Pith. sign in

REVIEW 3 major objections 2 minor 2 cited by

MATPAC++: Enhanced Masked Latent Prediction for Self-Supervised Audio Representation Learning

T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash

Pith's one-line read MATPAC++ claims that integrating Multiple Choice Learning into the masked prediction and unsupervised classification pretext tasks of MATPAC yields state-of-the-art self-supervised audio representations, with top AudioSet fine-tuning and do

desk verdict Submission mismatched: abstract claims a MATPAC++ audio SSL paper, body is an unrelated PDE paper—no support for any of the central claims. read the letter →

arxiv 2508.12709 v1 pith:BOVMV2ZP submitted 2025-08-18 cs.SD cs.AI

classification cs.SDcs.AI
keywords self-supervisedlearningaudiorepresentationmaskedlatentpredictionmultiplechoiceambiguitySetlinearprobingmusicpretraining
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 proposes MATPAC++, an enhancement of the MATPAC self-supervised audio model, arguing that the predictor at the output of a masked latent prediction system should explicitly handle the ambiguity of audio containing multiple simultaneous sources. To do this, it integrates Multiple Choice Learning (MCL) into both the prediction and the unsupervised classification pretext tasks, so the model must propose several candidate answers rather than one. The authors report that this integration yields state-of-the-art results when fine-tuned on AudioSet and overall state-of-the-art downstream scores, and that a music-only variant reaches state-of-the-art with better efficiency. A caveat, located in the submitted full text: the body and appendices are actually a different manuscript on estimating partial differential equations from data, so the only verifiable content here is the abstract; the empirical claims cannot currently be checked.

What carries the argument

Multiple Choice Learning (MCL): a training scheme in which a prediction module outputs $K$ candidate hypotheses and the loss is evaluated against the best candidate (often with an oracle/assignment step), so different hypotheses specialize to different modes of the target distribution. In MATPAC++ it is inserted into the two pretext tasks — masked latent prediction and unsupervised classification — replacing the single-target predictor of MATPAC. Its job is to model the inherent ambiguity of audio with multiple overlapping sources, and it is the load-bearing change claimed to improve representation quality.

What would settle it

Compare MATPAC++ against MATPAC under identical pretraining data, compute, and protocols; if linear-probe or AudioSet fine-tuning scores are not higher, the central claim fails. Also, in the supplied PDF, the body does not contain the MATPAC++ experiments at all, so inspecting the manuscript itself already falsifies the claim that the full text supports the abstract.

Watch

Extended reading notes

Core claim

On its own terms, the contribution is a specific architectural and training change: MATPAC++ keeps MATPAC's masked latent prediction framework but replaces deterministic prediction with Multiple Choice Learning, where the predictor generates several hypotheses and the training loss is computed against the best-matching hypothesis (or a subset). The same MCL treatment is applied to the unsupervised classification pretext task. The intended effect is that the encoder can no longer collapse the multiple plausible continuations of masked audio into a single averaged target; instead it learns representations that are informative about the ambiguity itself. The authors claim this gives better tran

Load-bearing premise

The load-bearing premise is that explicit multiple-choice conditioning on ambiguous audio — not added capacity, a different backbone, or extra training budget — is what improves the learned representations, and that the abstract's description matches the submitted experiments (the full text currently does not).

Editorial extensions

If this is right

  • If the claim holds, making the pretext predictor explicitly multi-modal is sufficient to raise the quality of self-supervised audio representations without changing the backbone or dataset.
  • AudioSet fine-tuning becomes a benchmark where MATPAC++ places above prior state-of-the-art SSL audio models under the paper's unified evaluation protocol.
  • Linear probing on downstream tasks improves, indicating the learned representations transfer better to tasks beyond pretraining.
  • Music-only pretraining with MCL gives state-of-the-art performance with substantially better efficiency, suggesting ambiguity modeling matters especially in music data.
  • The unified protocol enables comparisons across methods, so previously reported gaps between SSL audio methods may need re-measuring under one protocol.

