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REVIEW 5 major objections 8 minor 43 references

Data-Driven Predictive Modeling of Neuronal Dynamics using Long Short-Term Memory

T0 review · 5 major / 8 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read LSTM networks trained for longer prediction horizons forecast neuron spiking more accurately.

desk verdict A competent LSTM surrogate for a CA1 Hodgkin-Huxley model, but the headline horizon trend is confounded by closed-loop iteration count and missing baselines. read the letter →

arxiv 1908.07428 v1 pith:7GRJJYZI submitted 2019-08-11 q-bio.NC cs.LGstat.ML

Benjamin Plaster , Gautam Kumar This is my paper · ORCID
classification q-bio.NCcs.LGstat.ML
keywords longshort-termmemorybraindynamicsdata-drivenmodelingcomplexsystemsHodgkin-HuxleymodelCA1pyramidalneuronmulti-timesteppredictionsequence-to-sequencemapping
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

This paper tries to establish that a long short-term memory (LSTM) neural network can serve as a purely data-driven surrogate for a biophysical neuron model, predicting the membrane potential and gating variables of a hippocampal CA1 pyramidal neuron over hundreds of milliseconds. The proposed architecture stacks three LSTM layers with a single fully connected output layer and feeds inputs in reverse order through a sequence-to-sequence mapping, then chains copies of the network to iterate forecasts. Across regular spiking, irregular bursting, and regular bursting regimes, the paper reports that longer predictive horizons produce lower time-averaged error over 500 ms than single-step prediction. The motivation is a computationally cheap model that could later be embedded in control-theoretic neurostimulation strategies.

What carries the argument

The load-bearing object is a deep LSTM network with three stacked hidden layers of 324 units feeding a single fully connected output layer, trained on simulated traces of the 9-dimensional Hodgkin-Huxley CA1 neuron model. It makes multi-timestep predictions through sequence-to-sequence mapping in which the input sequence is presented in reverse order, so that early inputs correspond to early outputs through short-range dependencies while later inputs map through long-range dependencies; the paper credits this temporal symmetry for improved early-trajectory accuracy. To reach long horizons, copies of the trained network are chained: the predicted output block is concatenated with the next block of inputs and fed, again in reverse order, into the next copy. The iterative chaining plus reversed-order mapping is what carries the claim that a network trained on 20 ms blocks can forecast 500 ms of spiking behavior.

What would settle it

Take a trained $N_p=200$ network and start a 500 ms forecast from a conditioning history that is the true Hodgkin-Huxley trajectory shifted by 1 mV (or corrupted with Gaussian noise of comparable amplitude), then compare RMSE against the clean-history forecast; if the error grows steeply, the reported long-horizon improvement depends on perfectly known initial conditions, and if it does not, the improvement is robust to conditioning error.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that prediction accuracy improves with the length of the multi-timestep predictive horizon: time-averaged RMSE of the membrane potential decreases consistently as $N_p$ goes from 1 to 50 to 100 to 200 timesteps, in all three dynamical regimes, over 5000 random current-and-initial-condition realizations. Longer-horizon networks track the timing of spikes better, while shorter-horizon networks track spike amplitude better. The regular spiking regime is predicted with high accuracy over the full 500 ms; irregular bursting is captured only over roughly the first 100 ms; regular bursting is captured with reasonable accuracy over about 300 ms for $N_p = 200$. The paper also reports that one gating variable, $q_{sAHP}$, is not reconstructed because its magnitude approaches numerical precision.

Load-bearing premise

The load-bearing premise is that the true Hodgkin-Huxley state trajectory is available as the initial $N_p$-step input sequence for every forecast, so the paper never tests how the network behaves when the conditioning history contains errors or partial observations.

Editorial extensions

If this is right

  • In the regular spiking regime, a network trained to predict 20 ms blocks can be iterated over 500 ms with lower RMSE than a network trained for single-step prediction, so longer-horizon training is a viable route to long forecasts.
  • Across all three regimes, increasing $N_p$ shifts the error trade-off: spike timing improves while spike amplitude degrades, meaning the loss function directly shapes what the surrogate captures.
  • Irregular bursting is not predictable beyond about 100 ms by any of the trained horizons, which sets a concrete limit on neurostimulation control in that regime.
  • The slow calcium-activated potassium variable $q_{sAHP}$ is not learned to reasonable accuracy, so the surrogate does not fully reconstruct the 9-dimensional state even when membrane potential traces look right.
  • Longer horizons require substantially more offline training cost for the same number of examples, so choosing $N_p$ is a practical trade-off between forecast accuracy and training budget.

