Leveraging Transformer Models to Capture Multi-Scale Dynamics in Biomolecules by nano-GPT

Lu Zhang; Wenqi Zeng; Yuan Yao

REVIEW 4 major objections 4 minor 27 references

Leveraging Transformer Models to Capture Multi-Scale Dynamics in Biomolecules by nano-GPT

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

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Pith's one-line read Nano-GPT recovers microsecond folding kinetics from 20 ns simulation windows.

desk verdict A plausible two-pass scheduled-sampling transformer for MD state sequences, but the Fip35 headline timescales rest on an underspecified evaluation protocol and need a serious referee before they can be trusted. read the letter →

arxiv 2507.02734 v1 pith:UXVZLXAT submitted 2025-07-03 q-bio.QM

Wenqi Zeng , Lu Zhang , Yuan Yao This is my paper · ORCID

classification q-bio.QM

keywords moleculardynamicstransformerlong-timescalescheduledsamplingmeanfirstpassagetimeimpliedscalesproteinfoldingFip35WWdomain

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 sets out to establish that a lightweight GPT-style transformer, nano-GPT, can learn long-timescale biomolecular dynamics from short, unbiased molecular dynamics trajectories. The central evidence is the Fip35 WW domain: with a 20 ns training window, nano-GPT reproduces the slowest implied timescale of 14 µs and a random-coil-to-folded mean first passage time of 18 µs, while an LSTM baseline underestimates both. The mechanism is a two-pass training loop in which the first pass sees ground-truth MD tokens and a scheduled sampler gradually swaps in the model's own predictions, reducing the accumulation error that makes long autoregressive rollout unreliable. If the claim is right, rare conformational transitions on microsecond and longer scales could be probed with short simulations and without hand-crafted reaction coordinates.

What carries the argument

The load-bearing machinery is nano-GPT itself: a decoder-only transformer with multi-head self-attention over discrete MD state tokens, run in two passes linked by a scheduled sampler. In pass one the model reads ground-truth MD tokens and produces initial next-state probabilities; the sampler then chooses each token from the ground truth or from the first-pass prediction with a composite exponential decay probability; pass two consumes those sampled tokens and outputs the final distribution. Self-attention is the component that lets every frame attend to every earlier frame, which the paper argues is why distant information survives. The theoretical core is the kinetic-time ansatz $t_{lm} = 1/(P_l Q_{ml} + P_m Q_{lm})$, derived from a Taylor expansion of the softmax logits, together with the Maximum Caliber argument that cross-entropy training maximizes path entropy under first-order Markovianity and ergodicity.

What would settle it

Train nano-GPT on Fip35 windows drawn only from the first 80% of each trajectory, generate trajectories, and compare the 14 µs ITS and 18 µs MFPT against the held-out last 20%; if the slow timescales vanish or require generation lengths longer than the paper specifies, the extrapolation claim fails.

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Extended reading notes

Core claim

Nano-GPT's central claim is that an autoregressive transformer trained on short windows of discretized MD states can extend a trajectory so that its slow dynamics match the original simulation, even when the training window is orders of magnitude shorter than the slowest process. On Fip35, training on 20 ns windows yields a first implied timescale of 14 µs and an 18 µs MFPT from random coil to folded structure, compared with the expected ~20 µs folding time; the LSTM baseline gives 3 µs and a faster MFPT. On alanine dipeptide the same pattern holds in ψ, ϕ, and RMSD representations, with nano-GPT tracking the MD free energy, first ITS, and MFPT values while LSTM overestimates or underestimates them depending on the coordinate. The paper attributes the difference to self-attention, which retains information from distant frames that recurrent memory decays, and to the scheduled-sampling second pass, which narrows the train/inference gap. It also proves, under first-order Markovianity and ergodicity, that minimizing cross-entropy maximizes path entropy, and it argues via a softmax Taylor expansion that state embeddings encode kinetic time as $t_{lm} = 1/(P_l Q_{ml} + P_m Q_{lm})$.

Load-bearing premise

The reported 14 µs and 18 µs timescales are only meaningful if the generated trajectories used to compute them are long enough and numerous enough for converged transition statistics, and if shuffling short MD windows for training does not leak the slow-timescale information that the model is claimed to predict.