Reading between the lines

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

  • If the benefit of MCL comes primarily from having multiple hypotheses rather than from the best-loss selection, then a simpler multi-head predictor sharing the same capacity might reproduce part of the gain; this is testable by ablating the oracle assignment.
  • The ambiguity argument predicts the largest gains on polyphonic examples with several simultaneous sources; downstream tasks dominated by single-source sounds should show smaller improvements, which could be checked by stratifying AudioSet classes by source count.
  • Because the submitted full text is a different paper, an immediate next step is locating the actual MATPAC++ experimental section; until then the abstract-level claims rest on the authors' reporting alone.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The abstract of arXiv:2508.12709 announces MATPAC++, a self-supervised audio representation learning method that integrates Multiple Choice Learning (MCL) into the prediction and unsupervised classification pretext tasks of MATPAC, and claims state-of-the-art results on AudioSet fine-tuning and downstream linear-probing tasks, as well as improved efficiency for music-only training. However, the full text supplied with the submission is not the MATPAC++ paper. It is a manuscript titled 'Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data', with its own physicists' abstract, introduction, methods, synthetic benchmark experiments on Allen-Cahn/Cahn-Hilliard and reaction-diffusion systems, and a bibliography on sparse identification of dynamical systems. The body contains no mention of MATPAC, MATPAC++, MCL, masked latent prediction, audio representation learning, AudioSet, or any of the claimed experiments. The submitted document therefore provides no derivations, no architectural description, no training details, and no evaluation results for the claims made in the abstract.

Significance. If the MATPAC++ results described in the abstract were properly supported, the contribution could be significant: the idea of using MCL to model predictive ambiguity in masked audio SSL is a sensible direction, and the claimed broad state-of-the-art performance across AudioSet and multiple downstream tasks would be of considerable interest to the audio SSL community. However, as submitted, the manuscript provides no evidence whatsoever for these claims. There is no method section, no mathematical formulation of the MCL integration, no experimental setup, no tables, no error bars, and no comparison to prior work. The only substantive content is an unrelated PDE-estimation paper. Consequently, the significance of the claimed contribution cannot be assessed, and the manuscript in its present form has no scientific content relevant to its stated topic.

major comments (3)
  1. [Abstract vs. Full Text] The document is internally inconsistent at the most basic level. The abstract describes a self-supervised audio representation learning method, MATPAC++, with MCL and evaluation on AudioSet and downstream audio tasks. The full text is a manuscript about estimating PDE and delay-PDE models from data, authored by different authors (Mai, Kroll, Thiele, Kamps), with no mention of MATPAC, MCL, masked latent prediction, audio, or any of the claimed experiments. The central claim of state-of-the-art performance is therefore completely unsupported: no architecture, equations, training protocol, or results for MATPAC++ appear anywhere in the submitted text. This is a load-bearing failure that cannot be repaired by local revision.
  2. [Absence of method description] Even granting the abstract's content, the submitted text contains no description of the proposed MCL-based prediction or classification pretext tasks. There is no formulation of the predictor module, no explanation of how multiple choice hypotheses are generated or selected, no loss function, and no architectural details. Without these, the claimed contribution is neither reproducible nor checkable, and the abstract's assertions are unsupported assertions rather than scientific claims.
  3. [Absence of empirical evaluation] The abstract claims state-of-the-art fine-tuning results on AudioSet and overall state-of-the-art downstream scores, as well as improved efficiency for music-only training. The submitted text contains no experimental section, no dataset descriptions, no metrics, no comparison baselines, and no results tables. There is no way to verify these empirical claims or to assess whether the alleged improvements come from MCL or from other unstated factors such as model capacity or training schedule. The claimed experimental superiority is entirely unsubstantiated.
minor comments (2)
  1. [Title and metadata] The title of the submitted full text, 'Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data', matches arXiv:2508.12715, not the MATPAC++ title in the submission metadata. The abstract and body are from entirely different works; this should be resolved at the submission level before any review can proceed.
  2. [References and formatting] The bibliography and appendix of the submitted text are those of the PDE paper and are irrelevant to the abstract's claims. The text also contains typographical issues (e.g., 'sensitivtiy', 'spars', 'accomodate') that would need correction in any eventual revision of the intended manuscript.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation can be assessed: the body is an unrelated PDE-estimation paper, so the MATPAC++ SOTA claim is unsupported rather than circular.

