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Correcting model error bias in estimations of neuronal dynamics from time series observations.

Code ↔ Paper

5 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 5 matches
  1. [1] § Methods › Neuron models ↔ data_HodgkinHuxley.h, lines 25–140 · score 0.85 · gate kinetics, membrane capacitance, reversal potentials, steady state, Hodgkin Huxley, gate variables
  2. [2] § Methods › Neuron models ↔ data_HodgkinHuxley.h, lines 25–140 · score 0.74 · Runge Kutta Cash, gate kinetics, gate variables, Karp, neuron, HH
  3. [3] § Methods › Neuron models ↔ config_types.h, lines 11–55 · score 0.68 · membrane capacitance, reversal potentials, gate variables, model parameters, Leak, channels
  4. [4] § Methods › Reservoir architecture for a driven neuronal oscillator ↔ machine_learning.cpp, lines 22–63 · score 0.63 · adjacency matrix, spectral radius, reservoir state, nodes, connected, force
  5. [5] § Methods › Neuron models ↔ data_LorenzOscillator.h, lines 25–91 · score 0.60 · Runge Kutta Cash, Karp, oscillations

Paper

Loaded from Europe PMC by your browser, not stored by OSCR: doi.org · Europe PMC

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The authors' code

C/C++ header · 142 lines · 4.1 KB · no license · 2 matches

  1. #ifndef HODGKIN_HUXLEY_H
  2. #define HODGKIN_HUXLEY_H
  4. #include "config_types.h"
  5. #include "utils.h"
  7. #define _USE_MATH_DEFINES
  8. #include <cmath>
  9. #include <math.h>
  10. #include <vector>
  11. #include <iostream>
  12. #include <fstream>
  13. #include <sstream>
  14. #include <iomanip>
  15. #include <Eigen/Sparse>
  16. #include <Eigen/Dense>
  17. #include <Eigen/Eigenvalues>
  18. #include <Eigen/Core>
  19. #include <boost/numeric/odeint.hpp>
  21. using namespace boost::numeric::odeint;
  22. using namespace std;
  25. class HodgkinHuxley {
  26. private:
  27. public:
  28. // ----------------------------------------------------------------------------------------------------
  29. // Parameters
  31. // Runge-Kutta Cash-Karp 5(4) for integration
  32. runge_kutta_cash_karp54<vector<double>> rkck;
  34. // Export filepath.
  35. string export_filepath;
  37. // Stim Current parameters
  38. vector<string> stimFilePaths;
  39. double stimScale;
  40. int samplingInterval;
  41. vector<double> stim; // Resultant external stimulation array
  43. // Constants
  44. double TEMP_C; // Temperature
  45. double FARADAY = 96480;
  46. double PI = M_PI;
  48. // Model parameters
  49. double T; // Model duration in ms
  50. double dt; // Time step in ms
  51. int num_steps;
  53. // Neuron parameters
  54. double soma_len; // Soma length in cm
  55. double soma_diam; // Soma diameter in cm
  56. double Cm; // Membrane capacitance
  58. // Channel parameters
  59. double gNaT; // Sodium channel conductance
  60. double ENa; // Sodium reversal potential
  61. double gK; // Potassium channel conductance
  62. double EK; // Potassium reversal potential
  63. double gLeak; // Leak conductance
  64. double EL; // Leak reversal potential
  66. // Gating variable parameters
  67. double amV1, amV2, amV3; // parameters for m-gate
  68. double tm0, epsm;
  69. double ahV1, ahV2, ahV3; // parameters for h-gate
  70. double th0, epsh;
  71. double anV1, anV2, anV3; // parameters for n-gate
  72. double tn0, epsn;
  74. // Initial conditions
  75. double V_init; // Initial membrane potential
  76. double m_init; // Initial m-gate value
  77. double h_init; // Initial h-gate value
  78. double n_init; // Initial n-gate value
  79. double init_conditions[4]; // Array to store initial conditions
  81. // ----------------------------------------------------------------------------------------------------
  82. // Results
  84. vector<double> X;
  85. vector<vector<double>> time_series;
  87. Eigen::MatrixXd t;
  88. Eigen::MatrixXd I_stim;
  89. Eigen::MatrixXd V_mem;
  90. Eigen::MatrixXd m_gate;
  91. Eigen::MatrixXd h_gate;
  92. Eigen::MatrixXd n_gate;
  94. // ----------------------------------------------------------------------------------------------------
  95. // Constructor & Destructor
  97. HodgkinHuxley(const HH_ParamStruct& configSelected);
  98. ~HodgkinHuxley() = default;
  100. // ----------------------------------------------------------------------------------------------------
  101. // Load external stimulation files
  103. void loadStimulationCurrent();
  105. // ----------------------------------------------------------------------------------------------------
  106. // Gating Kinetics Functions
  108. double infSteadyState(double VV, double a1, double a2);
  109. double tauTimeConstant(double VV, double t0, double eps, double a1, double a3);
  110. double mm_inf(double VV);
  111. double mm_tau(double VV);
  112. double hh_inf(double VV);
  113. double hh_tau(double VV);
  114. double nn_inf(double VV);
  115. double nn_tau(double VV);
  117. // ----------------------------------------------------------------------------------------------------
  118. // Ionic Current Functions
  120. double I_Leak(double VV) const;
  121. double I_K(double VV, double nn) const;
  122. double I_NaT(double VV, double mm, double hh) const;
  124. // ----------------------------------------------------------------------------------------------------
  125. // Equations of Motion
  127. void dXdt(const vector<double>& X, vector<double>& dX, const int idx);
  129. // ----------------------------------------------------------------------------------------------------
  130. // Running the model
  132. void rkStepper(int i);
  133. void runModel();
  135. // ----------------------------------------------------------------------------------------------------
  136. // Export results the model
  138. void unpackTimeSeries();
  139. void exportResults();
  140. };
  142. #endif // HODGKIN_HUXLEY_H