Reading between the lines

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

  • Not tested in the paper: corrupting the conditioning sequence with observation noise, then checking whether the $N_p=200$ advantage survives.
  • Not tested in the paper: applying the same architecture to a chaotic or aperiodic system, which would show whether the reverse-order benefit generalizes beyond periodic spiking patterns.
  • Not tested in the paper: probing horizons beyond $N_p=200$ to see whether the RMSE trend saturates, plateaus, or reverses.
  • Not tested in the paper: retraining with norm-1 or weighted norm-2 losses to see if spike amplitude and timing can be recovered together, as the discussion leaves this open.
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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

5 major / 8 minor

Summary. The paper proposes a deep LSTM architecture with a single fully connected output layer and reversed-order sequence-to-sequence mapping for multi-step prediction of Hodgkin-Huxley CA1 pyramidal neuron dynamics. The authors train networks with predictive horizons Np = 1, 50, 100, and 200, and evaluate them in closed-loop iterative prediction over 500 ms across three firing regimes: regular spiking, irregular bursting, and regular bursting. The main claim is that time-averaged RMSE decreases as the predictive horizon Np increases. The paper also reports full-state prediction results in Appendix B and discusses limitations in Section 4.

Significance. If the horizon-dependent improvement is genuine and not an artifact of the evaluation protocol, the result would be useful for data-driven surrogate models in control-oriented neurostimulation, because larger multi-step horizons reduce the number of recursive rollouts and may mitigate error accumulation. The paper provides the complete Hodgkin-Huxley model equations in Appendix A and evaluates across three regimes with 5000 realizations, which are strengths. However, the central claim is currently under-supported by the absence of statistical significance tests, baselines, and an ablation separating horizon length from iteration count. The claimed architectural novelty (reverse-order mapping and the single dense output layer) is not directly validated against a forward-order or single-step baseline.