full rationale

The abstract claims that MATPAC++ achieves state-of-the-art results on AudioSet and downstream audio tasks via Multiple Choice Learning integrated into MATPAC's prediction and unsupervised classification pretext tasks. The full text, however, is 'Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data' by Mai, Kroll, Thiele, and Kamps (matching arXiv:2508.12715). It contains no MATPAC++, no MCL, no masked latent prediction, no AudioSet, no music benchmarks, and no downstream audio evaluation. There is therefore no derivation chain for the abstract's central claim to audit. Per the review rule, I flag this as an explicit missing-support / omitted-proof failure: the inserted body is in-scope evidence, not a pipeline artifact, and it provides no evidence for the claimed results. However, the specific circularity patterns enumerated—self-definitional equations, fitted inputs renamed as predictions, load-bearing self-citations, imported uniqueness theorems, ansatz-by-citation, or renaming known results—cannot be exhibited because the relevant derivation is simply absent. An unsupported assertion and a circular derivation are distinct failure modes; the former is severe but does not meet the threshold for circularity. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The abstract-only content means the ledger is nearly empty. No fitted parameters or new entities can be identified because the method body is absent. The two axioms listed are the load-bearing premises of the claimed improvement.

assumptions (2)
  • domain assumption The predictor module is a bottleneck in masked latent audio prediction and its ambiguity can be modeled with MCL.
    This is the design premise from the abstract; it justifies the proposed modification but is not derived or benchmarked in the provided text.
  • domain assumption The unified evaluation protocol allows fair comparison with prior SSL methods.
    The abstract claims a 'unified protocol' but no protocol details are present; fairness is assumed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of MATPAC++: Enhanced Masked Latent Prediction for Self-Supervised Audio Representation Learning." pith.science (2026). https://pith.science/paper/BOVMV2ZP

@misc{pith2026250812709,
  author       = {Pith},
  title        = {Pith review of: MATPAC++: Enhanced Masked Latent Prediction for Self-Supervised Audio Representation Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BOVMV2ZP}},
  note         = {Machine review of arXiv:2508.12709}
}
read the original abstract

Masked latent prediction has emerged as a leading paradigm in self-supervised learning (SSL), especially for general audio and music representation learning. While recent methods have demonstrated strong performance, the role of the predictor module used at the output of such SSL systems remains mainly overlooked, despite being crucial for solving the pretext task at hand. In particular, this module should be able to deal with the ambiguity inherent in audio content, especially when it is composed of multiple sound sources. This work proposes a novel enhancement: integrating Multiple Choice Learning (MCL) to explicitly model prediction ambiguity and improve representation quality. We build on top of the recently proposed MATPAC system, improving its prediction and unsupervised classification pretext tasks with MCL. We extensively evaluate our method, MATPAC++, through both linear probing across multiple downstream tasks and fine-tuning on AudioSet, employing a unified protocol that enables rigorous and fair comparisons with state-of-the-art SSL approaches. Results show that our proposal achieves state-of-the-art when fine-tuned on AudioSet and overall state-of-the-art scores on downstream tasks. Additionally, we examine domain specialisation by training exclusively on music data, where our model achieves state-of-the-art performance with significantly improved efficiency.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Self-Supervised Approach for Minimal-Annotation Hydroacoustic Data Exploration

    cs.SD 2026-07 conditional novelty 6.0 of 10

    Event-level MAE embeddings plus UMAP/HDBSCAN or K-Means clustering recover 15 hydroacoustic classes from multi-year Mayotte data with ~1 hour of annotation and detector-comparable F1.

  2. Unsupervised Evaluation of Deep Audio Embeddings for Music Structure Analysis

    cs.SD 2026-03 conditional novelty 5.0 of 10

    Off-the-shelf deep audio embeddings generally improve unsupervised music boundary detection over spectrogram features, with CBM the best segmenter, but not all models help and standard scores are inflated by edge boundaries.

