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REVIEW 3 major objections 6 minor 59 references

Meta-Learning for Physically-Constrained Neural System Identification

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Meta-learning over similar dynamical systems yields a neural state-space model that, after a few gradient steps on limited target data, beats target-only and pooled-data training and improves Kalman-filter estimation.

desk verdict A genuinely useful meta-learning-for-system-ID paper that is presently not reproducible as written because the formal state-transition equations omit the input term that every case study needs. read the letter →

arxiv 2501.06167 v1 pith:WCOMTJFR submitted 2025-01-10 cs.LG cs.SYeess.SYmath.OC

Ankush Chakrabarty , Gordon Wichern , Vedang M. Deshpande , Abraham P. Vinod , Karl Berntorp , Christopher R. Laughman This is my paper · ORCID
classification cs.LGcs.SYeess.SYmath.OC MSC 93B3068T0793E11
keywords meta-learningneuralstate-spacemodelssystemidentificationphysics-informedconstraintsextendedKalmanfilteringfew-shotadaptationMAMLANIL
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

Most neural black-box system identification trains a model from scratch on data from one target system, which fails when that data is scarce. This paper proposes to instead meta-train a neural state-space model (NSSM) across many similar source systems using MAML-style inner- and outer-loop updates, so that the resulting initialization adapts to a new target system with few data points and few gradient steps. On a Bouc-Wen hysteretic benchmark the meta-learned model attains roughly 95% fit and an RMSE of $2.83\times 10^{-5}$ mm, beating target-only, pooled-data, and transfer-learning baselines. The same recipe, augmented with physics constraint layers (polytopic pressure-flow constraints and a curl-free magnetic-field constraint), improves extended-Kalman-filter state estimation for a vapor-compression cycle and for indoor magnetic localization. The paper claims that related systems share enough structure for meta-learning to turn scarce target data into accurate predictive models.

What carries the argument

The central mechanism is bi-level MAML training: an inner loop (11) adapts the weights $\omega$ on each source system's context set, and an outer loop (12) updates the shared initialization so that it is easy to adapt. ANIL restricts the inner loop to a subnetwork $\omega_{\mathrm{in}}$, and the ablation study shows that adapting the later encoder layers and the state-transition operator matters most. Physical constraints enter as structured layers: polytopic constraints via $\mathcal{P}_x(\cdot)=\mathcal{R}\mu$ with $\mu=\mathrm{ReLU}\circ\mathrm{FC}_r(\cdot)$, and the curl-free constraint by setting $\mathcal{P}_y=\nabla$ with the output path $\bar{h}=\nabla \mathcal{D}_y\circ\mathcal{E}$, whose smoothness is guaranteed by the swish activation's non-constant higher derivatives (Theorem 2).

What would settle it

Run the same meta-training and adaptation protocol on a target system whose parameters are deliberately drawn outside the source range $\Theta$, or whose dynamics are structurally different, and check whether the meta-initialized model after $M$ adaptation steps still beats a randomly initialized model trained on the same target data; the paper's improvement claim would fail if the advantage disappears or becomes negative.

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Extended reading notes

Core claim

The paper claims that a reusable NSSM parameter vector $\omega$ trained with model-agnostic meta-learning over a family of source systems parameterized by $\theta_\ell \in \Theta$ can be fine-tuned on a target system with unknown $\theta^\star$ using few context samples and few inner-loop gradient steps (11), and that the adapted model predicts more accurately than an NSSM trained only on target data, than one trained on all source and target data pooled, and than a transfer-learned model. It further claims that when domain constraints are encoded in the network — outputs forced into a polytope via a ray-cone layer $\mathcal{P}_x(\cdot)=\mathcal{R}\,\mathrm{ReLU}(\cdot)$ and vector outputs forced to be curl-free by taking the gradient of a learned scalar potential with swish activations — the adapted NSSM improves downstream extended Kalman filtering, demonstrated on vapor-compression state estimation and magnetic-field indoor localization.

Load-bearing premise

The load-bearing premise is that the new system is similar to the systems used in training: the paper assumes its dynamics share the same equations with an unknown parameter that lies in a known range, and it never measures how different a target can be before the meta-learned starting point stops helping.

