Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

On the importance of structural identifiability for machine learning with partially observed dynamical systems

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Mapping time-series data to structurally identifiable parameter combinations, rather than raw parameter estimates, improves classifier generalization for partially observed dynamical models—most when training data are scarce.

desk verdict A sensible, simple representation trick for model-based time series classification, with real gains at low sample sizes—but the 'significant' claims need proper tests before they earn that word. read the letter →

arxiv 2502.04131 v1 pith:WAONRGCS submitted 2025-02-06 cs.LG

Janis Norden , Elisa Oostwal , Michael Chappell , Peter Tino , Kerstin Bunte This is my paper · ORCID
classification cs.LG MSC 68T0593B3034A55
keywords structuralidentifiabilitytimeseriesclassificationpartiallyobserveddynamicalsystemsmaximumaposterioriestimationidentifiableparametercombinationscompartmentalmodelsmodel-based
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

Partially observed dynamical models used to represent time series are often structurally unidentifiable: many different parameter settings produce exactly the same observable output, so point estimates of the parameters are ambiguous. The paper claims that training a classifier on such ambiguous estimates wastes capacity on separating models the data cannot distinguish, and proposes a cheap fix called Structural Identifiability Mapping (SIM). SIM computes a maximum-a-posteriori estimate for each time series, then projects it through the map $g$ onto the structurally identifiable parameter combinations $\Phi = g(\theta)$ before training any vectorial classifier. Across four example systems, including compartmental pharmacokinetic models and a microbial batch-reactor model, SIM reduces generalization error and classifier complexity relative to raw-parameter training, often bringing the partially observed classifier close to the fully observed ideal in the small-data regime. The paper's experiments show the gain persists under observational noise and under sparse and irregular sampling, which is exactly the data regime where model-based classification is most attractive.

What carries the argument

The central object is the identifiable parameter combination map $g : \mathbb{R}^n \to \mathbb{R}^m$ (with $m < n$) obtained from structural identifiability analysis, together with the equivalence classes $M_\Phi = \{\theta \in \mathbb{R}^n \mid \Phi = g(\theta)\}$ it defines; any two parameters in one class produce identical system trajectories. The pipeline computes a MAP estimate $\theta^k_{\mathrm{MAP}}$ for each time series under a uniform prior on a region of interest, applies $g$ to obtain $\Phi^k$, and trains a Gaussian-kernel support vector machine on the transformed data. The map $g$ does the work: it collapses the directions in parameter space along which the input-output behavior is invariant, guarantees that the classifier's decision boundary is constant on each equivalence class, and simplifies the geometry of the task (the toy model with $\Phi = ab$ becomes linearly separable in $\Phi$-space). For the linear compartmental models the combinations come from Laplace-transform output-equality analysis (adjacent rate products such as $k_{j,j-1}k_{j-1,j}$), and for the batch reactor from earlier identifiability studies giving $\Phi = (b_1, \mu_m, K_d, b_2 Y, b_2/K_s)$.

What would settle it

Construct the toy-model classification with labels drawn from the parameter $a$ alone while holding $ab$ fixed, so that two parameter vectors with identical output $x(t) = e^{-abt}$ carry different labels; if the SIM classifier trained on $\Phi = ab$ then shows higher test error than a classifier trained on raw $(a,b)$ MAP estimates, the equivalence-class assumption is violated and SIM has discarded label-relevant information.

Watch

Extended reading notes

Core claim

The paper's central claim is that structural identifiability—a property long studied in systems biology but largely ignored in machine learning—materially affects whether a model-based time-series classifier generalizes, and that accounting for it is nearly free. The mechanism is that two parameter vectors producing identical input-output behavior are observationally equivalent, so a classifier trained on raw MAP estimates can waste capacity separating parameter points that no data could distinguish. SIM removes this redundancy before learning: each estimate $\theta^k_{\mathrm{MAP}}$ is mapped to $\Phi^k = g(\theta^k_{\mathrm{MAP}})$, so the learned decision boundary in parameter space becomes a union of full equivalence classes $M_\Phi = \{\theta \mid g(\theta) = \Phi\}$, guaranteeing that output-equivalent parameters receive the same label. In experiments on four example systems—two catenary compartmental models, a loop compartmental model, and a nonlinear Michaelis-Menten batch reactor—SIM reduces the generalization error of the partially observed classifier in the low-training-data regime, often approaching the fully observed ideal, and it outperforms raw-parameter training across all tested noise levels and time grids. The authors position SIM as an alternative to reparametrising the model: it applies whenever identifiable combinations can be derived, even when a full reparametrisation is not feasible.

