases of water: Tip4p/2005. The Journal of chemical physics 123(23) (2005)

    2005

  25. [33]

    Neural computation 9(8), 1735–1780 (1997) 14

    Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural computation 9(8), 1735–1780 (1997) 14

    1997

  26. [34]

    arXiv preprint arXiv:1409.1259 (2014)

    Cho, K., Van Merri¨ enboer, B., Bahdanau, D., Bengio, Y.: On the proper- ties of neural machine translation: Encoder-decoder approaches. arXiv preprint arXiv:1409.1259 (2014)

    2014 arXiv

  27. [35]

    arXiv preprint arXiv:1406.1078 (2014)

    Cho, K., Van Merri¨ enboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., Bengio, Y.: Learning phrase representations using rnn encoder- decoder for statistical machine translation. arXiv preprint arXiv:1406.1078 (2014)

    2014 arXiv

  28. [36]

    Advances in neural information processing systems 27 (2014)

    Sutskever, I., Vinyals, O., Le, Q.V.: Sequence to sequence learning with neural networks. Advances in neural information processing systems 27 (2014)

    2014

  29. [37]

    In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp

    Graves, A., Mohamed, A.-r., Hinton, G.: Speech recognition with deep recurrent neural networks. In: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6645–6649 (2013). Ieee

    2013

  30. [38]

    In: International Conference on Machine Learning, pp

    Graves, A., Jaitly, N.: Towards end-to-end speech recognition with recurrent neu- ral networks. In: International Conference on Machine Learning, pp. 1764–1772 (2014). PMLR

    2014

  31. [39]

    Computer Methods in Applied Mechanics and Engineering 357, 112594 (2019)

    Ghavamian, F., Simone, A.: Accelerating multiscale finite element simulations of history-dependent materials using a recurrent neural network. Computer Methods in Applied Mechanics and Engineering 357, 112594 (2019)

    2019

  32. [40]

    Computer Methods in Applied Mechanics and Engineering 369, 113234 (2020)

    Wu, L., Kilingar, N.G., Noels, L., et al.: A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to ran- dom cyclic and non-proportional loading paths. Computer Methods in Applied Mechanics and Engineering 369, 113234 (2020)

    2020

  33. [41]

    International Journal of Plasticity136, 102852 (2021)

    Abueidda, D.W., Koric, S., Sobh, N.A., Sehitoglu, H.: Deep learning for plasticity and thermo-viscoplasticity. International Journal of Plasticity136, 102852 (2021)

    2021

  34. [42]

    Computers & Structures 258, 106678 (2022)

    Borkowski, L., Sorini, C., Chattopadhyay, A.: Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints. Computers & Structures 258, 106678 (2022)

    2022

  35. [43]

    arXiv preprint arXiv:1909.10124 (2019)

    Eslamibidgoli, M.J., Mokhtari, M., Eikerling, M.H.: Recurrent neural network- based model for accelerated trajectory analysis in aimd simulations. arXiv preprint arXiv:1909.10124 (2019)

    2019 arXiv

  36. [44]

    Nature communications 11(1), 5115 (2020)

    Tsai, S.-T., Kuo, E.-J., Tiwary, P.: Learning molecular dynamics with simple language model built upon long short-term memory neural network. Nature communications 11(1), 5115 (2020)

    2020

  37. [45]

    The Journal of Physical Chemistry C 124(27), 14838–14846 (2020) 15

    Wang, J., Li, C., Shin, S., Qi, H.: Accelerated atomic data production in ab initio molecular dynamics with recurrent neural network for materials research. The Journal of Physical Chemistry C 124(27), 14838–14846 (2020) 15

    2020

  38. [46]

    Chemical science 13(23), 7021–7033 (2022)

    Andrews, J., Gkountouna, O., Blaisten-Barojas, E.: Forecasting molecular dynamics energetics of polymers in solution from supervised machine learning. Chemical science 13(23), 7021–7033 (2022)

    2022

  39. [47]

    Machine Learning: Science and Technology 3(2), 025002 (2022)

    Kadupitiya, J., Fox, G.C., Jadhao, V.: Solving newton’s equations of motion with large timesteps using recurrent neural networks based operators. Machine Learning: Science and Technology 3(2), 025002 (2022)

    2022

  40. [48]

    arXiv preprint arXiv:2204.10348 (2022)

    Fu, X., Xie, T., Rebello, N.J., Olsen, B.D., Jaakkola, T.: Simulate time- integrated coarse-grained molecular dynamics with multi-scale graph networks. arXiv preprint arXiv:2204.10348 (2022)

    2022 arXiv

  41. [49]

    Machine Learning: Science and Technology 3(2), 025011 (2022)

    Winkler, L., M¨ uller, K.-R., Sauceda, H.E.: High-fidelity molecular dynamics tra- jectory reconstruction with bi-directional neural networks. Machine Learning: Science and Technology 3(2), 025011 (2022)

    2022

  42. [50]

    Scientific reports 13(1), 20995 (2023)

    L´ opez-Correa, J.M., K¨ onig, C., Vellido, A.: Gpcr molecular dynamics forecasting using recurrent neural networks. Scientific reports 13(1), 20995 (2023)

    2023

  43. [51]

    ChemRxiv preprint ChemRxiv 10.26434/chemrxiv-2025- ds2pb (2025)

    Dayhoff, G., Varma, S.: Mlmd: Machine learning velocities to propagate molecular dynamics simulations. ChemRxiv preprint ChemRxiv 10.26434/chemrxiv-2025- ds2pb (2025)