Editorial extensions

If this is right

  • A meta-trained NSSM can be adapted online in well under a second of gradient steps, making on-chip or embedded model updates feasible for control and estimation.
  • On the Bouc-Wen benchmark, meta-learning with a general architecture comes close to a specialized hysteresis model and beats NFIR and NARX baselines.
  • For families of related systems, one shared initialization replaces per-system-from-scratch training, which matters when target data is expensive to collect.
  • ANIL results indicate that adapting the later encoder layers and the state transition is more valuable than adapting only the state-transition layers, so lightweight adaptation can be targeted.
  • Physics-constrained adaptation improves downstream EKF state estimates, implying that constraints help when the fitted model is used for filtering, not only for open-loop prediction.

Reading between the lines

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

  • If the advantage holds across families, the same adapted NSSM should also provide gradients for model-predictive control, although the paper does not test closed-loop control.
  • The assumption that the target parameter lies in a known compact set $\Theta$ suggests a testable extension: use the distance between target data and the source manifold to decide when to trust the meta-initialization or trigger retraining.
  • The curl-free construction via a scalar potential could extend to other conservation-derived field constraints, such as divergence-free or symmetric-gradient fields, since only the output path of the decoder changes.
  • The paper's finding that 10% target data is too little for meta-inference implies a sample-complexity floor that practitioners would need to identify per application.
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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

3 major / 6 minor

Summary. The paper proposes a gradient-based meta-learning framework (MAML/ANIL) for neural state-space model (NSSM) identification, augmented with physics constraints of two types: polytopic state constraints and curl-free vector-field output constraints. The claim is that meta-training on a family of source systems yields an initialization that, after a few gradient steps on limited target data, produces more accurate predictions and better downstream EKF state estimation than training on target data alone or on the pooled source-plus-target data. The framework is evaluated on a Bouc-Wen hysteretic benchmark, a van der Pol oscillator family, and two case studies: vapor compression systems and magnetic-field indoor localization.

Significance. If the claims hold, the paper makes a useful practical contribution: it is, to my knowledge, the first systematic study of gradient-based meta-learning for physics-constrained neural state-space system identification. The paper includes open-source code, benchmark comparisons against several established system-identification methods, an ablation study of ANIL-style subnetwork fine-tuning, and two realistic case studies with physically motivated constraints. The analytical treatment of the swish activation and the use of standard results (Minkowski-Weyl and the Helmholtz/curl-free theorem) are also tangible strengths. The practical promise is real: few-shot identification of related nonlinear systems would be valuable for model-based control and estimation. However, the correctness of the central architecture as written and the direct evidence for the physics-constraint benefit need to be resolved before the claims can be fully accepted.