major comments (5)
  1. [Section 2.1, Section 2.4, Figures 7-12] The closed-loop evaluation is confounded with the number of recursive iterations. Section 2.1 states that each Deep LSTM block receives the predicted output sequence from the previous block, while Section 2.4 trains the network by Eq. (4) on true HH state sequences. Over the 500 ms evaluation window, the Np=1 network is rolled out 5000 times, whereas the Np=200 network is rolled out only 25 times. The observed decrease in RMSE with increasing Np may therefore reflect fewer opportunities for feedback-error accumulation rather than better learned dynamics. The manuscript does not report a control that fixes the number of iterations (e.g., re-supplying true states before each block or rolling out the Np=200 network for the same number of steps as Np=1). Without such a control, the abstract's claim that predictions improve with increasing predictive time-horizon is not supported as a property of the learned model.
  2. [Section 3, Figures 8, 10, 12] The 'decreased consistently' claim is descriptive only. Figures 8(b), 10(b), and 12(b) plot mean RMSE over 5000 realizations without confidence bands, standard deviations, or significance tests, and Figures 8(a), 10(a), and 12(a) compare four horizon values from a single trajectory. No repeated training runs with different seeds are reported, so the reader cannot judge whether the RMSE differences between Np values are larger than training variability. Additionally, no baseline architecture is evaluated: the claimed benefits of the single dense output layer and the reversed-order mapping (Section 2.2) are not tested against a forward-order sequence-to-sequence LSTM or a standard single-step LSTM with feedback. The experimental section therefore does not currently validate either the horizon trend or the architectural novelty.
  3. [Section 3.3, Figure 12(b)] The regular-bursting RMSE-vs-time panel excludes Np=50, with the text stating that the Np=50 network became unstable for some initial conditions. Since the central claim is that longer horizons uniformly improve accuracy, omitting the Np=50 curve without plotting it or reporting its RMSE prevents the reader from assessing whether the trend is monotone. If Np=50 was unstable, the authors should show the affected trajectories or quantify the failure rate; otherwise the selective exclusion weakens the cross-regime conclusion.
  4. [Abstract; Sections 3.2, 3.3; Appendix B] The abstract states that the network can predict multi-timescale dynamics 'with reasonable accuracy' and Section 3.1 concludes 'high accuracy over a long-time horizon,' but Sections 3.2 and 3.3 report that in the irregular-bursting regime none of the networks predicted spike timing beyond 100 ms, and in regular bursting the Np=200 network is reasonable only over the first 300 ms. Appendix B also acknowledges that the qsAHP state is not reconstructed. The summary of results should be revised to reflect these stated limitations rather than presenting the regular-spiking result as representative of all regimes.
  5. [Sections 2.3 and 3] The paper does not state whether the test currents and initial conditions used in Section 3 were excluded from the training set described in Section 2.3. Training currents were sampled uniformly in [0, 3] nA, and test currents are drawn from uniform distributions within subintervals of that range; if there is overlap, the evaluation is not out-of-sample. The authors should specify the splitting procedure and, ideally, ensure that the 50 test currents and the 100 initial conditions per current are disjoint from the training set.
minor comments (8)
  1. [Abstract] The abstract contains grammatical errors: 'are of interests' should be 'are of interest', and 'from the last several decades' should be 'over the last several decades'.
  2. [Equation (2)] The Xavier initialization bounds appear to be missing a square root around the denominator; standard Glorot initialization uses ±sqrt(6/(fan_in+fan_out)). Please correct the formula.
  3. [Equation (4)] The summation index k=0,...,NP and the use of 1/NP suggest the loss averages over NP+1 terms; clarify whether the horizon includes the initial condition or not.
  4. [Section 2.3] The text says 'we randomly and uniformly drew 50 samples (i.e., 104 data points)'; this arithmetic is unclear, as 50 samples of a 1000-ms trajectory at 0.1 ms would be much larger, and 104 appears to be a typo for 10^4.
  5. [Appendix A] The state variable z_M is sometimes written as u_KM in the initial conditions list, and the parameter list duplicates θ_c with different values; use consistent notation and check parameter labels.
  6. [Appendix B.3] The text contains a typo: 'LTSM' should be 'LSTM'.
  7. [Figures 8(b), 10(b), 12(b)] Consider plotting confidence intervals (e.g., percentiles or standard errors) rather than a single mean curve, since the number of realizations is large enough to make this informative.
  8. [General] The paper would benefit from a statement on data and code availability; the complete HH model in Appendix A is helpful, but the training and testing pipeline is not documented at the level needed for reproduction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central horizon-dependence claim is an empirical benchmark of four separately trained networks, not a derivation forced by the training objective or by self-citation.

full rationale

The central claim (Abstract; Section 3.1) that time-averaged RMSE decreases as the predictive-horizon parameter Np increases from 1 to 200 is an empirical comparison of four independently trained LSTM networks, not a quantity derived from the training objective. Equation (4) defines each network's training loss over its own NP, while the reported RMSE in Figures 8, 10, and 12 is evaluated over 500 ms on test currents and initial conditions largely outside the training set; no free parameter is fit to those RMSE curves, and no self-citation is load-bearing. The reverse-order sequence-to-sequence design is credited to an external reference [27]. The evaluation protocol does contain a strong and somewhat ambiguous premise: Section 2.3 assumes the initial output sequence 'is available to the deep LSTM neural network throughout our simulations,' while Figure 3 describes a closed-loop feedforward of predicted outputs. This ambiguity is a validity/robustness concern, not circularity, because even under either reading the decreasing-RMSE trend is not forced by construction. The paper's own Discussion also reports degraded spike-amplitude prediction and poor q_sAHP reconstruction, showing that the results are not definitionally guaranteed.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on borrowed domain machinery: the cited Hodgkin-Huxley model as ground truth, the oracle availability of true state histories, and constant-current-only inputs. No new physical entities are introduced.