    2025 doi

  44. [52]

    arXiv preprint arXiv:2111.15176 (2021)

    Zheng, T., Gao, W., Wang, C.: Learning large-time-step molecular dynamics with graph neural networks. arXiv preprint arXiv:2111.15176 (2021)

    2021 arXiv

  45. [53]

    Advances in Neural Information Processing Systems 36, 52863–52883 (2023)

    Klein, L., Foong, A., Fjelde, T., Mlodozeniec, B., Brockschmidt, M., Nowozin, S., No´ e, F., Tomioka, R.: Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics. Advances in Neural Information Processing Systems 36, 52863–52883 (2023)

    2023

  46. [54]

    Advances in Neural Information Processing Systems 36, 36449–36462 (2023)

    Schreiner, M., Winther, O., Olsson, S.: Implicit transfer operator learning: Multiple time-resolution models for molecular dynamics. Advances in Neural Information Processing Systems 36, 36449–36462 (2023)

    2023

  47. [55]

    arXiv preprint arXiv:2401.11037 (2024)

    Xu, M., Han, J., Lou, A., Kossaifi, J., Ramanathan, A., Azizzadenesheli, K., Leskovec, J., Ermon, S., Anandkumar, A.: Equivariant graph neural operator for modeling 3d dynamics. arXiv preprint arXiv:2401.11037 (2024)

    2024 arXiv

  48. [56]

    arXiv preprint arXiv:2409.17808 (2024)

    Jing, B., St¨ ark, H., Jaakkola, T., Berger, B.: Generative modeling of molecular dynamics trajectories. arXiv preprint arXiv:2409.17808 (2024)

    2024 arXiv

  49. [57]

    arXiv preprint arXiv:2503.23794 (2025)

    Thiemann, F.L., Resch¨ utzegger, T., Esposito, M., Taddese, T., Olarte-Plata, J.D., Martelli, F.: Force-free molecular dynamics through autoregressive equivariant networks. arXiv preprint arXiv:2503.23794 (2025)

    2025 arXiv

  50. [58]

    arXiv preprint arXiv:2505.19350 (2025)

    Bigi, F., Chong, S., Kristiadi, A., Ceriotti, M.: Flashmd: long-stride, universal 16 prediction of molecular dynamics. arXiv preprint arXiv:2505.19350 (2025)

    2025

  51. [59]

    Advances in neural information processing systems 27 (2014)

    Goodfellow, I.J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. Advances in neural information processing systems 27 (2014)

    2014

  52. [60]

    Advances in neural information processing systems 32 (2019)

    Yoon, J., Jarrett, D., Schaar, M.: Time-series generative adversarial networks. Advances in neural information processing systems 32 (2019)

    2019

  53. [61]

    arXiv preprint arXiv:1312.6114 (2013)

    Kingma, D.P., Welling, M., et al.: Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013)

    2013 arXiv

  54. [62]

    Advances in neural information processing systems 30 (2017)

    Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L., Polosukhin, I.: Attention is all you need. Advances in neural information processing systems 30 (2017)

    2017

  55. [63]

    SoftwareX 1, 19–25 (2015)

    Abraham, M.J., Murtola, T., Schulz, R., P´ all, S., Smith, J.C., Hess, B., Lin- dahl, E.: Gromacs: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1, 19–25 (2015)

    2015

  56. [64]

    Molecular physics 100(1), 191–198 (2002)

    NOS ´E, S.U.I.: A molecular dynamics method for simulations in the canonical ensemble. Molecular physics 100(1), 191–198 (2002)

    2002

  57. [65]

    Phys- ical review A 31(3), 1695 (1985)

    Hoover, W.G.: Canonical dynamics: Equilibrium phase-space distributions. Phys- ical review A 31(3), 1695 (1985)

    1985

  58. [66]

    Physical review letters 45(14), 1196 (1980)

    Parrinello, M., Rahman, A.: Crystal structure and pair potentials: A molecular- dynamics study. Physical review letters 45(14), 1196 (1980)

    1980

  59. [67]

    Verlet, L.: Computer” experiments” on classical fluids. i. thermodynamical properties of lennard-jones molecules. Physical review 159(1), 98 (1967)

    1967

  60. [68]

    Nature 379(6560), 55–57 (1996)

    Luzar, A., Chandler, D.: Hydrogen-bond kinetics in liquid water. Nature 379(6560), 55–57 (1996)

    1996

  61. [69]

    ACS nano 14(7), 8616–8623 (2020)

    Martelli, F., Crain, J., Franzese, G.: Network topology in water nanoconfined between phospholipid membranes. ACS nano 14(7), 8616–8623 (2020)

    2020

  62. [70]

    arXiv preprint arXiv:1803.08375 (2018)

    Agarap, A.F.: Deep learning using rectified linear units ( relu). arXiv preprint arXiv:1803.08375 (2018)

    2018 arXiv

  63. [71]

    arXiv preprint arXiv:1412.6980 (2014)

    Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)

    2014 arXiv

  64. [72]

    arXiv preprint arXiv:1607.06450 (2016)

    Ba, J.L., Kiros, J.R., Hinton, G.E.: Layer normalization. arXiv preprint arXiv:1607.06450 (2016)

    2016 arXiv

  65. [73]

    Curran Associates Inc., Red Hook, NY, USA (2019) 18

    Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., 17 Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., K¨ opf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: PyTorch: an impe...

    2019

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.