Load-bearing premise

The method assumes that any two parameter settings producing identical observed time series should receive the same class label, an assumption the synthetic experiments build in by construction but that real classification problems could violate.

Editorial extensions

If this is right

  • At the smallest training sizes tested (10 examples per class), SIM cuts mean generalization error on every example system—for the batch reactor from 0.3 to 0.1—and several SIM classifiers approach the performance of a fully observed model.
  • As training data grow, raw-parameter and SIM classifiers converge, so SIM acts as a regularizer for the scarce-data regime rather than imposing a ceiling on performance.
  • The improvement persists across the tested range of observational noise and across dense, sparse, and irregular time grids, meaning the method does not require high-quality observations to help.
  • Structural identifiability is a property of the model, not of the data, so computing the map $g$ is a one-time cost; after that, SIM adds no extra computation to classifier training.
  • Decision boundaries learned in the identifiable-combination space can be pulled back to the original parameter space through the pre-image $g^{-1}(\Phi)$, preserving interpretability for domain experts.

Reading between the lines

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

  • My inference: the equivalence-class argument should transfer to fully Bayesian pipelines, where the posterior is ridged along output-invariant directions, so projecting posterior draws through $g$ would regularise Bayesian classification the same way; the authors flag posterior sampling as future work but do not test this projection.
  • My inference: any parameter-estimation front end could be swapped in—amortized inference, recurrent encoders, or physics-informed networks that output parameter fits for unidentifiable ODEs should gain the same benefit from projecting through $g$, an experiment the paper recommends but does not run.
  • My inference: the untested risk is labels that depend on hidden internal states; if the class of a time series is set by an unobserved variable, the map $g$ discards exactly the information the label needs, and synthetic labels drawn from such a hidden state would likely make SIM underperform raw-parameter training.
  • My inference: SIM can be viewed as a principled, model-derived data-augmentation scheme for deep time-series classifiers in the biomedical small-data regime, since the equivalence structure $g$ supplies an invariance that a network would otherwise have to learn from very few examples.
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 / 5 minor

Summary. The paper proposes Structural Identifiability Mapping (SIM), a preprocessing step for model-based time series classification with partially observed dynamical systems. When the underlying ODE model is structurally unidentifiable, each time series is first represented by a MAP estimate of the model parameters, and that estimate is then mapped through the structurally identifiable parameter combinations Φ = g(θ). A vectorial classifier (an SVM in the experiments) is trained in this Φ-space rather than in the original parameter space. The method is tested on four synthetic binary classification tasks built from biomedical example models (toy model, two- and four-compartment catenary models, a compartment model with a loop, and a batch reactor model), with experiments varying the number of training samples, the observational noise level, and the density and regularity of the time grid. The central claim is that SIM improves generalization, especially in the small-training-sample regime, and that the learned decision boundary remains interpretable in the original parameter space via the pre-image g^{-1}(Φ).

Significance. The paper addresses a genuinely underappreciated issue: structural unidentifiability of a mechanistic model can mislead classifiers trained on MAP estimates of its parameters. The proposed SIM is simple, computationally cheap after the one-time identifiability analysis, and builds on established structural identifiability results from the systems-biology literature. The empirical study is broad in the sense that it covers linear and nonlinear ODE models, several noise levels, and three types of time grids, and the authors provide public code for reproducibility. The regularizing interpretation of SIM (it enforces that observationally equivalent parameters receive the same label) is plausible and coherent. However, the strength of the central claim is not matched by the statistical evidence: no significance tests are reported, and some of the headline comparisons are within one standard deviation. In addition, the method's key assumption—that class labels should be constant on equivalence classes of observationally indistinguishable parameters—is never tested, and the synthetic setup is constructed so that labels are functions of the identifiable combinations by design.