Editorial extensions

If this is right

A short unbiased simulation, not an enhanced-sampling method, would be sufficient in principle to expose rare-event kinetics: 20 ns windows produce a 14 µs slowest implied timescale and an 18 µs folding MFPT for Fip35.
The two-pass scheduled-sampling recipe is the component that prevents autoregressive error accumulation, so the same training scheme should extend to other long-horizon molecular sequence generators.
Because nano-GPT operates directly on discrete state tokens, it removes the need to select low-dimensional reaction coordinates such as phi and psi for complex systems.
Learned state embeddings carry kinetic time, so the model's internal representation can be read as a kinetic map of metastable states and their average interconversion times.
The LSTM baseline is not a reliable comparator across system complexity: it overestimates alanine dipeptide timescales and underestimates Fip35 timescales, while nano-GPT is claimed to track MD in both regimes.

Reading between the lines

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

Because the cross-entropy/path-entropy equivalence is inherited from the LSTM setting, it holds only under first-order Markovianity and ergodicity; for genuinely non-Markovian discrete-state dynamics the theoretical justification is weaker than the paper's 'non-Markovian dependencies' framing implies.
A cheap decisive comparison would be a Markov State Model built on the same 20 ns windows: if the MSM already recovers the 14 µs ITS, the transformer is not the component doing the timescale extrapolation.
The same two-pass scheduled-sampling scheme could be transported to other autoregressive sequence models, such as protein language models, to test whether the gain over LSTM holds beyond the three systems studied here.
The average-indirect-effect analysis suggests attention and embeddings can be used diagnostically: the frames with high indirect effect on a transition may point to the physical contacts that gate slow folding, turning a black-box generator into a source of mechanistic hypotheses.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new piece here is the two-pass GPT with scheduled sampling for fine-grained discrete MD states, and the consistent trend across all three systems—4-state, alanine dipeptide (ψ, φ, RMSD), and Fip35—is worth taking seriously. The alanine ϕ results, where nano-GPT tracks the 1st ITS around 80 ps and LSTM wanders up to 250 ps, are the kind of clean comparative evidence that makes you want to see more. The causal-trace analysis (AIE) is a nice touch, and the code is public, which helps. But the Fip35 numbers don't hold up as reported. Section 3.0.3 claims a 14 µs ITS and 18 µs MFPT from a 20 ns training window, yet the manuscript never says how long the generated trajectories are, how many independent runs were averaged, or whether the ITS/MFPT were computed from generated trajectories or from a transition matrix built from the model's probabilities. If from short generated trajectories, finite-length sampling can produce apparent slow timescales that are not converged; if from a transition matrix, there are no convergence checks or transition-count statistics. On top of that, the training windows are randomly shuffled from the concatenated full trajectory, so there is no temporal holdout. The same slow transitions used for evaluation could easily appear in the training data—not necessarily by cheating, but it means the 14 µs and 18 µs values are not cleanly a prediction from truly short data. The LSTM comparison doesn't fix this, because both models are evaluated under the same unspecified protocol. The theoretical section is honest but modest. The cross-entropy/path-entropy equivalence is borrowed from Tsai et al. with an ansatz for the transition probability, and Eq. 9 defines kinetic time rather than deriving it. That is fine if framed as a heuristic, but it is not a proof, and the paper would benefit from saying so more clearly. These are addressable gaps, not a fatal flaw. The architecture and the observed trends justify a proper review, but only if the authors can supply the missing evaluation details. For a serious referee, I would ask for: generation length and number of runs, a temporal holdout in the data preparation, explicit computation of ITS/MFPT from either trajectories or transition matrix, and at least one additional baseline (e.g., an MSM) for calibration. Then the Fip35 claim might actually land. For now, treat it as an interesting but unverified result, and bring it to the reading group for a discussion on evaluation standards in learned-dynamics papers.

Referee Report

4 major / 4 minor

Summary. The paper proposes nano-GPT, a two-pass GPT-style model with scheduled sampling that learns to predict discrete MD state sequences, and validates it on a four-state model potential, alanine dipeptide (in ψ, ϕ, and RMSD representations), and the Fip35 WW domain. The central claim is that nano-GPT, trained on short windows (e.g., 20 ns for Fip35), can generate trajectories whose slowest implied timescales and mean first-passage times match microsecond MD ground truth, outperforming an LSTM baseline. The paper also offers a theoretical argument that token embeddings encode kinetic time and that cross-entropy training maximizes path entropy under Markovian and ergodicity assumptions.