major comments (3)
  1. [Section II-B, Eqs. (2a) and (4a)] The formal definition of the state-transition operator is inconsistent with the rest of the paper. Eqs. (2a) and (4a) define psi_{t+1} = A_psi(psi_t), so the latent dynamics are autonomous after the initial encoding. Yet Remark 1 states that multi-step prediction uses A_psi 'and inputs u_{k:k+N_S-1}', and both case studies require the model to respond to exogenous inputs (compressor/EEV commands; steering and wheel-speed inputs). If the equations are literal, the architecture cannot predict the effects of future inputs, and the reported EKF improvements for input-driven systems are unexplained. If the equations are intended to include inputs (e.g., A_psi(psi_t, u_t) or A_psi(psi_t, u_{t+1})), then the stated formulation is not reproducible as written. Please correct the equations and the surrounding text so that the input dependence of the transition operator is explicit and unambiguous.
  2. [Section VI-A2, Results and Discussion] The paper's title and abstract emphasize physically constrained NSSMs, and the VCS case study states that incorporating the polytopic pressure constraints 'enhanced the estimation performance of both NSSMs and EKFs'. However, the quantitative comparison between constrained and unconstrained NSSMs is not reported, with the text saying only that the results are 'not included in this paper for brevity' and deferred to the self-cited reference [56]. A self-citation cannot substitute for the direct evidence supporting a central claim of this paper. Please either include the constrained-versus-unconstrained comparison in Section VI-A2 or explicitly qualify the abstract and case-study claims so that they do not assert an unshown improvement.
  3. [Tables II and III] The main benchmark comparison (Table II) and the meta-learning algorithm comparison (Table III) report only mean RMSE and fit values, with no standard deviations, confidence intervals, or per-run distributions, despite the text stating that the metrics are averaged over 20 independent runs. Because the central claim is that MAML-NSSM outperforms all baselines, the absence of dispersion measures makes it difficult to assess whether the reported gaps are significant or whether particular runs drive the improvement. Please report standard deviations or confidence intervals, and, where possible, indicate the number of independent runs used for each entry in Table III.
minor comments (6)
  1. [Section III, first paragraph] The text contains a typo: 'MAML is one one of the most well-known and widely used meta-learning algorithms' should read 'one of the most well-known'.
  2. [Section VI-B, opening sentence] The phrase 'An another motivating application' is grammatically incorrect; it should be 'Another motivating application'.
  3. [Section VI-B3 and Appendix D] There are several instances of 'Fig. Fig. 12'; the repeated 'Fig.' should be removed.
  4. [Section IV-B, Theorem 2] The theorem statement uses both sigma and the custom symbol varsigma for the swish function; please use a single consistent notation throughout.
  5. [Table II header] The column headers 'META UNIV SUP/TR20 S UP/TR80' are garbled and should be reformatted so that the three comparison models are clearly labeled.
  6. [Section V-A and Appendix B] The sentence stating that the target dataset contains 'a context and target set comprising 40960 samples and 8192 samples, respectively' is ambiguous: it should be clarified whether these numbers are per trajectory, total across the target set, or split in another way.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the meta-learning evaluation is out-of-sample and the physics constraints are constructive, not fitted-then-relabeled.

full rationale

The paper's derivation chain is self-contained. The NSSM is defined in Eqs. (2) and (4), and training minimizes standard multi-step MSE losses (3) and (5) on source and target data. MAML/ANIL updates in Eqs. (11)-(13) are standard bi-level optimizations, and the benchmark comparisons in Tables II-III evaluate predictions on target trajectories that are not used for adaptation, so the central 'meta-learning improves few-shot identification' claim is not a fitted input relabeled as a prediction. The physics constraints are also constructive rather than circular: the polytopic constraint uses the Minkowski-Weyl theorem and builds a feasible output by construction in Eq. (15), and the curl-free constraint invokes an external theorem (Theorem 1) and enforces curl-freeness by defining the output as a gradient, with smoothness supported by an independent proof (Lemma 1, Theorem 2). The only self-referential element is the statement in Section VI-A.2 that constraint incorporation improves VCS estimation, deferred to the authors' prior work [56]; that is a secondary empirical claim and does not reduce any equation or prediction in this paper to its own inputs, so it does not constitute circularity. The reviewer-level concern that Eqs. (2a)/(4a) omit an explicit input term despite Remark 1 and the input-driven case studies is a reproducibility/correctness issue, not a circularity issue.

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

No new physical entities are introduced. The learned latent state is an architectural device, not a new conserved quantity or force. The free parameters are standard meta-learning hyperparameters chosen by hand. The key domain assumptions are the similarity of source and target systems and the validity of the simulation surrogates for real physics.