major comments (3)
  1. [Section IV.A, Tables III, IV, V] The abstract and conclusion claim that SIM "significantly improves" generalization, but no statistical significance tests are reported, and several of the reported differences are within one standard deviation. In Table III, the CCM2 row at Nmin shows a mean generalization error of .07 (.04) for PO versus .06 (.05) for PO + SIM, a difference of 0.01 with overlapping standard deviations. In Table V, the CCM2 irregular-grid row shows identical means of .2 (.09) vs .2 (.04). The claim of a consistent, significant improvement is therefore not supported by the presented statistics. The authors should either add paired significance tests across the 20 random subsamples, provide confidence intervals, or substantially temper the wording of the central claim.
  2. [Section II.B and Section III.B.1] The method rests on the assumption, stated in Section II.B, that any two parameter values yielding identical system output "should therefore be associated with the same class." This is a substantive modeling assumption, not a mathematical consequence. The synthetic experiments do not test it: in every case the class-conditional parameter means differ only in identifiable combinations—for BR, the classes differ in Y, which enters Φ4 = b2Y; for CCM2 and CCM4, the classes differ in conversion rates k12, k21, which enter the identifiable products Φ2_j; for CML the same pattern holds. If a real-world classification label depended on an unidentifiable direction (e.g., on b2 separately from Y in the batch reactor, or on the unobserved substrate concentration), SIM would discard label-relevant information and could systematically degrade accuracy. The paper needs to either add an experiment in which the class label depends on a non-identifiable parameter or an unobserved state, or provide a clear argument why such dependence cannot occur in the intended applications.
  3. [Section III.B.1, Eq. (24)] The MAP problem in Eq. (24) is non-unique under structural unidentifiability, as the paper acknowledges, and the actual solution found by simulannealbnd will be an arbitrary point on the equivalence manifold, subject to optimizer convergence and noise. The invariance of Φ under exact equivalence is mathematical, but with finite noisy data and numerical optimization the MAP estimate may not lie exactly on the true manifold, and the paper does not analyze how optimization error propagates through g. This is a secondary concern compared to the label-assumption issue, but a short analysis of the sensitivity of Φ-representations to MAP estimation error would strengthen the method's practical claims.
minor comments (5)
  1. [Section III.B.3] The text states that "the choices for tdense for the different example models are reported in Table I," but the dense grids are listed in Table II; the cross-reference should be corrected.
  2. [Section III.A.2] The description of the clinical model underlying CCM2 is slightly confusing: "Their 3-compartment model is equivalent to a CCM with 2 compartments with non-zero input." Clarifying whether the equivalence is to a two-compartment catenary model with an input term, and how the third compartment is absorbed, would help the reader.
  3. [Appendix A] In the AutoRepar reparametrisation of CCM2, the second equation reads "˙˜x2 = ˜k21x1 + 2˜x2," which appears to use the original state x1 instead of the transformed state ˜x1; this is likely a typographical error and should be checked.
  4. [Section IV.A, Figure 5] The learning curves in Figure 5 show error bars but no indication of the number of repetitions or the method used to compute the standard deviations; the caption should state that these are over the 20 random subsamples mentioned in Section III.B.1.
  5. [General] The term "significantly" is used repeatedly in Sections I, IV, and VI without a statistical test backing it; the authors should either perform tests and report p-values or replace this wording with "consistently lower" or "noticeably lower" where appropriate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the identifiable-parameter combinations are external SI results, the comparison is empirical on held-out data, and the self-citations are building blocks rather than load-bearing validation.

full rationale

The central derivation chain is not circular. SIM's mapping g is taken from external structural-identifiability results (Chen et al. 1985 for CCM, Meshkat & Sullivant 2014 for CML, Holmberg 1982 and Chappell & Godfrey 1992 for the batch reactor), not fitted to the classification data. The paper's claimed improvement is an empirical comparison of generalization error on held-out test sets between three SVM pipelines (FO, PO, PO+SIM), with hyperparameters chosen by cross-validation; no quantity is 'predicted' from a fitted parameter in a way that is forced by construction. The statement that observationally equivalent parameters 'should therefore be associated with the same class' (Section II.B) is a modeling assumption about the labeling, not a conclusion derived from the method; the synthetic experiments realize this assumption by choosing class means that differ in identifiable combinations, which is an experimental-design choice rather than a circular derivation. The self-citations [7] (model-based MAP representation) and [34] (clinical model configuration) are used as building blocks for the experimental setup, and the Discussion explicitly acknowledges the limitations of MAP point estimates and the situation-dependence of SIM; neither citation substitutes for the empirical validation. Consequently, no load-bearing step reduces to its own input, and no self-citation chain forces the result.

