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A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation.

Code ↔ Paper

3 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 3 matches · 2 of them tie a paragraph to a whole file without given lines: weak matches, whose lines are not tinted
  1. [1] § Results › Benchmark evaluation of TASC-DMD ↔ examples/generate_NLS_data.m, the whole file · a weak match · score 0.56 · Nonlinear Schr dinger, soliton solution, NLS, physical, benchmark, TASC DMD · Report a mismatch
  2. [2] § Results › Benchmark evaluation of TASC-DMD ↔ examples/generate_NLS_data.m, the whole file · a weak match · score 0.54 · nonlinear Schr dinger, soliton solution, periodic, Fourier, NLS, fields · Report a mismatch
  3. [3] § Results › Benchmark evaluation of TASC-DMD ↔ examples/Schrodinger_equ_TASCDMD.m, lines 1 to 44 · score 0.51 · Nonlinear Schr dinger, fbDMD, exact DMD, NLS, benchmark, eigenvalues · Report a mismatch

Paper

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The authors' code

MATLAB · 79 lines · 3 KB · MIT · 2 matches

  1. % GENERATE_NLS_DATA Solve the Nonlinear Schrödinger (NLS) equation
  2. % using a split-step Fourier method via ode45.
  3. %
  4. % Equation: i*psi_t + (1/2)*psi_xx + |psi|^2 * psi = 0
  5. % Initial condition: psi(x, 0) = 2*sech(x) (2-soliton solution)
  6. %
  7. % This script generates the spatiotemporal data (psi_sol) that is used
  8. % as input to the TASC-DMD benchmark in Schrodinger_equ_TASCDMD.m.
  9. %
  10. % Output variable saved to workspace:
  11. % psi_sol - Complex field [nt x n_points] |psi(x,t)|
  12. % x - Spatial grid [1 x n_points]
  13. % t - Time vector [nt x 1]
  14. %
  15. % Dependencies:
  16. % nls_rhs.m (must be on MATLAB path)
  17. %
  18. % Reference:
  19. % [TASC DMD Paper — citation to be added after publication]
  22. clc; clear; close all;
  24. % -------------------------------------------------------------------------
  25. % Spatial domain
  26. % -------------------------------------------------------------------------
  27. x_min = -5;
  28. x_max = 5;
  29. n_points = 500;
  31. x_full = linspace(x_min, x_max, n_points + 1);
  32. x = x_full(1:n_points); % Periodic domain (drop repeated endpoint)
  34. % -------------------------------------------------------------------------
  35. % Time domain
  36. % -------------------------------------------------------------------------
  37. t = linspace(0, pi, 21)'; % 21 snapshots over [0, pi]
  39. % -------------------------------------------------------------------------
  40. % Initial condition: 2-soliton psi(x,0) = 2*sech(x)
  41. % -------------------------------------------------------------------------
  42. psi0 = 2 * sech(x)'; % Column vector [n_points x 1]
  44. % Fourier wave numbers (consistent with periodic BC on [x_min, x_max])
  45. k = (2*pi / (x_max - x_min)) * [0 : n_points/2-1, -n_points/2 : -1]';
  47. % Transform initial condition to Fourier space
  48. psit0 = fft(psi0);
  50. % -------------------------------------------------------------------------
  51. % Integrate in Fourier space using ode45
  52. % -------------------------------------------------------------------------
  53. opts = odeset('RelTol', 1e-8, 'AbsTol', 1e-10);
  54. [t, psit_sol] = ode45(@(tt, pp) nls_rhs(tt, pp, [], k), t, psit0, opts);
  56. % Transform back to physical space
  57. psi_sol = zeros(size(psit_sol));
  58. for j = 1 : length(t)
  59. psi_sol(j, :) = ifft(psit_sol(j, :));
  60. end
  62. % -------------------------------------------------------------------------
  63. % Visualization: |psi(x,t)|
  64. % -------------------------------------------------------------------------
  65. [Tgrid, Xgrid] = meshgrid(t, x);
  67. figure;
  68. surf(Xgrid, Tgrid, abs(psi_sol)', 'EdgeColor', 'none');
  69. colormap('cool');
  70. xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 18);
  71. ylabel('$t$', 'Interpreter', 'latex', 'FontSize', 18);
  72. zlabel('$|\psi(x,t)|$', 'Interpreter', 'latex', 'FontSize', 18);
  73. title('Nonlinear Schrödinger Equation — Original (no noise)', 'FontSize', 14);
  74. colorbar;
  75. set(gca, 'FontSize', 13, 'FontWeight', 'bold');
  77. % Save data for use in the TASC-DMD script
  78. save('NLS_data.mat', 'psi_sol', 'x', 't', 'Xgrid', 'Tgrid');
  79. fprintf('Data saved to NLS_data.mat\n');

