LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification

Arunabh Singh; Joyjit Mukherjee

REVIEW 3 major objections 5 minor 15 references

LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read LeARN meta-learns the basis-function library and selection matrix from data, matching SINDy's quadrotor dynamics error without a predefined library.

desk verdict A genuinely new way to learn SINDy basis functions via MAML, with plausible SINDy-competitive errors, but the key Lipschitz regularizer is mis-specified and its hyperparameters are unreported. read the letter →

arxiv 2412.12036 v2 pith:GVNXITE7 submitted 2024-12-16 cs.LG cs.RO

Arunabh Singh , Joyjit Mukherjee This is my paper · ORCID

classification cs.LGcs.RO

keywords systemidentificationmeta-learningbasisfunctionlibrarysparseofnonlineardynamicsquadrotorNeuralFlydatasetMAMLadaptive

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

LeARN is a system identification method that removes the human step of choosing a basis-function library: it meta-learns both the library $\Theta(X;\psi)$ and the coefficient-selection matrix $E(X;\phi)$ from data using MAML, then adapts the pair to a new dynamical regime with a few gradient steps. On the Neural Fly quadrotor benchmark, the reported adaptation errors on four unseen wind conditions are competitive with SINDy's, which uses a hand-picked trigonometric library. The authors' aim is to show that interpretable, linear-in-basis dynamics can be discovered autonomously, without domain-specific interventions, while staying competitive with a strong baseline.

What carries the argument

The load-bearing object is the parameterized pair $(\Theta(X;\psi),\, E(X;\phi))$: a lightweight DNN with GELU activations produces a small set of learned basis functions, and a second DNN produces the feature-selection matrix that linearly combines them, mirroring SINDy's $\Theta E$ structure. MAML's inner loop adapts $\psi$ and $\phi$ on a task's training data, while the outer loop optimizes the meta-parameters over the distribution of wind tasks. At adaptation time, Eq. (9)--(10) adds a regularizer that enforces $L$-Lipschitz continuity of the state features, tying the learned representation to a stability assumption about the new regime.

What would settle it

Take a test wind condition with a sharp discontinuity, such as a sudden step change in wind speed, estimate the actual Lipschitz constant of the data, and run LeARN's adaptation with $\lambda=0$ versus the reported $\lambda$. If the adaptation error does not stay close to the reported values whenever the chosen $L$ is violated, the claimed fast adaptation depends on a tuning assumption rather than a general guarantee. Alternatively, a sweep of $L$ and $\lambda$ over a decade each would show whether reported errors are stable or isolated points.

Watch

Extended reading notes

Core claim

The central claim is that model-agnostic meta-learning can internalize a basis-function library and its feature selection so that fast adaptation to new dynamics becomes possible without redesigning the model. The paper models the dynamics as $\dot{x} \approx \Theta(X;\psi) E(X;\phi)^T$, with $\psi$ and $\phi$ meta-trained over wind conditions from 0 to 50 m/s and adapted to 35, 70psin20, 70, and 100 m/s conditions. For full quadrotor dynamics, the reported LeARN adaptation errors are 0.264041, 0.335513, 0.379029, and 0.644668, compared with SINDy's 0.306774, 0.339417, 0.375176, and 0.632472; generalization errors are likewise close. The authors emphasize that the gap shrinks as the concatenated input dimension grows, making the learned-library approach most competitive for higher-dimensional systems.

Load-bearing premise

The adaptation step assumes the state features are $L$-Lipschitz continuous with a constant $L$ and a regularization weight $\lambda$ that are chosen but neither estimated from data nor reported, and no sensitivity analysis shows how the results depend on them.

Editorial extensions

If this is right

System identification can proceed without a hand-crafted library; the learned $\Theta(X;\psi)$ supplies the basis terms directly from data.
Adaptation to a new wind regime needs only the meta-trained parameters and a short inner-loop update, so deployment-time re-tuning is lightweight.
The linear-in-basis form is retained, so the contributing terms in the learned model remain inspectable in the same way SINDy's are.
For higher-dimensional input features, LeARN's performance gap to SINDy narrows, suggesting the approach scales better as more state and control channels are added.