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

The method introduces no new physical entities or fitted parameters. It depends on three main assumptions: labels correspond to observable behavior, literature-derived identifiable combinations are correct, and the stochastic MAP optimizer yields a usable representative of the equivalence class. These are reasonable but not formally guaranteed.

assumptions (3)
  • domain assumption Class labels are determined by observable system behavior.
    In Section II.B the paper states that any two parameters with identical output should be associated with the same class. This is an assumption about the classification task, not proven; synthetic labels are generated from hidden parameter distributions.
  • standard math Identifiable parameter combinations from prior SI analyses are correct.
    The paper relies on results from Chen et al. (CCM, Ref [33]), Meshkat & Sullivant (CML, Ref [35]), and Holmberg/Chappell & Godfrey (BR, Refs [37]-[39]) without re-deriving them.
  • domain assumption MAP estimates obtained by simulated annealing provide a representative point on the unidentifiable level set.
    Section II.B, Eq. (8) and Section III.B use simulannealbnd; the argmax is not unique, and the optimizer's output is used as-is for the mapping.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the importance of structural identifiability for machine learning with partially observed dynamical systems." pith.science (2026). https://pith.science/paper/WAONRGCS

@misc{pith2026250204131,
  author       = {Pith},
  title        = {Pith review of: On the importance of structural identifiability for machine learning with partially observed dynamical systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WAONRGCS}},
  note         = {Machine review of arXiv:2502.04131}
}
read the original abstract

The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.

Figures

Figures reproduced from arXiv: 2502.04131 by the authors.

Figure 1
Figure 1. Geometric intuition behind the mechanism of SIM with data from the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Catenary n-compartmental model. where x ∈ R is the state variable with x(0) = 1 known, t ∈ [0, 1], and a, b ∈ R + are the system parameters. The parameters are further restricted to lie within the region of interest (ROI) R = [0.1, 3] × [0.1, 3]. From Eq. (10) it can be seen that any parameter configuration a and b such that Φ = ab is constant, will produce identical system output for a given value of Φ. 2) Catenary… view at source ↗
Figure 3
Figure 3. Compartment Model with a Loop (CML). For experimentation, we consider the work by Bunte et al. [34] in which the data from a clinical study concerning the interaction between the metabolites prednisone and prednisolone is analysed. The authors employed a 3- compartment model and used a probabilistic mixture of such models to analyse the data of 12 patients and found that the patients could be stratified into 4 group… view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Binary classification task for time series from the batch reactor [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Experiment 1 showing improved classification with partially observed [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: Experiment 3 for the partially observed batch reactor model showing SIM is robust to changes in regularity and sparsity of the observed time series [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Experiment 1 with partially observed CCM2 model. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Experiment 1 with partially observed CCM4 model. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Experiment 1 with partially observed CML model. [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Experiment 2 with toy model. 10 20 30 40 50 60 0 0.2 0.4 10 20 30 40 50 60 0 0.5 1 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: Experiment 2 with partially observed CCM2 model. [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 15
Figure 15. Figure 15: Experiment 3 with toy model. 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: Experiment 3 with partially observed CCM2 model. [PITH_FULL_IMAGE:figures/full_fig_p015_16.png]
Figure 17
Figure 17. Figure 17: Experiment 3 with partially observed CCM4 model. [PITH_FULL_IMAGE:figures/full_fig_p015_17.png]
Figure 18
Figure 18. Figure 18: Experiment 3 with partially observed CML model. [PITH_FULL_IMAGE:figures/full_fig_p015_18.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Structural Identifiability of Compartmental Models: Recent Progress and Future Directions

    stat.ME 2025-07 accept

    A survey of recent theory and applications of structural identifiability in compartmental models, including identifiable reparametrizations and graph-based criteria.