Significance. If the central results hold, nano-GPT would be a useful contribution to learning long-timescale biomolecular dynamics from short simulations, especially because it operates directly on fine-grained discrete state sequences and uses attention to capture long-range dependencies. The paper provides a code repository, evaluates on three systems of increasing complexity, and reports a striking match to the Fip35 slow timescale. The experimental evaluation, however, currently omits essential details about how the model-generated trajectories are produced and analyzed, and the training data preparation lacks a temporal holdout. The theoretical derivation also contains unproven approximations. These issues must be resolved before the claims can be accepted; they are fixable within the scope of a revision.

major comments (4)

[Section 3.0.3 and Fig. 5] The headline claims for Fip35—1st ITS of 14 µs and random-coil-to-folded MFPT of 18 µs—are not supported by the information given. The manuscript does not specify the number and length of generated trajectories, the number of independent seeds, whether ITS and MFPT are computed from sampled trajectories or from the model's transition matrix, or the lag time at which the 1st ITS is read. Finite-length generated trajectories can produce apparent slow timescales as sampling artifacts, so convergence diagnostics (e.g., number of observed folding transitions, spectral gap vs. lag time, error bars as in Fig. 3) are essential. As written, the values in Fig. 5 are as consistent with measurement artifacts as with learned dynamics.
[Section 2, data preparation] The training windows are randomly shuffled from concatenated MD trajectories, and the Fip35 dataset spans 1.1 ms with a 20 ns training window. Without a temporal train/test split, the model may be trained on frames that contain the same slow transitions that are later used to define the 18 µs MFPT and 14 µs ITS. The current protocol does not rule out leakage of the slow-timescale information that the paper claims to predict. Please demonstrate that the model's generated trajectories are not reproducing training segments, for example by withholding all frames after a cutoff time and evaluating only on a held-out temporal interval.
[Section 2, Eq. 7-9] The derivation of the kinetic-time interpretation is not established. The Taylor expansion of fθ(H(l)) around X = m in Eq. 7 drops the residual without a bound, the correction term Cm is stated to be negligible without a supporting estimate, and Eq. 8 is introduced as an 'ansatz.' Equation 9 is then a definition of t_lm in terms of model probabilities. As written, the statement that embeddings 'hold information for kinetic time' is a definition rather than a falsifiable prediction. Please provide quantitative justification for the neglected terms or reframe this passage as a heuristic.
[Section 2, Eq. 11-13] The proof that cross-entropy minimization maximizes path entropy is not actually given; the text defers to reference [9] and states that 'we do not provide an extensive proof.' Moreover, Eq. 12 and Eq. 13 are inconsistent: Eq. 12 contains the factor Pl Pml, while Eq. 13 replaces the ensemble average with a time average of Pml alone. Since the theoretical framing of the paper relies on this equivalence, please provide the full derivation or state precisely which quantity is being averaged and under which assumptions the two expressions coincide.

minor comments (4)

[Figure 4 and Section 3.0.2] The text in the 'Whole phase space' paragraph refers to 'Fig. 4(c) presents an in-depth analysis' of average indirect effect, but the AIE panel is labeled (e) in the figure caption. Please correct the subplot references.
[Equation 9] Equation 9 defines t_lm as a reciprocal transition probability, but the conversion from token counts to physical time (e.g., ps or µs) is not stated. Please explain how the model's discrete time steps are mapped to the reported timescales.
[Abstract and Introduction] The abstract and introduction state that LSTM methods are 'constrained to low-dimensional reaction coordinates,' yet the LSTM baseline is applied to the 100-state RMSD setting and the tICA-discretized Fip35 system in Section 3. Please reconcile this characterization with the experimental setup.
[Section 2, LSTM baseline] The description of the LSTM comparison is incomplete: please state whether scheduled sampling was also applied to LSTM, how many independent runs were averaged, and whether the same data preparation and evaluation protocol were used for both models, so that the comparison is controlled.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the reported ITS/MFPT are post-hoc statistics of the learned transition model, not fitted targets.

full rationale

After tracing the derivation chain, I find no circular step. Model parameters are optimized by next-token cross-entropy on short MD windows (Eq. 11); the reported ITS and MFPT values are computed from the learned transition probabilities or generated trajectories as post-hoc statistics, not as fitted targets. The kinetic time in Eq. 9 is a definition in terms of the model's own interconversion probabilities, and the statement that embeddings 'hold information for kinetic time' is therefore a tautological interpretation rather than a predicted result. No equation is used both as input and output, and no fitted parameter is renamed as a prediction. The self-citations (refs 22-24) concern clustering/geometric methods and are not load-bearing for the central claim. The unspecified evaluation protocol (generation length, seeds) is a reproducibility concern, not circularity.