Reading between the lines

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

A natural extension is to estimate $L$ from data and report sensitivity to $\lambda$; the paper leaves both as chosen constants, so the adaptation guarantee is conditional on them.
The two-basis-function DNN suffices because the evaluation trajectories are oscillatory (figure-eight); for non-oscillatory regimes a larger learned library would likely be needed.
The Lipschitz regularizer in Eq. (10) suggests an online, sample-by-sample adaptation loop, which the paper presents but does not push to a continual-learning setting.

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.

Desk Editor's Note

read the letter

Worth knowing: this is the first system-ID paper I've seen that meta-learns the basis-function library itself rather than coordinates or residual terms. The idea is simple and clean: a light DNN outputs both Theta(X; psi) and E(X; phi), and MAML adapts them per wind condition on the Neural Fly dataset. The reported errors are close to SINDy across all three dynamics formulations, and the gap narrows as input dimension grows. That is a real, if modest, contribution.

The setup is also fair: SINDy gets sin/cos basis functions, which suit the oscillatory figure-eight trajectory, and LeARN uses just two learned basis functions. The paper explicitly acknowledges the trajectory's trigonometric nature, which is honest.

Soft spots, in ascending order. First, the regularizer in Eq. (10) is not a Lipschitz penalty. A true Lipschitz bound on f w.r.t. X would need ||f(X_t)-f(X_{t-1})|| <= L||X_t-X_{t-1}||. The term written is a temporal output smoothness constraint that ignores input displacement. The text's claim that it ensures L-Lipschitz continuity of state inputs is simply not what the formula does. Second, neither lambda nor L is reported anywhere, and there is no sensitivity analysis. If those matter—and the adaptation step depends on them—the results are under-specified. Third, there are no error bars, no seeds, and no code, so the point estimates are not trustable at face value. Fourth, the conclusion's statement that the method provides a generalization 'guarantee' is not derived from anything in the paper and should be removed.

The citation pattern looks fine: Brunton, Finn, O'Connell are all placed correctly, and the related work is not misleading. This is a paper with a clear, new mechanism and honest reporting of the central comparison, but with a load-bearing technical detail that is mis-specified and unreported hyperparameters that need to be pinned down.

I would send this to a serious referee. The idea is worth exploring and the experiments are directionally supportive, but the regularizer needs to be corrected or re-justified, hyperparameters reported, and ideally variance accounted for. A revised version with those fixes could be solid. For now, treat the numbers as plausible but unconfirmed.

Referee Report

3 major / 5 minor

Summary. The paper proposes LeARN, a meta-learning framework for nonlinear system identification that replaces SINDy's hand-crafted basis-function library with a learned library Θ(X; ψ) and a learned feature-selection matrix E(X; ϕ), optimized via MAML and then adapted online to new wind conditions. The method is evaluated on the Neural Fly quadrotor dataset for full, attitude, and translational dynamics, and the reported mean-squared errors are competitive with SINDy across four unseen wind conditions. The paper also claims that learning the basis functions removes the need for domain expertise and that the adaptation procedure offers a generalization guarantee.

Significance. If the empirical claims are substantiated, LeARN is a useful contribution to data-driven system identification: it demonstrates that a lightweight meta-learned representation can reach SINDy-level accuracy on a challenging robotics benchmark without a predefined trigonometric library, and it addresses a known limitation of SINDy. The paper's strengths include evaluation on a public dataset, comparison across three dynamics formulations, transparent numerical tables, and a clear qualitative comparison. Its significance is currently limited by the absence of uncertainty quantification, the unsupported 'guarantee' in the conclusion, and the mis-specified regularizer that underlies the adaptation mechanism.

major comments (3)