data_HodgkinHuxley.h at commit ee4d8b9, no license · at the source

Overview

Authors: Ian Williams1, Joseph D. Taylor1, Alain Nogaret1
ORCID iDs: Alain Nogaret
  1. Department of Physics, University of Bath,BA2 7AY Bath, UK
Institutions: University of Bath (United Kingdom)
Journal: Scientific reports, volume 16, issue 1, article 13120
Dates: received 27 August 2025; accepted 3 March 2026; published online 11 March 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1038/s41598-026-43346-6 · PMID 41813839 · PMCID PMC13100080 · OpenAlex W7135102811
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: systems (subfield)
Methods: Statistics, Spectral & time-frequency
Keywords: Biophysics, Computational biology and bioinformatics, Engineering, Neuroscience, Physics
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Citations: not cited yet (Europe PMC); 36 references in the paper

Abstract

Neuron models built from experimental data have successfully predicted observed voltage oscillations within and beyond training range. A tantalising prospect is the possibility of estimating the unobserved dynamics of ion channels, which is largely inaccessible to experiment, from membrane voltage recordings. The main roadblock here is our lack of knowledge of the equations governing biological neurons which forces us to rely on surrogate models and parameter estimates biassed by model error. Error correction algorithms are therefore needed to infer both observed and unobserved dynamics, and ultimately the actual parameters of a biological neuron. Here we use a recurrent neural network to correct the outputs of a surrogate Hodgkin-Huxley (HH) model. The reservoir-surrogate HH model hybrid was trained on the voltage oscillations of a reference HH model and its driving current waveform. Out of the six reservoir-surrogate model architectures investigated, we identify one that most accurately recovers the reference membrane voltage and ion channel dynamics. The reservoir was thus effective in correcting model error in an externally driven nonlinear oscillator and in reconstructing the dynamics of both observed and unobserved state variables from the reference model mimicking an actual neuron.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 5 matches between paragraphs and lines of code.

IanWilliams01/driven-hybrid-reservoir-computing

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: ee4d8b9b807d0cac1854d07847aea1bf8981a38e, 19 November 2025
Languages: C/C++ (6), C++ (6)
Size: 18 files, 12 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
13 files
At the source: github.com/IanWilliams01/driven-hybrid-reservoir-computing

Code availability

https://github.com/IanWilliams01/driven-hybrid-reservoir-computing.

Reproduced under the paper's license (CC BY), from the paper cited above.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 12 scripts, each with its path and the digest of its content;
  • 5 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

The data and code that support the findings of this study are available within the article and from the authors.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 30 references.

Cite

This paper

Williams, I., Taylor, J. D., & Nogaret, A. (2026). Correcting model error bias in estimations of neuronal dynamics from time series observations. Scientific reports, 16(1), 13120. https://doi.org/10.1038/s41598-026-43346-6

BibTeX

@article{williams2026correcting,
author = {Williams, Ian and Taylor, Joseph D. and Nogaret, Alain},
title = {{Correcting model error bias in estimations of neuronal dynamics from time series observations}},
journal = {Scientific reports},
year = {2026},
month = mar,
volume = {16},
number = {1},
pages = {13120},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-43346-6},
url = {https://doi.org/10.1038/s41598-026-43346-6},
pmid = {41813839},
pmcid = {PMC13100080}
}

RIS

TY - JOUR
AU - Williams, Ian
AU - Taylor, Joseph D.
AU - Nogaret, Alain
TI - Correcting model error bias in estimations of neuronal dynamics from time series observations
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/03/11
VL - 16
IS - 1
SP - 13120
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-43346-6
UR - https://doi.org/10.1038/s41598-026-43346-6
LA - en
ER -

CSL-JSON

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