free parameters (5)
  • inner-loop learning rate beta_in = 0.001 (Bouc-Wen, localization), 0.01 (van der Pol)
    Chosen by hand and varied across experiments; the method's stability and convergence depend on this value.
  • outer-loop learning rate beta_out = 0.001 (Bouc-Wen), 0.001 (van der Pol), 0.0001 (localization)
    Hand-selected meta-training hyperparameter; performance is known to be sensitive to this choice.
  • number of inner-loop adaptation steps M = 40 (Bouc-Wen, van der Pol), 10 (localization)
    Adaptation budget chosen by hand; the paper notes a practical lower bound near 10% target data for the van der Pol case.
  • latent dimension n_psi = 16 (Bouc-Wen), 128 (van der Pol, localization)
    Determined by architecture search; the dimensionality of the learned Koopman-like latent space is a key capacity choice.
  • past window length H and prediction horizon H_p = H=20 Bouc-Wen; H=10, H_p=5 van der Pol
    User-defined window lengths that define the structure of the state-space model and affect the learning task.
assumptions (5)
  • domain assumption Source and target systems share a parameter space Theta and the target parameter lies in Theta
    Section II-D assumes theta* in compact Theta and samples source systems uniformly from Theta; this is the basis for transfer and is not validated on out-of-distribution targets.
  • domain assumption Measurement and process noise are zero-mean Gaussian with known covariances for EKF
    Section II-C assumes Gaussian uncertainties; the neural model mismatch is folded into w and eta.
  • standard math The polytopic state constraints can be represented as a cone generated by a fixed ray matrix R (Minkowski-Weyl)
    Section IV-A uses the conic representation of a homogeneous polytope; valid when Gx <= 0 is homogeneous.
  • standard math Curl-free magnetic fields can be represented as gradients of a scalar potential (Poincare lemma)
    Section IV-B invokes Theorem 1 from vector calculus.
  • ad hoc to paper Varying heat-exchanger pipe lengths emulates varying refrigerant mass in the VCS simulator
    Section VI-A.1 uses pipe length variation as a surrogate for refrigerant mass; the equivalence is not demonstrated.

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Cite this review

Pith. "Pith review of Meta-Learning for Physically-Constrained Neural System Identification." pith.science (2026). https://pith.science/paper/WCOMTJFR

@misc{pith2026250106167,
  author       = {Pith},
  title        = {Pith review of: Meta-Learning for Physically-Constrained Neural System Identification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WCOMTJFR}},
  note         = {Machine review of arXiv:2501.06167}
}
read the original abstract

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.

Figures

Figures reproduced from arXiv: 2501.06167 by the authors.

Figure 1
Figure 1. Neural state-space models: general abstraction, and specific models for different target dataset composition. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Performance of meta-learning for Example 1. [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Comparison of MAML-SSM with baselines. ( [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: RMSE (averaged over 20 runs) heatmap produced by tuning subnetworks with ANIL. [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Range of HVAC dynamics induced by variable refrigerant mass. [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: Reference state trajectories (black) and those estimated by EKF using Meta-NSSM ( [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: (Left) Histograms of predictive error distribution between swish and tanh MAML. (Right) Boxplots demonstrating state estimation RMSE across different meta-learning EKF for 20 unknown target systems. 1) System Description: The scenario we consider is the example used in…
Figure 8
Figure 8. Figure 8: Performance of MetaL-EKF with MAML-FT/Swish for a randomly chosen test vehicle under uncertain [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Schematic diagram of the overall meta-learning process. [PITH_FULL_IMAGE:figures/full_fig_p027_9.png]
Figure 10
Figure 10. Figure 10: (Left) Various hysteresis loops over all source systems by varying parameters. (Right) Clusters obtained by clustering hysteresis loops [PITH_FULL_IMAGE:figures/full_fig_p029_10.png]
Figure 11
Figure 11. Figure 11: The unbounded swish and bounded tanh activation function and their derivatives [PITH_FULL_IMAGE:figures/full_fig_p030_11.png]
Figure 12
Figure 12. Figure 12: Illustration of magnetic field estimation error with MAML with different activation functions. [PITH_FULL_IMAGE:figures/full_fig_p030_12.png]

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Works this paper leans on

59 extracted references · 50 canonical work pages

  1. [56]

    Physics-constrained deep autoencoded kalman filters for estimating vapor compression system states,

    V . M. Deshpande, A. Chakrabarty, A. P. Vinod et al. , “Physics-constrained deep autoencoded kalman filters for estimating vapor compression system states,” IEEE Control Systems Letters , vol. 7, pp. 3483–3488, 2023

    work page 2023

  2. [1]

    State-space neural network. Properties and application,

    J. M. Zamarre ˜no and P. Vega, “State-space neural network. Properties and application,” Neural networks, vol. 11, no. 6, pp. 1099–1112, 1998

    work page 1998

  3. [2]

    Identification of state-space linear parameter-varying models using artificial neural networks,

    Y . Bao, J. M. Velni, A. Basina et al., “Identification of state-space linear parameter-varying models using artificial neural networks,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 5286–5291, 2020

    work page 2020

  4. [3]

    Learning neural state-space models: do we need a state estimator?