[Section 4.2, Eq. (10)] The regularizer in Eq. (10) is not a Lipschitz penalty as claimed. A Lipschitz condition on f with respect to X requires bounding ||f(X_t) - f(X_{t-1})|| by L·||X_t - X_{t-1}||, but the implemented term omits the input displacement ||X_t - X_{t-1}|| and instead penalizes the temporal output difference. At a fixed sampling rate this enforces temporal output smoothness, not Lipschitz continuity in the state, so the stated assumption is not implemented. Moreover, the values of λ and L are not reported anywhere, and no sensitivity analysis is given, so the adaptation results in Tables 1-6 could depend on unreported and possibly mis-specified hyperparameters. Please correct the regularizer to reflect the stated assumption, or rephrase the claim, and report the chosen values together with a sensitivity study.
[Section 5.2, Tables 1-6] All reported errors are point estimates with no error bars, no multiple seeds, and no statistical comparison. Several differences between SINDy and LeARN are small (for example, full dynamics 70wind: 0.379029 vs. 0.375176; translational 35wind: 0.154989 vs. 0.155732), and without variance estimates it is impossible to judge whether 'competitive performance' is a stable outcome or within run-to-run noise. Please report the mean and standard deviation over multiple random seeds, and where possible a paired comparison across the same evaluation folds.
[Section 6, Conclusion] The statement that the approach 'provides a guarantee that given sufficient gradient steps, the model can generalize effectively to challenging dynamical conditions' is not derived anywhere in the paper and is not established by the experiments. No convergence or generalization theorem is proved, and the empirical results are limited to four wind conditions. Please remove the claim or replace it with a precise statement of what is actually shown.

minor comments (5)

[Section 5.1] The sentence 'We use a lightweight fully connected DNN parameterized by ψ, with GELU activations to model the basis function library' is repeated verbatim, with the second occurrence adding 'Θ'. Please delete the duplicate.
[Section 2 and Section 3.2] There are several typographical errors: 'machine learnin' should be 'machine learning', 'SINDy (Brunton et al., 2016) represents formulates' is ungrammatical, and 'the optimal meta-parametersθ∗' is missing a space. Please proofread the text.
[Section 3.2, Eq. (2) and Algorithm 1] Eq. (2) shows a single gradient-based adaptation step, while Algorithm 1 performs n inner-loop rounds. Please clarify whether the formulation in Eq. (2) is intended to represent the general case or a simplified one-step special case.
[Figure 1 caption] The dimension notation is inconsistent: the caption states E(X; ϕ) ∈ R^{I×P(I+U)} but later refers to 'n = I sets of coefficients' with e_k ∈ R^{1×(P+U)}. Please align the notation and define P and U consistently with Section 4.2.
[Section 5.1] The claim that the method needs no prior domain knowledge is partly softened by the design choice to set the number of learned basis functions to two based on 'extensive experimentation' with the Neural Fly dataset. Please clarify how the number of basis functions is selected and whether this choice transfers to other systems.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation found: LeARN's basis functions are meta-learned from data and evaluated on held-out wind conditions, so the reported SINDy-competitive errors are empirical measurements rather than constructed equivalences.

full rationale

The paper's central claim is that the meta-learned basis functions in Eq. (8), trained via MAML in Algorithm 1, achieve competitive dynamical error to SINDy on unseen wind conditions. This claim is supported by held-out evaluation: the meta-training tasks are wind conditions from nowind through 50wind, while the reported adaptation and generalization errors are for 35wind, 70psin20, 70wind, and 100wind. The learned library is not defined in terms of the evaluation metric, and the coefficients E(X; phi) are optimized on training tasks rather than fitted to the target wind condition before evaluation. There is no fitted parameter that is renamed a prediction, no load-bearing self-citation chain, and no uniqueness theorem imported from the authors' prior work. The regularizer in Eq. (10) is mis-specified as a Lipschitz penalty because it omits the input displacement ||X_t - X_{t-1}||, and the hyperparameters lambda and L are not reported; however, this is an experimental specification and reporting issue, not a circularity, because the reported errors still depend on data rather than being equivalent to the model's inputs by construction. Overall, the derivation chain is self-contained and the empirical comparison is a standard train/evaluate procedure.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or conserved quantities. It does introduce several modeling choices that act as free parameters or untested assumptions: the Lipschitz regularizer (L, lambda), the number of basis functions, and the DNN architecture. These are not fitted from data in the traditional sense but are chosen ad hoc and not reported, which affects reproducibility. The rigid-body quadrotor model is a standard domain assumption, and the meta-learning task distribution is assumed to generalize to unseen wind conditions.