Reference graph

Works this paper leans on

41 extracted references · 40 canonical work pages · cited by 1 Pith paper

  1. [1]

    Learning similarities between irregularly sampled short multivariate time series from ehrs,

    K. Ø. Mikalsen, F. M. Bianchi, C. Soguero-Ruiz, S. O. Skrøvseth, R.-O. Lindsetmo, A. Revhaug, and R. Jenssen, “Learning similarities between irregularly sampled short multivariate time series from ehrs,” Proc. 3rd Int. Workshop Pattern Recognit. Healthcare Anal. , pp. 1–6, 12 2016

    work page 2016

  2. [2]

    Arma modelled time-series classification for structural health monitoring of civil infrastructure,

    E. Peter Carden and J. M. Brownjohn, “Arma modelled time-series classification for structural health monitoring of civil infrastructure,” Mechanical Systems and Signal Processing , vol. 22, no. 2, pp. 295– 314, 2008

    work page 2008

  3. [3]

    Emotion recognition from speech signals via a probabilistic echo-state network,

    E. Trentin, S. Scherer, and F. Schwenker, “Emotion recognition from speech signals via a probabilistic echo-state network,” Pattern Recog- nition Letters, vol. 66, pp. 4–12, 2015. Pattern Recognition in Human Computer Interaction

    work page 2015

  4. [4]

    Multi- variate time-series classification using the hidden-unit logistic model,

    W. Pei, H. Dibeklio ˘glu, D. M. J. Tax, and L. van der Maaten, “Multi- variate time-series classification using the hidden-unit logistic model,” IEEE Transactions on Neural Networks and Learning Systems , vol. 29, no. 4, pp. 920–931, 2018

    work page 2018

  5. [5]

    Reservoir computing approaches for representation and classification of multivari- ate time series,

    F. M. Bianchi, S. Scardapane, S. Løkse, and R. Jenssen, “Reservoir computing approaches for representation and classification of multivari- ate time series,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 5, pp. 2169–2179, 2021

    work page 2021

  6. [6]

    Multiclass sparse centroids with application to fast time series classification,

    T. Bradde, G. Fracastoro, and G. C. Calafiore, “Multiclass sparse centroids with application to fast time series classification,” IEEE Transactions on Neural Networks and Learning Systems , pp. 1–6, 2021

    work page 2021

  7. [7]

    Classification framework for partially observed dynamical systems,

    Y . Shen, P. Tino, and K. Tsaneva-Atanasova, “Classification framework for partially observed dynamical systems,” Physical Review E , vol. 95, no. 4, p. 043303, 2017

    work page 2017

  8. [8]

    Aleatory and epistemic uncertainty in probability elicita- tion with an example from hazardous waste management,

    S. C. Hora, “Aleatory and epistemic uncertainty in probability elicita- tion with an example from hazardous waste management,” Reliability Engineering & System Safety , vol. 54, no. 2-3, pp. 217–223, 1996

    work page 1996

Show all 41 references
  1. [9]

    Aleatory or epistemic? does it matter?,

    A. D. Kiureghian and O. Ditlevsen, “Aleatory or epistemic? does it matter?,” Structural Safety , vol. 31, no. 2, pp. 105–112, 2009. Risk Acceptance and Risk Communication

    2009

  2. [10]

    Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods,

    E. H ¨ullermeier and W. Waegeman, “Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods,” Machine Learning, vol. 110, pp. 457–506, 2021

    2021

  3. [11]

    On structural identifiability,

    R. Bellman and K. J. ˚Astr¨om, “On structural identifiability,” Mathemat- ical biosciences, vol. 7, no. 3-4, pp. 329–339, 1970

    1970

  4. [12]

    System identifiability based on the power series ex- pansion of the solution,

    H. Pohjanpalo, “System identifiability based on the power series ex- pansion of the solution,” Mathematical biosciences , vol. 41, no. 1-2, pp. 21–33, 1978

    1978

  5. [13]

    On the identifiability and distinguishability of nonlinear parametric models,

    E. Walter and L. Pronzato, “On the identifiability and distinguishability of nonlinear parametric models,” Mathematics and computers in simu- lation, vol. 42, no. 2-3, pp. 125–134, 1996

    1996

  6. [14]