    M. Forgione, M. Mejari, and D. Piga, “Learning neural state-space models: do we need a state estimator?” arXiv preprint arXiv:2206.12928, 2022

    arXiv 2022

  5. [4]

    Constructing Neural Network-Based Models for Simulating Dynamical Systems

    C. M. Legaard, T. Schranz, G. Schweiger et al., “Constructing neural network-based models for simulating dynamical systems,” arXiv preprint arXiv:2111.01495, 2021

    work page Pith review arXiv 2021

  6. [5]

    Model structures and fitting criteria for system identification with neural networks,

    M. Forgione and D. Piga, “Model structures and fitting criteria for system identification with neural networks,” in 2020 IEEE 14th International Conference on Application of Information and Communication Technologies (AICT) . IEEE, 2020, pp. 1–6

    work page 2020

  7. [6]

    dynoNet: A neural network architecture for learning dynamical systems,

    ——, “dynoNet: A neural network architecture for learning dynamical systems,” International Journal of Adaptive Control and Signal Processing, vol. 35, no. 4, pp. 612–626, 2021

    work page 2021

  8. [7]

    Automating discovery of physics-informed neural state space models via learning and evolution,

    E. Skomski, J. Drgo ˇna, and A. Tuor, “Automating discovery of physics-informed neural state space models via learning and evolution,” in Learning for Dynamics and Control . PMLR, 2021, pp. 980–991

    work page 2021

Show all 59 references
  1. [8]

    Learning nonlinear state–space models using autoencoders,

    D. Masti and A. Bemporad, “Learning nonlinear state–space models using autoencoders,” Automatica, vol. 129, p. 109666, 2021

    2021

  2. [9]

    Deep identification of nonlinear systems in Koopman form,

    L. C. Iacob, G. I. Beintema, M. Schoukens et al. , “Deep identification of nonlinear systems in Koopman form,” in 2021 60th IEEE Conference on Decision and Control (CDC) . IEEE, 2021, pp. 2288–2293

    2021

  3. [10]

    On learning Hamiltonian systems from data,

    T. Bertalan, F. Dietrich, I. Mezi ´c et al., “On learning Hamiltonian systems from data,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 12, p. 121107, 2019

    2019

  4. [11]

    Nonlinear state-space identification using deep encoder networks,

    G. Beintema, R. Toth, and M. Schoukens, “Nonlinear state-space identification using deep encoder networks,” in Learning for Dynamics and Control. PMLR, 2021, pp. 241–250

    2021

  5. [12]

    Dynamical systems of continuous spectra,

    B. O. Koopman and J. van Neumann, “Dynamical systems of continuous spectra,” Proceedings of the National Academy of Sciences , vol. 18, no. 3, pp. 255–263, 1932

    1932

  6. [13]

    Deep learning for universal linear embeddings of nonlinear dynamics,

    B. Lusch, J. N. Kutz, and S. L. Brunton, “Deep learning for universal linear embeddings of nonlinear dynamics,” Nature communications, vol. 9, no. 1, pp. 1–10, 2018

    2018

  7. [14]

    Identifying the dynamics of a system by leveraging data from similar systems,

    L. Xin, L. Ye, G. Chiu et al. , “Identifying the dynamics of a system by leveraging data from similar systems,” in 2022 American Control Conference (ACC), 2022, pp. 818–824

    2022

  8. [15]

    From system models to class models: An in-context learning paradigm,

    M. Forgione, F. Pura, and D. Piga, “From system models to class models: An in-context learning paradigm,” IEEE Control Systems Letters, 2023

    2023

  9. [16]

    On the adaptation of in-context learners for system identification,

    D. Piga, F. Pura, and M. Forgione, “On the adaptation of in-context learners for system identification,” IFAC-PapersOnLine, vol. 58, no. 15, pp. 277–282, 2024