free parameters (5)

Lipschitz constant L = not reported
Introduced in Eq (10) for the adaptation regularizer; the paper does not estimate it and provides no sensitivity analysis.
Lipschitz regularizer weight lambda = not reported
Hyperparameter in Eq (10) that controls the penalty strength; its value is not given.
Number of learned basis functions P = 2
Set to two to match the sin(x), cos(x) library chosen for SINDy, per Section 5.1.
SINDy sparsity threshold = 0.2
Set for the SINDy baseline in Section 5.1; influences the comparison.
Inner-loop and meta-learning step sizes alpha and beta = not reported
MAML training hyperparameters in Alg 1; values are not reported.

assumptions (4)

domain assumption The quadrotor dynamics decompose as in Eq (3)-(4), with known rigid-body equations.
Used to set up the learning problem; standard physics but an assumption about the system being modeled.
domain assumption Tasks defined by training wind conditions form a distribution from which unseen wind conditions are drawn.
Underpins the meta-learning framing; not proven for the evaluation wind conditions.
ad hoc to paper A lightweight DNN with GELU activations can represent a sufficiently expressive basis library.
Architecture choice in Section 5.1; no analysis of representational sufficiency or capacity bounds.
ad hoc to paper State features are L-Lipschitz continuous as used in the adaptation regularizer.
Assumed in Eq (9)-(10) without estimation of L, and the claim of fast adaptation depends on it.

how reviews work

0 comments

Cite this review

Pith. "Pith review of LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification." pith.science (2026). https://pith.science/paper/GVNXITE7

@misc{pith2026241212036,
  author       = {Pith},
  title        = {Pith review of: LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GVNXITE7}},
  note         = {Machine review of arXiv:2412.12036}
}

read the original abstract

System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach, distilling complex dynamical behaviors into interpretable linear combinations of basis functions. However, SINDy's reliance on domain-specific expertise to construct its foundational 'library' of basis functions limits its adaptability and universality. In this work, we introduce a nonlinear system identification framework LeARN that transcends the need for prior domain knowledge by learning the library of basis functions directly from data. To enhance adaptability to evolving system dynamics under varying noise conditions, we employ a novel meta-learning-based system identification approach that utilizes a light-weight Deep Neural Network (DNN) to dynamically refine these basis functions. This not only captures intricate system behaviors but also adapts effectively to new dynamical regimes. We validate our framework on the Neural Fly dataset, showcasing its robust adaptation and generalization capabilities. Despite its simplicity, our LeARN achieves competitive dynamical error performance to SINDy. This work presents a step towards autonomous discovery of dynamical systems, paving the way for a future where machine learning uncovers the governing principles of complex systems without requiring extensive domain-specific interventions.

Figures

Figures reproduced from arXiv: 2412.12036 by the authors.

**Figure 2.** Qualitative results of the full dynamics modeled by SINDy and LeARN across different wind conditions. Background represents the ground truth dynamics. Then, we have Adaptation performance , and the Generalization performance on unseen data. The horizontal axis runs across 2511 data points and the vertical axis represents the value. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 3 canonical work pages

[10]

doi: 10.1126/scirobotics.abm6597

ISSN 2470-9476. doi: 10.1126/scirobotics.abm6597. URL http://dx.doi.org/ 10.1126/scirobotics.abm6597. M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics , 378:686–707,

doi:10.1126/scirobotics.abm6597
[11]

doi: https://doi.org/10

ISSN 0021-9991. doi: https://doi.org/10. 1016/j.jcp.2018.10.045. URL https://www.sciencedirect.com/science/article/pii/ S0021999118307125. 11 SINGH MUKHERJEE Spencer M. Richards, Navid Azizan, Jean-Jacques Slotine, and Marco Pavone. Adaptive-control-oriented meta-learning for nonlinear systems,

work page 2018
[13]