Reference graph

Works this paper leans on

54 extracted references · 35 canonical work pages · cited by 2 Pith papers

  1. [1]

    Springer Berlin Heidelberg, 1993

    Solving Ordinary Differential Equations I . Springer Berlin Heidelberg, 1993. doi: 10.1007/ 978-3-540-78862-1

  2. [2]

    Ahmed, Omer San, and Sivaramakrishnan Lakshmivarahan

    Shady E. Ahmed, Omer San, and Sivaramakrishnan Lakshmivarahan. Forward Sensitivity Analysis of the FitzHugh–Nagumo System: Parameter Estimation, pages 93–103. Springer International Publish- ing, 2021. ISBN 9783030811709. doi: 10.1007/978-3-030-81170-9 9

  3. [3]

    Aranson and Lorenz Kramer

    Igor S. Aranson and Lorenz Kramer. The world of the complex ginzburg-landau equation. Reviews of Modern Physics, 74(1):99–143, 2002. doi: 10.1103/revmodphys.74.99

  4. [4]

    M. Baer. findiff software package, 2018. https://github.com/maroba/findiff

  5. [5]

    Allen-cahn equation for modeling temporal evolution of non-conserved field variables in cancer cell 21 Preprint– contact: oliver.mai@uni-muenster.de – September 18, 2025 migration

    Jo ˜ao Gabriel Piraine Bandeira, Daniela Buske, R ´egis Sperotto de Quadros, and Gustavo Braz Kurz. Allen-cahn equation for modeling temporal evolution of non-conserved field variables in cancer cell 21 Preprint– contact: oliver.mai@uni-muenster.de – September 18, 2025 migration. Ciˆencia e Natura, 46(esp. 1):e87268, 2024. doi: 10.5902/2179460x87268

  6. [6]

    Bergstra et al

    J. Bergstra et al. Algorithms for Hyper-Parameter Optimization. In J. Shawe-Taylor, R. Zemel, P. Bartlett, F. Pereira, and K.Q. Weinberger, editors,Advances in Neural Information Processing Sys- tems, volume 24. Curran Associates, Inc., 2011

  7. [7]

    Hyperopt: a python library for model selection and hyperparameter optimization

    James Bergstra, Brent Komer, Chris Eliasmith, Dan Yamins, and David D Cox. Hyperopt: a python library for model selection and hyperparameter optimization. Computational Science & Discovery, 8 (1):014008, 2015. doi: 10.1088/1749-4699/8/1/014008

  8. [8]

    Bock and K.J

    H.G. Bock and K.J. Plitt. A multiple shooting algorithm for direct solution of optimal control problems *. IFAC Proceedings Volumes, 17(2):1603–1608, 1984. doi: 10.1016/s1474-6670(17)61205-9

Show all 54 references
  1. [9]

    Brunton, Joshua L

    Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15):3932–3937, 2016. doi: 10.1073/pnas.1517384113

  2. [10]

    Fitting partial differential equations to space-time dynamics

    Markus B ¨ar, Rainer Hegger, and Holger Kantz. Fitting partial differential equations to space-time dynamics. Physical Review E, 59(1):337–342, 1999. doi: 10.1103/physreve.59.337

  3. [11]

    J. W. Cahn and A. Novick-Cohen. Evolution equations for phase separation and ordering in binary alloys. Journal of Statistical Physics, 76(3-4):877–909, 1994. doi: 10.1007/bf02188691

  4. [12]

    Six decades of the fitzhugh–nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines

    Daniel Cebri ´an-Lacasa, Pedro Parra-Rivas, Daniel Ruiz-Reyn ´es, and Lendert Gelens. Six decades of the fitzhugh–nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines. Physics Reports, 1096:1–39, 2024. doi: 10.1016/j.physrep.2024.09.014

  5. [13]

    Kutz, and Steven Brunton

    Brian de Silva, Kathleen Champion, Markus Quade, Jean-Christophe Loiseau, J. Kutz, and Steven Brunton. Pysindy: A python package for the sparse identification of nonlinear dynamical systems from data. Journal of Open Source Software, 5(49):2104, 2020. doi: 10.21105/joss.02104