    New results for identifiability of nonlinear systems,

    E. Tunali and T.-J. Tarn, “New results for identifiability of nonlinear systems,” IEEE Transactions on Automatic Control , vol. 32, no. 2, pp. 146–154, 1987

    1987

  7. [15]

    State isomorphism approach to global identifi- ability of nonlinear systems,

    S. Vajda and H. Rabitz, “State isomorphism approach to global identifi- ability of nonlinear systems,” IEEE Transactions on Automatic Control , vol. 34, no. 2, pp. 220–223, 1989

    1989

  8. [16]

    Existence and uniqueness of minimal realizations of nonlinear systems,

    H. J. Sussmann, “Existence and uniqueness of minimal realizations of nonlinear systems,” Mathematical systems theory , vol. 10, no. 1, pp. 263–284, 1976

    1976

  9. [17]

    Nonlinear observability, identifiability, and per- sistent trajectories,

    S. Diop and M. Fliess, “Nonlinear observability, identifiability, and per- sistent trajectories,” in [1991] Proceedings of the 30th IEEE Conference on Decision and Control , pp. 714–719, IEEE, 1991

    1991

  10. [18]

    On global identifiability for arbitrary model parametrizations,

    L. Ljung and T. Glad, “On global identifiability for arbitrary model parametrizations,” Automatica, vol. 30, no. 2, pp. 265–276, 1994

    1994

  11. [19]

    A priori parameter identi- fiability in models with non-rational functions,

    R. Jain, S. Narasimhan, and N. P. Bhatt, “A priori parameter identi- fiability in models with non-rational functions,” Automatica, vol. 109, p. 108513, 2019

    2019

  12. [20]

    On structural and practical identifiability,

    F.-G. Wieland, A. L. Hauber, M. Rosenblatt, C. T ¨onsing, and J. Timmer, “On structural and practical identifiability,” Current Opinion in Systems Biology, vol. 25, pp. 60–69, 2021

    2021

  13. [21]

    Autorepar: A method to obtain identifiable and observable reparameterizations of dynamic models with mechanistic insights,

    G. Massonis, J. R. Banga, and A. F. Villaverde, “Autorepar: A method to obtain identifiable and observable reparameterizations of dynamic models with mechanistic insights,” International Journal of Robust and Nonlinear Control, 2021

    2021

  14. [22]

    Structural Identifiability of Dynamic Systems Biology Models,

    A. F. Villaverde, A. Barreiro, and A. Papachristodoulou, “Structural Identifiability of Dynamic Systems Biology Models,” PLOS Computa- tional Biology, vol. 12, no. 10, p. e1005153, 2016

    2016

  15. [23]

    Finding and breaking lie symmetries: Implications for structural identifiability and observability in biological modelling,

    G. Massonis and A. F. Villaverde, “Finding and breaking lie symmetries: Implications for structural identifiability and observability in biological modelling,” Symmetry, vol. 12, no. 3, 2020

    2020

  16. [24]

    Web-based structural identifiability analyzer,

    I. Ilmer, A. Ovchinnikov, and G. Pogudin, “Web-based structural identifiability analyzer,” in Computational Methods in Systems Biology (E. Cinquemani and L. Paulev ´e, eds.), (Cham), pp. 254–265, Springer International Publishing, 2021

    2021

  17. [25]

    On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and combos: a novel web implementation,

    N. Meshkat, C. E.-z. Kuo, and J. DiStefano III, “On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and combos: a novel web implementation,” PloS one , vol. 9, no. 10, p. e110261, 2014

    2014

  18. [26]

    Differential elimination for dynamical models via projections with applications to structural identifiability,

    R. Dong, C. Goodbrake, H. A. Harrington, and G. Pogudin, “Differential elimination for dynamical models via projections with applications to structural identifiability,” SIAM Journal on Applied Algebra and Geometry, vol. 7, no. 1, pp. 194–235, 2023

    2023

  19. [27]

    Benchmarking tools for a priori identifiability analysis,

    X. Rey Barreiro and A. F. Villaverde, “Benchmarking tools for a priori identifiability analysis,” Bioinformatics, vol. 39, 01 2023. btad065

    2023

  20. [28]