    2024

  10. [17]

    Linear and nonlinear system identification under ℓ1-and group-lasso regularization via L-BFGS-B,

    A. Bemporad, “Linear and nonlinear system identification under ℓ1-and group-lasso regularization via L-BFGS-B,” arXiv:2403.03827, 2024

    2024 arXiv

  11. [18]

    Calibrating building simulation models using multi-source datasets and meta-learned Bayesian optimization,

    S. Zhan, G. Wichern, C. Laughman et al. , “Calibrating building simulation models using multi-source datasets and meta-learned Bayesian optimization,” Energy and Buildings , vol. 270, p. 112278, 2022

    2022

  12. [19]

    Optimizing closed-loop performance with data from similar systems: A Bayesian meta-learning approach,

    A. Chakrabarty, “Optimizing closed-loop performance with data from similar systems: A Bayesian meta-learning approach,” in Proc. IEEE Conf. Dec. Control (CDC) . IEEE, 2022, p. To appear

    2022

  13. [20]

    Adaptive-control-oriented meta-learning for nonlinear systems,

    S. M. Richards, N. Azizan, J. E. Slotine et al. , “Adaptive-control-oriented meta-learning for nonlinear systems,” CoRR, vol. abs/2103.04490, 2021

    2021 arXiv

  14. [21]

    Meta learning MPC using finite-dimensional Gaussian process approximations,

    E. Arcari, A. Carron, and M. N. Zeilinger, “Meta learning MPC using finite-dimensional Gaussian process approximations,” arXiv preprint arXiv:2008.05984, 2020

    2008 arXiv

  15. [22]

    Meta-learning guarantees for online receding horizon learning control,

    D. Muthirayan and P. P. Khargonekar, “Meta-learning guarantees for online receding horizon learning control,” arXiv preprint arXiv:2010.11327, 2020

    2010 arXiv

  16. [23]

    MPC of uncertain nonlinear systems with meta-learning for fast adaptation of neural predictive models,

    J. Yan, A. Chakrabarty, A. Rupenyan et al. , “MPC of uncertain nonlinear systems with meta-learning for fast adaptation of neural predictive models,” in 2024 IEEE 20th International Conference on Automation Science and Engineering (CASE) , 2024, pp. 1910–1915. 24

    2024

  17. [24]

    Model-agnostic meta-learning for fast adaptation of deep networks,

    C. Finn, P. Abbeel, and S. Levine, “Model-agnostic meta-learning for fast adaptation of deep networks,” in International conference on machine learning . PMLR, 2017, pp. 1126–1135

    2017

  18. [25]

    How to train your MAML,

    A. Antoniou, H. Edwards, and A. Storkey, “How to train your MAML,” in Proc. of the Int. Conf. on Learning Representations (ICLR) , 2019

    2019

  19. [26]

    Rapid learning or feature reuse? Towards understanding the effectiveness of MAML,

    A. Raghu, M. Raghu, S. Bengio et al., “Rapid learning or feature reuse? Towards understanding the effectiveness of MAML,” in Proc. of the Int. Conf. on Learning Representations (ICLR) , 2019

    2019

  20. [27]

    Meta-learning with implicit gradients,

    A. Rajeswaran, C. Finn, S. M. Kakade et al. , “Meta-learning with implicit gradients,” Advances in neural information processing systems, vol. 32, 2019

    2019

  21. [28]

    Reptile: a scalable metalearning algorithm,

    A. Nichol and J. Schulman, “Reptile: a scalable metalearning algorithm,” arXiv preprint arXiv:1803.02999 , vol. 2, no. 3, p. 4, 2018

    2018 arXiv

  22. [29]

    A new first-order meta-learning algorithm with convergence guarantees,

    E. M. Chayti and M. Jaggi, “A new first-order meta-learning algorithm with convergence guarantees,” arXiv preprint arXiv:2409.03682, 2024

    2024 arXiv

  23. [30]

    Mauroy, Y

    A. Mauroy, Y . Susuki, and I. Mezi ´c, Koopman Operator In Systems And Control . Springer, 2020

    2020

  24. [31]