  6. [14]

    An improved sparse identification of nonlinear dynamics with akaike information criterion and group sparsity

    Xin Dong, Yu-Long Bai, Yani Lu, and Manhong Fan. An improved sparse identification of nonlinear dynamics with akaike information criterion and group sparsity. Nonlinear Dynamics, 111(2):1485– 1510, 2022. doi: 10.1007/s11071-022-07875-9

  7. [15]

    Identification of the fitzhugh–nagumo model dynamics via deter- ministic learning

    Xunde Dong and Cong Wang. Identification of the fitzhugh–nagumo model dynamics via deter- ministic learning. International Journal of Bifurcation and Chaos , 25(12):1550159, 2015. doi: 10.1142/s021812741550159x

  8. [16]

    Asymptotic behaviour of travelling waves for the delayed fisher–kpp equation

    Arnaud Ducrot and Gr ´egoire Nadin. Asymptotic behaviour of travelling waves for the delayed fisher–kpp equation. Journal of Differential Equations , 256(9):3115–3140, 2014. doi: 10.1016/j. jde.2014.01.033. 22 Preprint– contact: oliver.mai@uni-muenster.de – September 18, 2025

  9. [17]

    Automatically discovering ordinary differential equa- tions from data with sparse regression

    Kevin Egan, Weizhen Li, and Rui Carvalho. Automatically discovering ordinary differential equa- tions from data with sparse regression. Communications Physics , 7(1), 2024. doi: 10.1038/ s42005-023-01516-2

  10. [18]

    R. A. FISHER. The wave of advance of advantageous genes. Annals of Eugenics, 7(4):355–369, 1937. doi: 10.1111/j.1469-1809.1937.tb02153.x

  11. [19]

    Impulses and physiological states in theoretical models of nerve membrane

    Richard FitzHugh. Impulses and physiological states in theoretical models of nerve membrane. Bio- physical Journal, 1(6):445–466, 1961. doi: 10.1016/s0006-3495(61)86902-6

  12. [20]

    Parameter identification in noisy extended systems: A hydrodynamic case

    Jos ´eMar´ıa Fullana, Maurice Rossi, and St ´ephane Zaleski. Parameter identification in noisy extended systems: A hydrodynamic case. Physica D: Nonlinear Phenomena , 103(1-4):564–575, 1997. doi: 10.1016/s0167-2789(96)00286-2

  13. [21]

    Guay and D.D

    M. Guay and D.D. McLean. Optimization and sensitivity analysis for multiresponse parameter esti- mation in systems of ordinary differential equations. Computers & Chemical Engineering , 19(12): 1271–1285, December 1995. ISSN 0098-1354. doi: 10.1016/0098-1354(94)00120-0

  14. [22]

    Harris, K

    Charles R. Harris, K. Jarrod Millman, St ´efan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Pi- cus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Haldane, Jaim...

  15. [23]

    A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology , 117(4):500–544, 1952. doi: 10. 1113/jphysiol.1952.sp004764

  16. [24]

    A Tutorial on Numerical Methods for State and Parameter Estimation in Nonlinear Dynamic Systems, pages 67–88

    Boris Houska, Filip Logist, Moritz Diehl, and Jan Van Impe. A Tutorial on Numerical Methods for State and Parameter Estimation in Nonlinear Dynamic Systems, pages 67–88. Springer London, 2012. ISBN 9781447122210. doi: 10.1007/978-1-4471-2221-0 5

  17. [25]

    An approximate analytical solution of the allen-cahn equation using homotopy perturbation method and homotopy analysis method.Heliyon, 5(12):e03060, 2019

    Safdar Hussain, Abdullah Shah, Sana Ayub, and Asad Ullah. An approximate analytical solution of the allen-cahn equation using homotopy perturbation method and homotopy analysis method.Heliyon, 5(12):e03060, 2019. doi: 10.1016/j.heliyon.2019.e03060

  18. [26]

    Basic principles and practical applications of the cahn–hilliard equation

    Junseok Kim, Seunggyu Lee, Yongho Choi, Seok-Min Lee, and Darae Jeong. Basic principles and practical applications of the cahn–hilliard equation. Mathematical Problems in Engineering , 2016: 1–11, 2016. doi: 10.1155/2016/9532608. 23 Preprint– contact: oliver.mai@uni-muenster.d...