    A bayesian framework for parameter estimation in dynamical models,

    F. C. Coelho, C. T. Codec ¸o, and M. G. M. Gomes, “A bayesian framework for parameter estimation in dynamical models,” PloS one , vol. 6, no. 5, p. e19616, 2011

    2011

  21. [29]

    Bayesian parameter esti- mation for dynamical models in systems biology,

    N. J. Linden, B. Kramer, and P. Rangamani, “Bayesian parameter esti- mation for dynamical models in systems biology,” PLOS Computational Biology, vol. 18, no. 10, p. e1010651, 2022

    2022

  22. [30]

    J. A. Jacquez et al., Compartmental analysis in biology and medicine . New York, Elsevier Pub. Co., 1972

    1972

  23. [31]

    Usefulness of the two-compartment open model in pharmacokinetics,

    C. M. Metzler, “Usefulness of the two-compartment open model in pharmacokinetics,” Journal of the American Statistical Association , vol. 66, no. 333, pp. 49–53, 1971

    1971

  24. [32]

    Phys- iologically based pharmacokinetic (pbpk) modeling and simulation ap- proaches: A systematic review of published models, applications, and model verification,

    J. E. Sager, J. Yu, I. Ragueneau-Majlessi, and N. Isoherranen, “Phys- iologically based pharmacokinetic (pbpk) modeling and simulation ap- proaches: A systematic review of published models, applications, and model verification,” Drug Metabolism and Disposition , vol. 43, no. 1...

    2015

  25. [33]

    Algorithms for the identifiable parameter combinations and parameter bounds of uniden- tifiable catenary compartmental models,

    B. C.-M. Chen, E. M. Landaw, and J. J. DiStefano, “Algorithms for the identifiable parameter combinations and parameter bounds of uniden- tifiable catenary compartmental models,” Mathematical Biosciences , vol. 76, no. 1, pp. 59–68, 1985

    1985

  26. [34]

    Learning pharmacokinetic models for in vivo glucocorticoid activation,

    K. Bunte, D. J. Smith, M. J. Chappell, Z. K. Hassan-Smith, J. W. Tomlinson, W. Arlt, and P. Ti ˇno, “Learning pharmacokinetic models for in vivo glucocorticoid activation,” Journal of Theoretical Biology , vol. 455, pp. 222–231, 2018

    2018

  27. [35]

    Identifiable reparametrizations of lin- ear compartment models,

    N. Meshkat and S. Sullivant, “Identifiable reparametrizations of lin- ear compartment models,” Journal of Symbolic Computation , vol. 63, pp. 46–67, 2014

    2014

  28. [36]

    Kinetics of nutrient-limited transport and microbial growth,

    D. K. Button, “Kinetics of nutrient-limited transport and microbial growth,” Microbiological reviews, vol. 49, no. 3, pp. 270–297, 1985

    1985

  29. [37]

    On the practical identifiability of microbial growth mod- els incorporating michaelis-menten type nonlinearities,

    A. Holmberg, “On the practical identifiability of microbial growth mod- els incorporating michaelis-menten type nonlinearities,” Mathematical Biosciences, vol. 62, no. 1, pp. 23–43, 1982

    1982

  30. [38]

    Structural identifiability of the pa- rameters of a nonlinear batch reactor model,

    M. J. Chappell and K. R. Godfrey, “Structural identifiability of the pa- rameters of a nonlinear batch reactor model,” Mathematical Biosciences, vol. 108, no. 2, pp. 241–251, 1992

    1992

  31. [39]

    Extensions to a procedure for gener- ating locally identifiable reparameterisations of unidentifiable systems,

    N. D. Evans and M. J. Chappell, “Extensions to a procedure for gener- ating locally identifiable reparameterisations of unidentifiable systems,” Mathematical biosciences, vol. 168, no. 2, pp. 137–159, 2000

    2000

  32. [40]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

    M. Raissi, P. Perdikaris, and G. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational Physics, vol. 378, pp. 686–707, 2019

    2019

  33. [41]

    Deep learning for time series classification: a review,

    H. Ismail Fawaz, G. Forestier, J. Weber, L. Idoumghar, and P.-A. Muller, “Deep learning for time series classification: a review,” Data mining and knowledge discovery, vol. 33, no. 4, pp. 917–963, 2019. THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICATION. COPYRIG...

    2019

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.