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

No new physical entities are introduced. The load-bearing modeling choices are the state counts, window sizes, and sampling schedule constants; the theoretical claims rest on ergodicity and Markovianity assumptions and a proof borrowed from prior LSTM work.

free parameters (3)

Number of discrete states K = 20 (alanine dihedral), 100 (alanine RMSD and Fip35)
Chosen per system and affects transition statistics; an ablation is mentioned in SI but not shown.
Training window size = 10 ps (alanine dihedral), 20 ps or 100 ps (alanine RMSD), 20 ns (Fip35)
Defines the temporal context for each prediction and is a key factor in the claimed extrapolation.
Scheduled sampling decay constants epsilon and k = Not reported in main text
Hand-chosen constants in the composite schedule of Eq. 10; values are said to be in SI but absent from the arXiv text.

assumptions (4)

domain assumption First-order Markovianity and ergodicity of the discretized molecular dynamics
Invoked for the equivalence of cross-entropy minimization and path-entropy maximization in Eqs. 11-13, though the method is motivated by non-Markovian dynamics.
domain assumption The path-entropy proof from Tsai et al. (ref 9) transfers unchanged from LSTM to GPT
Stated directly in Methods: 'The proof established by [9] for LSTM models is directly applicable to nano-GPT.'
ad hoc to paper Taylor expansion residual and the Cm correction term in Eq. 7 are negligible so that Eq. 8 follows
The kinetic-time ansatz relies on dropping the remainder of the Taylor expansion without an error bound.
domain assumption tICA and k-center discretization preserve the slow dynamical modes
Used to build the 100-state Fip35 and alanine RMSD representations; standard practice but an assumption about state-space fidelity.

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Cite this review

Pith. "Pith review of Leveraging Transformer Models to Capture Multi-Scale Dynamics in Biomolecules by nano-GPT." pith.science (2026). https://pith.science/paper/UXVZLXAT

@misc{pith2026250702734,
  author       = {Pith},
  title        = {Pith review of: Leveraging Transformer Models to Capture Multi-Scale Dynamics in Biomolecules by nano-GPT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UXVZLXAT}},
  note         = {Machine review of arXiv:2507.02734}
}

read the original abstract

Long-term biomolecular dynamics are critical for understanding key evolutionary transformations in molecular systems. However, capturing these processes requires extended simulation timescales that often exceed the practical limits of conventional models. To address this, shorter simulations, initialized with diverse perturbations, are commonly used to sample phase space and explore a wide range of behaviors. Recent advances have leveraged language models to infer long-term behavior from short trajectories, but methods such as long short-term memory (LSTM) networks are constrained to low-dimensional reaction coordinates, limiting their applicability to complex systems. In this work, we present nano-GPT, a novel deep learning model inspired by the GPT architecture, specifically designed to capture long-term dynamics in molecular systems with fine-grained conformational states and complex transitions. The model employs a two-pass training mechanism that incrementally replaces molecular dynamics (MD) tokens with model-generated predictions, effectively mitigating accumulation errors inherent in the training window. We validate nano-GPT on three distinct systems: a four-state model potential, the alanine dipeptide, a well-studied simple molecule, and the Fip35 WW domain, a complex biomolecular system. Our results show that nano-GPT effectively captures long-timescale dynamics by learning high-order dependencies through attention mechanism, offering a novel perspective for interpreting biomolecular processes.

Figures

Figures reproduced from arXiv: 2507.02734 by the authors.

**Figure 2.** Performance in 4-state across (a) free energy landscape. (b) projection on x-axis [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Results on alanine dipeptide for ψ (upper row) and ϕ (lower row): Performance comparison across free energy landscape, ITS, and MFPT. (a) Free energy landscape, (b) ITS, and (c) MFPT for alanineψ; (d) Free energy landscape, (e) ITS, and (f) MFPT for alanineϕ. Shaded areas in (a)(b)(d)(e) and error bars in (c)(f) represent the standard deviation computed over 3 independent simulations for both LSTM and nano-GPT. The … view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Analysis on AlanineRMSD : (a) Ramachandran plot of alanine dipeptide: four metastable states (β, αR, αL, C7ax) with ψ on the vertical axis and ϕ on the horizontal axis. The metastable states are located at: β (C7eq) in the top-left, αR (alpha helix) in the left-center,…

**Figure 5.** Figure 5: Analysis on Fip35 WW domain, from left to right: (a) representative structure of [PITH_FULL_IMAGE:figures/full_fig_p023_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 26 canonical work pages

[9]