generate_NLS_data.m at commit d6105fb, under MIT · at the source

Overview

Authors: Amir H. G. Arani1,2, Ahmed A. Alshareef3, Dzung L. Pham4, Ruth J. Okamoto1, Philip V. Bayly1
  1. Mechanical Engineering and Materials Science, Washington University,St. Louis, MO USA
  2. Department of Neurosurgery, School of Medicine, Washington University,St. Louis, MO USA
  3. Department of Biomedical Engineering, University of South Carolina,Columbia, SC USA
  4. Department of Radiology and Radiological Sciences, Uniformed Services University,Bethesda, MD USA
Institutions: University of Washington (United States); Washington University in St. Louis (United States); University of South Carolina (United States); Department of Radiology and Radiological Sciences, Uniformed Services University,Bethesda, MD USA
Journal: Scientific reports, volume 16, issue 1, article 14468
Dates: received 16 October 2025; accepted 24 February 2026; published online 21 March 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41598-026-41995-1 · PMID 41864995 · PMCID PMC13149987 · OpenAlex W7139980951
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: structural MRI / diffusion (modality), human (organism), methods / tools (subfield)
Keywords: Brain dynamics, Tagged MRI, Time-delay embedding, DMD, SINDy, Fluid dynamics, Computational biology and bioinformatics, Mathematics and computing, Neuroscience, Physics
MeSH: Brain*, Algorithms, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Nonlinear Dynamics (* major topic)
Topic: Model Reduction and Neural Networks (Statistical and Nonlinear Physics, Physics and Astronomy), according to OpenAlex
Funding: national institutes of health (U01 NS112120)
Citations: not cited yet (Europe PMC); 47 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

Its files are read in the Code ↔ Paper reader above, with 3 matches between paragraphs and lines of code.

amir-arani/TASC-DMD

License: MIT
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: d6105fb2a81e7d5f9b2e91a29a314ed721a737c2, 2 March 2026
Languages: MATLAB (7)
Size: 10 files, 7 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: README, license file, documentation
Not found: CITATION.cff, environment file, tests, continuous integration
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
9 files
At the source: github.com/amir-arani/TASC-DMD

The paper's code and data availability statement is in the Data section.

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.

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  • 7 scripts, each with its path and the digest of its content;
  • 3 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

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

Code and data availability statement

The paper has a code and data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41598-026-41995-1.

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 10 keywords, 6 MeSH terms, 1 funder, 46 references.

Cite

This paper

Arani, A. H. G., Alshareef, A. A., Pham, D. L., Okamoto, R. J., & Bayly, P. V. (2026). A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation. Scientific reports, 16(1), 14468. https://doi.org/10.1038/s41598-026-41995-1

BibTeX

@article{arani2026novel,
author = {Arani, Amir H. G. and Alshareef, Ahmed A. and Pham, Dzung L. and Okamoto, Ruth J. and Bayly, Philip V.},
title = {{A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation}},
journal = {Scientific reports},
year = {2026},
month = mar,
volume = {16},
number = {1},
pages = {14468},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-41995-1},
url = {https://doi.org/10.1038/s41598-026-41995-1},
pmid = {41864995},
pmcid = {PMC13149987}
}

RIS

TY - JOUR
AU - Arani, Amir H. G.
AU - Alshareef, Ahmed A.
AU - Pham, Dzung L.
AU - Okamoto, Ruth J.
AU - Bayly, Philip V.
TI - A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/03/21
VL - 16
IS - 1
SP - 14468
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-41995-1
UR - https://doi.org/10.1038/s41598-026-41995-1
LA - en
ER -

CSL-JSON

{
"id": "10.1038/s41598-026-41995-1",
"type": "article-journal",
"title": "A novel spatiotemporal decomposition and identification of sparse equations for human brain deformation",
"container-title": "Scientific reports",
"author": [
{
"family": "Arani",
"given": "Amir H. G."
},
{
"family": "Alshareef",
"given": "Ahmed A."
},
{
"family": "Pham",
"given": "Dzung L."
},
{
"family": "Okamoto",
"given": "Ruth J."
},
{
"family": "Bayly",
"given": "Philip V."
}
],
"container-title-short": "Sci Rep",
"volume": "16",
"issue": "1",
"page": "14468",
"DOI": "10.1038/s41598-026-41995-1",
"PMID": "41864995",
"PMCID": "PMC13149987",
"ISSN": "2045-2322",
"publisher": "Nature Publishing Group",
"URL": "https://doi.org/10.1038/s41598-026-41995-1",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
21
]
]
}
}

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