  19. [27]

    J. Koch. Data-driven modeling of nonlinear traveling waves. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(4), 2021. doi: 10.1063/5.0043255

  20. [28]

    Kolmogorov, I

    A. Kolmogorov, I. Petrovskii, and N. Piscounov. A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem. VM Tikhomirov editor. Bull. Moscow Univ. Math. Mech, 1, 1937

  21. [29]

    T. W. Kroll and O. Kamps. Sparse identification of evolution equations via Bayesian model selection. arXiv:2501.01476, 2025

  22. [30]

    L. Ljung. System identification: Theory for the user . Prentice Hall information and system sciences series. Prentice Hall, Philadelphia, PA, 2 edition, 1998

  23. [31]

    Pde-net 2.0: Learning pdes from data with a numeric- symbolic hybrid deep network

    Zichao Long, Yiping Lu, and Bin Dong. Pde-net 2.0: Learning pdes from data with a numeric- symbolic hybrid deep network. Journal of Computational Physics, 399:108925, 2019. doi: 10.1016/ j.jcp.2019.108925

  24. [32]

    Machlanski, S

    D. Machlanski, S. Samothrakis, and P. Clarke. Hyperparameter Tuning and Model Evaluation in Causal Effect Estimation, 2023

  25. [33]

    Cheeseman, Ivo F

    Suryanarayana Maddu, Bevan L. Cheeseman, Ivo F. Sbalzarini, and Christian L. M ¨uller. Stability selection enables robust learning of differential equations from limited noisy data. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 478(2262)...

  26. [34]

    TSME PyPi repository, 2024

    Oliver Mai. TSME PyPi repository, 2024. URL https://pypi.org/project/tsme/. https://pypi.org/project/tsme/

  27. [35]

    TSME examples GitHub repository, 2025

    Oliver Mai. TSME examples GitHub repository, 2025. URL https://github. com/CeNoS-CoSy/tsme_examples. https://github.com/CeNoS-CoSy/tsme_ examples

  28. [36]

    N. M. Mangan, J. N. Kutz, S. L. Brunton, and J. L. Proctor. Model selection for dynamical systems via sparse regression and information criteria. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2204):20170009, 2017. doi: 10.1098/rspa.2017.0009

  29. [37]

    Messenger and David M

    Daniel A. Messenger and David M. Bortz. Weak sindy: Galerkin-based data-driven model selection. Multiscale Modeling & Simulation, 19(3):1474–1497, 2021. doi: 10.1137/20m1343166

  30. [38]

    Nagumo, S

    J. Nagumo, S. Arimoto, and S. Yoshizawa. An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50(10):2061–2070, 1962. doi: 10.1109/jrproc.1962.288235

  31. [39]

    Naozuka, Heber L

    Gustavo T. Naozuka, Heber L. Rocha, Renato S. Silva, and Regina C. Almeida. Sindy-sa framework: 24 Preprint– contact: oliver.mai@uni-muenster.de – September 18, 2025 enhancing nonlinear system identification with sensitivity analysis. Nonlinear Dynamics , 110(3): 2589–2609, 20...

  32. [40]

    Probabilistic gram- mars for modeling dynamical systems from coarse, noisy, and partial data

    Nina Omejc, Bo ˇstjan Gec, Jure Brence, Ljup ˇco Todorovski, and Saˇso Dˇzeroski. Probabilistic gram- mars for modeling dynamical systems from coarse, noisy, and partial data. Machine Learning, 113 (10):7689–7721, 2024. doi: 10.1007/s10994-024-06522-1

  33. [41]