Learning molecular dynamics with simple language model built upon long short-term memory neural network

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 2020, 11, 1--11

work page 2020
[1]

J.; Reich, S.; Skeel, R

Leimkuhler, B. J.; Reich, S.; Skeel, R. D. Mathematical Approaches to biomolecular structure and dynamics; Springer, 1996; pp 161--185

work page 1996
[2]

Symplectic splitting methods for rigid body molecular dynamics

Dullweber, A.; Leimkuhler, B.; McLachlan, R. Symplectic splitting methods for rigid body molecular dynamics. The Journal of chemical physics 1997, 107, 5840--5851

work page 1997
[3]

D.; Singhal, N.; Pande, V

Chodera, J. D.; Singhal, N.; Pande, V. S.; Dill, K. A.; Swope, W. C. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. The Journal of chemical physics 2007, 126, 04B616

work page 2007
[4]

C.; Roux, B

Pan, A. C.; Roux, B. Building Markov state models along pathways to determine free energies and rates of transitions. The Journal of chemical physics 2008, 129, 064107

work page 2008
[5]

A variational approach to modeling slow processes in stochastic dynamical systems

No \'e , F.; Nuske, F. A variational approach to modeling slow processes in stochastic dynamical systems. Multiscale Modeling & Simulation 2013, 11, 635--655

work page 2013
[6]

E.; Pande, V

Husic, B. E.; Pande, V. S. Markov state models: From an art to a science. Journal of the American Chemical Society 2018, 140, 2386--2396

work page 2018
[7]

A.; Schmidhuber, J.; Cummins, F

Gers, F. A.; Schmidhuber, J.; Cummins, F. Learning to forget: Continual prediction with LSTM. Neural computation 2000, 12, 2451--2471

work page 2000

Show all 27 references

[8]

R.; Beauchamp, K

Bowman, G. R.; Beauchamp, K. A.; Boxer, G.; Pande, V. S. Progress and challenges in the automated construction of Markov state models for full protein systems. The Journal of chemical physics 2009, 131

2009
[10]

Path sampling of recurrent neural networks by incorporating known physics

Tsai, S.-T.; Fields, E.; Xu, Y.; Kuo, E.-J.; Tiwary, P. Path sampling of recurrent neural networks by incorporating known physics. Nature Communications 2022, 13, 7231

2022
[11]

Do RNN and LSTM have long memory? International Conference on Machine Learning

Zhao, J.; Huang, F.; Lv, J.; Duan, Y.; Qin, Z.; Li, G.; Tian, G. Do RNN and LSTM have long memory? International Conference on Machine Learning. 2020; pp 11365--11375

2020
[12]

B.; Gao, J.; Wang, C.; Paisley, J

Dieng, A. B.; Gao, J.; Wang, C.; Paisley, J. TopicRNN: A Recurrent Neural Network with Long-Range Semantic Dependency. The 5th International Conference on Learning Representations (ICLR). 2017

2017
[13]

Can Recurrent Neural Networks Warp Time? The 6th International Conference on Learning Representations (ICLR)

Tallec, C.; Ollivier, Y. Can Recurrent Neural Networks Warp Time? The 6th International Conference on Learning Representations (ICLR). 2018

2018
[14]

Improving the gating mechanism of recurrent neural networks

Gu, A.; Gulcehre, C.; Paine, T.; Hoffman, M.; Pascanu, R. Improving the gating mechanism of recurrent neural networks. International conference on machine learning. 2020; pp 3800--3809

2020
[15]

D.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; Askell, A.; others

Brown, T.; Mann, B.; Ryder, N.; Subbiah, M.; Kaplan, J. D.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; Askell, A.; others. Language models are few-shot learners. Advances in neural information processing systems 2020, 33, 1877--1901

2020
[16]

Long Range Arena: A Benchmark for Efficient Transformers

Tay, Y.; Dehghani, M.; Abnar, S.; Shen, Y.; Bahri, D.; Pham, P.; Rao, J.; Yang, L.; Ruder, S.; Metzler, D. Long Range Arena: A Benchmark for Efficient Transformers. The 9th International Conference on Learning Representations (ICLR). 2021

2021
[17]

Accurate prediction of the kinetic sequence of physicochemical states using generative artificial intelligence

Bera, P.; Mondal, J. Accurate prediction of the kinetic sequence of physicochemical states using generative artificial intelligence. Chemical Science 2025,

2025
[18]