free parameters (5)
  • Number of LSTM hidden units per layer = 324 (4n^2 for n=9)
    Selected by systematically varying hidden dimensionality and evaluating training performance (Section 2.1).
  • Number of stacked LSTM layers = 3
    Selected by increasing layers until validation performance plateaued (Section 2.1).
  • Predictive horizon Np = 1, 50, 100, 200 timesteps
    These are the four network variants compared; the central claim depends on comparing them.
  • Adam learning rate = 0.001
    Standard from [42], Section 2.4.
  • Training epochs = 200 (Np>1), 1000 (Np=1)
    Chosen for computational tractability, Section 2.4.
assumptions (4)
  • domain assumption The Golomb et al. Hodgkin-Huxley model [29] is an experimentally validated ground truth for CA1 pyramidal neuron dynamics
    All training and evaluation data are generated by simulating this model; the paper does not verify it against experimental recordings.
  • domain assumption The initial sequence of true states is available to condition every prediction
    Section 2.3 states this availability is assumed throughout simulations; real measurements would be noisy or partial.
  • domain assumption Constant stimulating currents uniformly sampled in [0,3] nA cover the relevant dynamical regimes
    Training and test currents are restricted to this range; no time-varying inputs are tested.
  • ad hoc to paper The norm-2 loss equally weighting all 9 states is an appropriate training objective
    The authors note the q_sAHP state is not captured and suspect the equally weighted loss (Discussion).

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Cite this review

Pith. "Pith review of Data-Driven Predictive Modeling of Neuronal Dynamics using Long Short-Term Memory." pith.science (2026). https://pith.science/paper/7GRJJYZI

@misc{pith2026190807428,
  author       = {Pith},
  title        = {Pith review of: Data-Driven Predictive Modeling of Neuronal Dynamics using Long Short-Term Memory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7GRJJYZI}},
  note         = {Machine review of arXiv:1908.07428}
}
read the original abstract

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of developing computationally efficient models of brain dynamics to use in designing control-theoretic neurostimulation strategies, we have developed a novel data-driven approach in a long short-term memory (LSTM) neural network architecture to predict the temporal dynamics of complex systems over an extended long time-horizon in future. In contrast to recent LSTM-based dynamical modeling approaches that make use of multi-layer perceptrons or linear combination layers as output layers, our architecture uses a single fully connected output layer and reversed-order sequence-to-sequence mapping to improve short time-horizon prediction accuracy and to make multi-timestep predictions of dynamical behaviors. We demonstrate the efficacy of our approach in reconstructing the regular spiking to bursting dynamics exhibited by an experimentally-validated 9-dimensional Hodgkin-Huxley model of hippocampal CA1 pyramidal neurons. Through simulations, we show that our LSTM neural network can predict the multi-time scale temporal dynamics underlying various spiking patterns with reasonable accuracy. Moreover, our results show that the predictions improve with increasing predictive time-horizon in the multi-timestep deep LSTM neural network.

Figures

Figures reproduced from arXiv: 1908.07428 by the authors.

Figure 1
Figure 1. A schematic illustrating the overall data-driven approach developed in this paper for multi-timestep predictions [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. A schematic illustrating the internal gating operation in a single LSTM cell. The "+" represents an additive [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Iterative prediction of the system’s outputs over a long time-horizon. Each "Deep LSTM" receives the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (24 more)
Figure 4
Figure 4. Figure 4: Forward and reversed sequence-to-sequence mapping approach for translating letters (inputs) to their [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Diversity in the spiking patterns of hippocampal CA1 pyramidal neurons to applied currents. (a) Regular [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Training and validation loss for the deep LSTM neural network with multi-timestep predictive horizon. (a) 1 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Comparison of predicted membrane potential traces by the deep LSTM neural network (“LSTM Network”) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: The effect of the length of predictive horizon of the deep LSTM neural network on the accuracy of regular [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Comparison of predicted membrane potential traces by the deep LSTM neural network (“LSTM Network”) [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: The effect of the prediction horizon of the deep LSTM neural network on the accuracy of irregular bursting [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Comparison of predicted membrane potential traces by the LSTM network (“NN Prediction”) to the [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: The effect of the prediction horizon of the multi-timestep LSTM network on the accuracy of regular bursting [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p020_13.png]
Figure 14
Figure 14. Figure 14: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p021_14.png]
Figure 15
Figure 15. Figure 15: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]
Figure 16
Figure 16. Figure 16: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]
Figure 17
Figure 17. Figure 17: The root mean squared error (RMSE) versus simulation time for 5000 independent realizations, drawn from [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]
Figure 18
Figure 18. Figure 18: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]
Figure 19
Figure 19. Figure 19: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p026_19.png]
Figure 20
Figure 20. Figure 20: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p027_20.png]
Figure 21
Figure 21. Figure 21: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p028_21.png]
Figure 22
Figure 22. Figure 22: The root mean squared error (RMSE) versus simulation time for 5000 independent realizations, drawn from [PITH_FULL_IMAGE:figures/full_fig_p029_22.png]
Figure 23
Figure 23. Figure 23: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p030_23.png]
Figure 24
Figure 24. Figure 24: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p031_24.png]
Figure 25
Figure 25. Figure 25: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p032_25.png]
Figure 26
Figure 26. Figure 26: Comparison between the Hodgkin-Huxley model (“HH Model”) states’ dynamics and the iterative predictions [PITH_FULL_IMAGE:figures/full_fig_p033_26.png]
Figure 27
Figure 27. Figure 27: The root mean squared error (RMSE) versus simulation time for 5000 independent realizations, drawn from [PITH_FULL_IMAGE:figures/full_fig_p034_27.png]