    J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems . Chapman and Hall/CRC, 2004

    2004

  25. [32]

    Double description method revisited,

    K. Fukuda and A. Prodon, “Double description method revisited,” in Franco-Japanese and Franco-Chinese conference on combinatorics and computer science . Springer, 1995, pp. 91–111

    1995

  26. [33]

    Constrained smoothers for state estimation of vapor compression cycles,

    V . M. Deshpande, C. R. Laughman, Y . Ma et al., “Constrained smoothers for state estimation of vapor compression cycles,” in Proc. American Control Conference, 2022, pp. 2333–2340

    2022

  27. [34]

    Constrained Kalman filtering via density function truncation for turbofan engine health estimation,

    D. Simon and D. L. Simon, “Constrained Kalman filtering via density function truncation for turbofan engine health estimation,” International Journal of Systems Science , vol. 41, no. 2, pp. 159–171, 2010

    2010

  28. [35]

    Constrained state estimation – a review,

    N. Amor, G. Rasool, and N. C. Bouaynaya, “Constrained state estimation – a review,” 2022, arXiv:1807.03463

    2022 arXiv

  29. [36]

    Multi-pass extended kalman smoother with partially-known constraints for estimation of vapor compression cycles,

    V . M. Deshpande and C. R. Laughman, “Multi-pass extended kalman smoother with partially-known constraints for estimation of vapor compression cycles,” in 22nd IFAC World Congress, 2023

    2023

  30. [37]

    Modeling magnetic fields using Gaussian processes,

    N. Wahlstr ¨om, M. Kok, T. B. Sch ¨on et al., “Modeling magnetic fields using Gaussian processes,” in Int. Conf. Acoustics, Speech, and Signal Process., 2013

    2013

  31. [38]

    Linearly constrained neural networks,

    J. Hendriks, C. Jidling, A. Wills et al., “Linearly constrained neural networks,” arXiv preprint arXiv:2002.01600 , 2020

    2002 arXiv

  32. [39]

    S. J. Colley, Vector Calculus, 4th ed. Upper Saddle River, NJ: Pearson, Sep. 2011

    2011

  33. [40]

    Swish: A self-gated activation function,

    P. Ramachandran, B. Zoph, and Q. V . Le, “Swish: A self-gated activation function,” arXiv preprint arXiv:1710.05941 , 2017

    2017 arXiv

  34. [41]

    Hysteretic benchmark with a dynamic nonlinearity,

    J.-P. Noel and M. Schoukens, “Hysteretic benchmark with a dynamic nonlinearity,” in Workshop on nonlinear system identification benchmarks, 2016, pp. 7–14

    2016

  35. [42]

    On the initialization of nonlinear lfr model identification with the best linear approximation,

    M. Schoukens and R. T ´oth, “On the initialization of nonlinear lfr model identification with the best linear approximation,” IFAC- PapersOnLine, vol. 53, no. 2, pp. 310–315, 2020

    2020

  36. [43]

    dynoNet: A neural network architecture for learning dynamical systems,

    M. Forgione and D. Piga, “ dynoNet: A neural network architecture for learning dynamical systems,” International Journal of Adaptive Control and Signal Processing , vol. 35, no. 4, pp. 612–626, 2021

    2021

  37. [44]

    Polynomial state-space model decoupling for the identification of hysteretic systems,

    A. F. Esfahani, P. Dreesen, K. Tiels et al. , “Polynomial state-space model decoupling for the identification of hysteretic systems,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 458–463, 2017

    2017

  38. [45]

    Automatic modeling with local model networks for benchmark processes,

    J. Belz, T. M ¨unker, T. O. Heinz et al., “Automatic modeling with local model networks for benchmark processes,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 470–475, 2017

    2017

  39. [46]

    PyTorch: An imperative style, high-performance deep learning library,

    A. Paszke, S. Gross, F. Massa et al., “PyTorch: An imperative style, high-performance deep learning library,” in Advances in Neural Information Processing Systems 32 . Curran Associates, Inc., 2019, pp. 8024–8035

    2019

  40. [47]

    How transferable are features in deep neural networks?