Scheduled Sampling Based on Decoding Steps for Neural Machine Translation

Liu, Y.; Meng, F.; Chen, Y.; Xu, J.; Zhou, J. Scheduled Sampling Based on Decoding Steps for Neural Machine Translation. Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. 2021; pp 3285--3296

2021
[19]

Press \'e , S.; Ghosh, K.; Lee, J.; Dill, K. A. Principles of maximum entropy and maximum caliber in statistical physics. Reviews of Modern Physics 2013, 85, 1115

2013
[20]

Y.; He, H

Pang, R. Y.; He, H. Text Generation by Learning from Demonstrations. The 9th International Conference on Learning Representations (ICLR). 2021

2021
[21]

K.; Sun, J.; Sander, P.; Huang, X

Zhao, Y.; Sheong, F. K.; Sun, J.; Sander, P.; Huang, X. A fast parallel clustering algorithm for molecular simulation trajectories. Journal of computational chemistry 2013, 34, 95--104

2013
[22]

Sun, J.; Yao, Y.; Huang, X.; Pande, V.; Carlsson, G.; Guibas, L. J. A Well-controlled Fast Geometric Clustering Method on Conformation Space of Biomolecules. Biomedical Computation at Stanford (BCATS). 2008

2008
[23]

J.; Carlsson, G

Yao, Y.; Sun, J.; Huang, X.; Bowman, G.; Singh, G.; Lesnick, M.; Pande, V.; Guibas, L. J.; Carlsson, G. Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways. J. Chem. Phys. 2009, 130, 144115

2009
[24]

Z.; Bowman, G

Yao, Y.; Cui, R. Z.; Bowman, G. R.; Silva, D. A.; Sun, J.; Huang, X. Hierarchical Nyström methods for constructing Markov state models for conformational dynamics. J. Chem. Phys. 2013, 138, 174106

2013
[25]

Locating and editing factual associations in GPT

Meng, K.; Bau, D.; Andonian, A.; Belinkov, Y. Locating and editing factual associations in GPT. Advances in Neural Information Processing Systems 2022, 35, 17359--17372

2022
[26]

E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R

Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K.; Piana, S.; Dror, R. O.; Eastwood, M. P.; Bank, J. A.; Jumper, J. M.; Salmon, J. K.; Shan, Y.; others. Atomic-level characterization of the structural dynamics of proteins. Science 2010, 330, 341--346

2010
[27]

Identification of slow molecular order parameters for Markov model construction

P \'e rez-Hern \'a ndez, G.; Paul, F.; Giorgino, T.; De Fabritiis, G.; No \'e , F. Identification of slow molecular order parameters for Markov model construction. The Journal of Chemical Physics 2013, 139, 015102--015102 mcitethebibliography main_final.tex00006640000000000000...

2013 arXiv

Pith tools

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

[1] [9]

Learning molecular dynamics with simple language model built upon long short-term memory neural network

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 2020, 11, 1--11

work page 2020

[2] [1]

J.; Reich, S.; Skeel, R

Leimkuhler, B. J.; Reich, S.; Skeel, R. D. Mathematical Approaches to biomolecular structure and dynamics; Springer, 1996; pp 161--185

work page 1996

[3] [2]

Symplectic splitting methods for rigid body molecular dynamics

Dullweber, A.; Leimkuhler, B.; McLachlan, R. Symplectic splitting methods for rigid body molecular dynamics. The Journal of chemical physics 1997, 107, 5840--5851

work page 1997

[4] [3]

D.; Singhal, N.; Pande, V

Chodera, J. D.; Singhal, N.; Pande, V. S.; Dill, K. A.; Swope, W. C. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. The Journal of chemical physics 2007, 126, 04B616

work page 2007

[5] [4]

C.; Roux, B

Pan, A. C.; Roux, B. Building Markov state models along pathways to determine free energies and rates of transitions. The Journal of chemical physics 2008, 129, 064107

work page 2008

[6] [5]

A variational approach to modeling slow processes in stochastic dynamical systems

No \'e , F.; Nuske, F. A variational approach to modeling slow processes in stochastic dynamical systems. Multiscale Modeling & Simulation 2013, 11, 635--655

work page 2013

[7] [6]

E.; Pande, V

Husic, B. E.; Pande, V. S. Markov state models: From an art to a science. Journal of the American Chemical Society 2018, 140, 2386--2396

work page 2018

[8] [7]

A.; Schmidhuber, J.; Cummins, F

Gers, F. A.; Schmidhuber, J.; Cummins, F. Learning to forget: Continual prediction with LSTM. Neural computation 2000, 12, 2451--2471

work page 2000