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Reference graph

Works this paper leans on

43 extracted references · 33 canonical work pages

  1. [1]

    Dynamics of brain activation during picture naming

    R Salmelin, R Hari, OV Lounasmaa, and M Sams. Dynamics of brain activation during picture naming. Nature, 368(6470):463, 1994

    work page 1994

  2. [2]

    The human brain is intrinsically organized into dynamic, anticorrelated functional networks

    Michael D Fox, Abraham Z Snyder, Justin L Vincent, Maurizio Corbetta, David C Van Essen, and Marcus E Raichle. The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proceedings of the National Academy of Sciences, 102(27):9673–9678, 2005

    work page 2005

  3. [3]

    A hierarchy of time-scales and the brain

    Stefan J Kiebel, Jean Daunizeau, and Karl J Friston. A hierarchy of time-scales and the brain. PLoS computational biology, 4(11):e1000209, 2008

    2008

  4. [4]

    Cambridge University Press, 2014

    Wulfram Gerstner, Werner M Kistler, Richard Naud, and Liam Paninski.Neuronal dynamics: From single neurons to networks and models of cognition. Cambridge University Press, 2014

    2014

  5. [5]

    Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools

    Constantinos Siettos and Jens Starke. Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 8(5):438–458, 2016

    work page 2016

  6. [6]

    Dynamic models of large-scale brain activity

    Michael Breakspear. Dynamic models of large-scale brain activity. Nature neuroscience, 20(3):340, 2017

    work page 2017

  7. [7]

    Modeling single-neuron dynamics and computations: a balance of detail and abstraction

    Andreas VM Herz, Tim Gollisch, Christian K Machens, and Dieter Jaeger. Modeling single-neuron dynamics and computations: a balance of detail and abstraction. science, 314(5796):80–85, 2006

    work page 2006

  8. [8]

    How good are neuron models? Science, 326(5951):379–380, 2009

    Wulfram Gerstner and Richard Naud. How good are neuron models? Science, 326(5951):379–380, 2009

    work page 2009

Show all 43 references
  1. [9]

    Neural networks for nonlinear dynamic system modelling and identification

    SABS Chen and SA Billings. Neural networks for nonlinear dynamic system modelling and identification. International journal of control, 56(2):319–346, 1992

    1992

  2. [10]

    Nonlinear system identification using neural networks

    S Purwar, IN Kar, and AN Jha. Nonlinear system identification using neural networks. IETE journal of research, 53(1):35–42, 2007

    2007

  3. [11]

    Application of feedforward neural networks to dynamical system identification and control

    John G Kuschewski, Stefen Hui, and Stanislaw H Zak. Application of feedforward neural networks to dynamical system identification and control. IEEE Transactions on Control Systems Technology, 1(1):37–49, 1993

    1993

  4. [12]

    Long-time predictive modeling of nonlinear dynamical systems using neural networks