    J. Yosinski, J. Clune, Y . Bengio et al. , “How transferable are features in deep neural networks?” Advances in neural information processing systems, vol. 27, 2014

    2014

  41. [48]

    Digital twin design with on-line calibration for HV AC systems in buildings,

    C. Vering, S. Borges, D. Coakley et al., “Digital twin design with on-line calibration for HV AC systems in buildings,” in Proceedings of Building Simulation 2021: 17th Conference of IBPSA , ser. Building Simulation, vol. 17. Bruges, Belgium: IBPSA, September 2021, pp. 2938–2945

    2021

  42. [49]

    Digital Twins of Vapor Compression Cycles: Challenges and Opportunities,

    C. R. Laughman, V . M. Deshpande, H. Qiao et al. , “Digital Twins of Vapor Compression Cycles: Challenges and Opportunities,” in Proc. Int. Congress of Refrigeration (ICR) , 2023

    2023

  43. [50]

    𝐻∞ loop-shaped model predictive control with heat pump application,

    S. Bortoff, P. Schwerdtner, C. Danielson et al. , “𝐻∞ loop-shaped model predictive control with heat pump application,” in 18th European Control Conference, 2019, pp. 2386–2393

    2019

  44. [51]

    Scalable Bayesian optimization for model calibration: Case study on coupled building and HV AC dynamics,

    A. Chakrabarty, E. Maddalena, H. Qiao et al., “Scalable Bayesian optimization for model calibration: Case study on coupled building and HV AC dynamics,”Energy and Buildings , vol. 253, p. 111460, 2021

    2021

  45. [52]

    Controller tuning by Bayesian optimization an application to a heat pump,

    M. Khosravi, A. Eichler, N. Schmid et al., “Controller tuning by Bayesian optimization an application to a heat pump,” in Proc. 18th European Control Conference. IEEE, 2019, pp. 1467–1472

    2019

  46. [53]

    Accelerating self-optimization control of refrigerant cycles with bayesian optimization and adaptive moment estimation,

    A. Chakrabarty, C. Danielson, S. A. Bortoff et al., “Accelerating self-optimization control of refrigerant cycles with bayesian optimization and adaptive moment estimation,” Applied Thermal Engineering , vol. 197, p. 117335, 2021

    2021

  47. [54]

    Transient modeling of a flash tank vapor injection heat pump system–Part I: Model development,

    H. Qiao, V . Aute, and R. Radermacher, “Transient modeling of a flash tank vapor injection heat pump system–Part I: Model development,” International Journal of Refrigeration , vol. 49, pp. 169–182, 2015. 25

    2015

  48. [55]

    Learning residual dynamics via physics-augmented neural networks: Application to vapor compression cycles,

    R. Chinchilla, V . M. Deshpande, A. Chakrabarty et al., “Learning residual dynamics via physics-augmented neural networks: Application to vapor compression cycles,” in 2023 American Control Conference (ACC) , 2023, pp. 4069–4076

    2023

  49. [57]

    Constrained gaussian-process state-space models for online magnetic-field estimation,

    K. Berntorp and M. Menner, “Constrained gaussian-process state-space models for online magnetic-field estimation,” in Proc. 26th Int. Conf. on Information Fusion (FUSION) . IEEE, 2023, pp. 1–7

    2023

  50. [58]

    How feasible is the use of magnetic field alone for indoor positioning?

    B. Li, T. Gallagher, A. G. Dempster et al. , “How feasible is the use of magnetic field alone for indoor positioning?” in Int. Conf. Indoor Positioning and Indoor Navigation , 2012

    2012

  51. [59]

    Characterization of the indoor magnetic field for applications in localization and mapping,

    M. Angermann, M. Frassl, M. Doniec et al., “Characterization of the indoor magnetic field for applications in localization and mapping,” in Int. Conf. Indoor Positioning and Indoor Navigation , 2012. 26 APPENDIX A OVERALL META -LEARNING PROCESS WITH MAML AND SYSTEM IDENTIFICAT...

    2012

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.