    Brunton, and J

    Samuel Rudy, Alessandro Alla, Steven L. Brunton, and J. Nathan Kutz. Data-driven identification of parametric partial differential equations. SIAM Journal on Applied Dynamical Systems , 18(2): 643–660, 2019. doi: 10.1137/18m1191944

  34. [42]

    Rudy, Steven L

    Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. Data-driven discovery of partial differential equations. Science Advances, 3(4), 2017. doi: 10.1126/sciadv.1602614

  35. [43]

    Gottwald, Gilles Vilmart, and Karl Perron

    Antoine Sandoz, Verena Ducret, Georg A. Gottwald, Gilles Vilmart, and Karl Perron. Sindy for delay- differential equations: application to model bacterial zinc response. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2269), 2023. doi: ...

  36. [44]

    Shraiman, A

    B.I. Shraiman, A. Pumir, W. van Saarloos, P.C. Hohenberg, H. Chat ´e, and M. Holen. Spatiotemporal chaos in the one-dimensional complex ginzburg-landau equation. Physica D: Nonlinear Phenomena, 57(3-4):241–248, 1992. doi: 10.1016/0167-2789(92)90001-4

  37. [45]

    Gurevich, and Uwe Thiele

    Fenna Stegemerten, Svetlana V . Gurevich, and Uwe Thiele. Bifurcations of front motion in passive and active allen–cahn-type equations. Chaos: An Interdisciplinary Journal of Nonlinear Science , 30 (5), 2020. doi: 10.1063/5.0003271

  38. [46]

    Stephany

    R. Stephany. DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data, 2024

  39. [47]

    Weakident: Weak formulation for identifying differential equation using narrow-fit and trimming

    Mengyi Tang, Wenjing Liao, Rachel Kuske, and Sung Ha Kang. Weakident: Weak formulation for identifying differential equation using narrow-fit and trimming. Journal of Computational Physics , 483:112069, 2023. doi: 10.1016/j.jcp.2023.112069

  40. [48]

    Oliphant, Matt Haberland, Tyler Reddy, David Courna- peau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St ´efan J

    Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Courna- peau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St ´efan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelso...

  41. [49]

    V oss, M

    H. V oss, M. B ¨unner, and M. Abel. Identification of continuous, spatiotemporal systems. Physical Review E, 57(3):2820–2823, 1998. doi: 10.1103/physreve.57.2820

  42. [50]

    V oss, Paul Kolodner, Markus Abel, and J ¨urgen Kurths

    Henning U. V oss, Paul Kolodner, Markus Abel, and J ¨urgen Kurths. Amplitude equations from spa- tiotemporal binary-fluid convection data. Physical Review Letters , 83(17):3422–3425, 1999. doi: 10.1103/physrevlett.83.3422

  43. [51]

    VOSS, JENS TIMMER, and J ¨URGEN KURTHS

    HENNING U. VOSS, JENS TIMMER, and J ¨URGEN KURTHS. Nonlinear dynamical system iden- tification from uncertain and indirect measurements. International Journal of Bifurcation and Chaos, 14(06):1905–1933, 2004. doi: 10.1142/s0218127404010345

  44. [52]

    Experiment data-driven mod- eling of tokamak discharge in east

    Chenguang Wan, Zhi Yu, Feng Wang, Xiaojuan Liu, and Jiangang Li. Experiment data-driven mod- eling of tokamak discharge in east. Nuclear Fusion, 61(6):066015, 2021. doi: 10.1088/1741-4326/ abf419

  45. [53]

    Z. Wang, X. Huan, and K. Garikipati. Variational system identification of the partial differential equations governing the physics of pattern-formation: Inference under varying fidelity and noise. Computer Methods in Applied Mechanics and Engineering , 356:44–74, 2019. doi: 10...

  46. [54]

    Wave fronts for a class of delayed fisher–kpp equa- tions

    Jinrui Zhang, Haijun Hu, and Chuangxia Huang. Wave fronts for a class of delayed fisher–kpp equa- tions. Applied Mathematics Letters, 163:109406, 2025. doi: 10.1016/j.aml.2024.109406. 26 Preprint– contact: oliver.mai@uni-muenster.de – September 18, 2025 evaluations) that will ...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.