    Shaowu Pan and Karthik Duraisamy. Long-time predictive modeling of nonlinear dynamical systems using neural networks. Complexity, 2018, 2018

    2018

  5. [13]

    Modeling robot dynamics using dynamic neural networks

    Pramod Gupta and Naresh K Sinha. Modeling robot dynamics using dynamic neural networks. IFAC Proceedings Volumes, 30(11):755–759, 1997

    1997

  6. [14]

    Identification of nonlinear dynamic systems using functional link artificial neural networks

    Jagdish Chandra Patra, Ranendra N Pal, BN Chatterji, and Ganapati Panda. Identification of nonlinear dynamic systems using functional link artificial neural networks. IEEE transactions on systems, man, and cybernetics, part b (cybernetics), 29(2):254–262, 1999. 15 Data-Driven Pr...

    1999

  7. [15]

    Neural network dynamics for model- based deep reinforcement learning with model-free fine-tuning

    Anusha Nagabandi, Gregory Kahn, Ronald S Fearing, and Sergey Levine. Neural network dynamics for model- based deep reinforcement learning with model-free fine-tuning. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 7559–7566. IEEE, 2018

    2018

  8. [16]

    Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication

    Herbert Jaeger and Harald Haas. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. science, 304(5667):78–80, 2004

    2004

  9. [17]

    A recurrent neural network for modelling dynamical systems

    Coryn AL Bailer-Jones, David JC MacKay, and Philip J Withers. A recurrent neural network for modelling dynamical systems. network: computation in neural systems, 9(4):531–547, 1998

    1998

  10. [18]

    Deepmpc: Learning deep latent features for model predictive control

    Ian Lenz, Ross A Knepper, and Ashutosh Saxena. Deepmpc: Learning deep latent features for model predictive control. In Robotics: Science and Systems. Rome, Italy, 2015

    2015

  11. [19]

    On the difficulty of training recurrent neural networks

    Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio. On the difficulty of training recurrent neural networks. In International conference on machine learning, pages 1310–1318, 2013

    2013

  12. [20]

    Multistep prediction of dynamic systems with recurrent neural networks

    Nima Mohajerin and Steven L Waslander. Multistep prediction of dynamic systems with recurrent neural networks. IEEE transactions on neural networks and learning systems, 2019

    2019

  13. [21]

    Deep learning-based human-driven vehicle trajectory prediction and its application for platoon control of connected and autonomous vehicles

    Lei Lin, Siyuan Gong, Tao Li, and Srinivas Peeta. Deep learning-based human-driven vehicle trajectory prediction and its application for platoon control of connected and autonomous vehicles. In The Autonomous Vehicles Symposium, volume 2018, 2018

    2018

  14. [22]

    Non-linear system modeling using lstm neural networks

    Jesús Gonzalez and Wen Yu. Non-linear system modeling using lstm neural networks. IFAC-PapersOnLine, 51(13):485–489, 2018

    2018

  15. [23]

    A new concept using LSTM neural networks for dynamic system identification

    Yu Wang. A new concept using LSTM neural networks for dynamic system identification. In 2017 American Control Conference (ACC), pages 5324–5329. IEEE, 2017

    2017

  16. [24]

    Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

    Pantelis R Vlachas, Wonmin Byeon, Zhong Y Wan, Themistoklis P Sapsis, and Petros Koumoutsakos. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences,...

    2018

  17. [25]

    Long short-term memory

    Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural computation, 9(8):1735–1780, 1997

    1997

  18. [26]

    Understanding the difficulty of training deep feedforward neural networks

    Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249–256, 2010

    2010

  19. [27]

    Sequence to sequence learning with neural networks

    Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pages 3104–3112, 2014

    2014

  20. [28]

    CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging

    Erin C McKiernan and Diano F Marrone. CA1 pyramidal cells have diverse biophysical properties, affected by development, experience, and aging. PeerJ, 5:e3836, 2017

    2017

  21. [29]

    Contribution of persistent na+ current and m-type k+ current to somatic bursting in ca1 pyramidal cells: combined experimental and modeling study

    David Golomb, Cuiyong Yue, and Yoel Yaari. Contribution of persistent na+ current and m-type k+ current to somatic bursting in ca1 pyramidal cells: combined experimental and modeling study. Journal of neurophysiology, 96(4):1912–1926, 2006

    1912

  22. [30]

    A unified model of CA1/3 pyramidal cells: An investigation into excitability

    Jakub Nowacki, Hinke M Osinga, Jon T Brown, Andrew D Randall, and Krasimira Tsaneva-Atanasova. A unified model of CA1/3 pyramidal cells: An investigation into excitability. Progress in biophysics and molecular biology, 105(1-2):34–48, 2011

    2011

  23. [31]

    Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context

    Katie A Ferguson, Carey YL Huh, Benedicte Amilhon, Sylvain Williams, and Frances K Skinner. Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context. F1000Research, 3, 2014

    2014

  24. [32]

    Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell

    Panayiota Poirazi, Terrence Brannon, and Bartlett W Mel. Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. Neuron, 37(6):977–987, 2003

    2003

  25. [33]

    Role of ax- onal NaV1

    Michel Royeck, Marie-Therese Horstmann, Stefan Remy, Margit Reitze, Yoel Yaari, and Heinz Beck. Role of ax- onal NaV1. 6 sodium channels in action potential initiation of CA1 pyramidal neurons.Journal of neurophysiology, 100(4):2361–2380, 2008

    2008

  26. [34]

    Synapse distribution suggests a two-stage model of dendritic integration in CA1 pyramidal neurons.Neuron, 63(2):171–177, 2009

    Yael Katz, Vilas Menon, Daniel A Nicholson, Yuri Geinisman, William L Kath, and Nelson Spruston. Synapse distribution suggests a two-stage model of dendritic integration in CA1 pyramidal neurons.Neuron, 63(2):171–177, 2009

    2009

  27. [35]

    On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons

    Daniela Bianchi, Addolorata Marasco, Alessandro Limongiello, Cristina Marchetti, Helene Marie, Brunello Tirozzi, and Michele Migliore. On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Journal of computational neuroscience,...

    2012

  28. [36]

    Fast and accurate low-dimensional reduction of biophysically detailed neuron models

    Addolorata Marasco, Alessandro Limongiello, and Michele Migliore. Fast and accurate low-dimensional reduction of biophysically detailed neuron models. Scientific reports, 2(928):1–7, 2012

    2012

  29. [37]

    Dendritic sodium spikes are required for long-term potentiation at distal synapses on hippocampal pyramidal neurons

    Yujin Kim, Ching-Lung Hsu, Mark S Cembrowski, Brett D Mensh, and Nelson Spruston. Dendritic sodium spikes are required for long-term potentiation at distal synapses on hippocampal pyramidal neurons. Elife, 4:(e06414) 1–30, 2015

    2015

  30. [38]

    Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit

    Marianne J Bezaire, Ivan Raikov, Kelly Burk, Dhrumil Vyas, and Ivan Soltesz. Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit. Elife, 5:(e18566) 1–106, 2016

    2016

  31. [39]

    Generalization of backpropagation with application to a recurrent gas market model

    Paul J Werbos. Generalization of backpropagation with application to a recurrent gas market model. Neural networks, 1(4):339–356, 1988

    1988

  32. [40]

    Backpropagation through time: what it does and how to do it

    Paul J Werbos et al. Backpropagation through time: what it does and how to do it. Proceedings of the IEEE, 78(10):1550–1560, 1990

    1990

  33. [41]

    A focused backpropagation algorithm for temporal

    Michael C Mozer. A focused backpropagation algorithm for temporal. Backpropagation: Theory, architectures, and applications, 137, 1995

    1995

  34. [42]

    Adam: A method for stochastic optimization

    Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. A Hodgkin-Huxley Model of CA1 Pyramidal Neuron Dynamics We used the following Hodgkin-Huxley model of CA1 pyramidal neuron from [29] to demonstrate the efficacy of ...

    2014 arXiv

  35. [43]

    HH Model

    across all the states exceptqsAHP for the similar reason we provided for the regular spiking and irregular bursting regimes. More importantly, the LTSM network predicted the temporal correlations with high accuracy over the time- 19 Data-Driven Predictive Modeling of Neuronal ...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.