URL https://doi.org/10.1109/ICRA.2019.8794351

doi: 10.1109/ICRA.2019.8794351. URL https://doi.org/10.1109/ICRA.2019.8794351. Guanya Shi, Wolfgang H ¨onig, Yisong Yue, and Soon-Jo Chung. Neural-swarm: Decentralized close- proximity multirotor control using learned interactions,

arXiv 2019
[14]

Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions

URL https://arxiv.org/abs/ 2003.02992. Russ Tedrake. Underactuated Robotics

work page Pith review arXiv 2003
[1980]

URL https://digital-library

doi: 10.1049/ip-d.1980.0047. URL https://digital-library. 10 LEARNABLE BASIS FUNCTIONS FOR SYSTEM IDENTIFICATION theiet.org/doi/abs/10.1049/ip-d.1980.0047. 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 Scien...

work page arXiv 1980
[1990]

Michael O’Connell, Guanya Shi, Xichen Shi, Kamyar Azizzadenesheli, Anima Anandkumar, Yisong Yue, and Soon-Jo Chung

doi: 10.1109/72.80202. Michael O’Connell, Guanya Shi, Xichen Shi, Kamyar Azizzadenesheli, Anima Anandkumar, Yisong Yue, and Soon-Jo Chung. Neural-fly enables rapid learning for agile flight in strong winds. Science Robotics, 7(66), May

doi:10.1109/72.80202
[1996]

URL http://www.jstor.org/ stable/2346178

ISSN 00359246. URL http://www.jstor.org/ stable/2346178. Vladimir N Vapnik. The Nature of Statistical Learning Theory. Springer,

arXiv
[1998]

doi: 10.1007/978-1-4612-1768-8

ISBN 978-1-4612-1768-8. doi: 10.1007/978-1-4612-1768-8

doi:10.1007/978-1-4612-1768-8

Show all 15 references

[2010]

doi: https://doi.org/10.1016/j.arcontrol.2009.12.001

ISSN 1367-5788. doi: https://doi.org/10.1016/j.arcontrol.2009.12.001. URL https://www. sciencedirect.com/science/article/pii/S1367578810000027. K.S. Narendra and K. Parthasarathy. Identification and control of dynamical systems using neural networks. IEEE Transactions on Neura...

2009 doi
[2016]

URL https://www.pnas.org/doi/ abs/10.1073/pnas.1517384113

doi: 10.1073/pnas.1517384113. URL https://www.pnas.org/doi/ abs/10.1073/pnas.1517384113. Kathleen Champion, Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton. Data-driven discovery of co- ordinates and governing equations. Proceedings of the National Academy of Sciences , 1...

doi
[2017]

Edward Grefenstette, Brandon Amos, Denis Yarats, Phu Mon Htut, Artem Molchanov, Franziska Meier, Douwe Kiela, Kyunghyun Cho, and Soumith Chintala

URL https://arxiv.org/abs/1703.03400. Edward Grefenstette, Brandon Amos, Denis Yarats, Phu Mon Htut, Artem Molchanov, Franziska Meier, Douwe Kiela, Kyunghyun Cho, and Soumith Chintala. Generalized inner loop meta-learning. arXiv preprint arXiv:1910.01727,

1910 arXiv
[2019]

URL https://www.pnas.org/doi/abs/10

doi: 10.1073/pnas.1906995116. URL https://www.pnas.org/doi/abs/10. 1073/pnas.1906995116. 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 system...

doi
[2020]

URL https://doi.org/10

doi: 10.21105/joss.02104. URL https://doi.org/10. 21105/joss.02104. Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks,

doi
[2021]

Guanya Shi, Xichen Shi, Michael O’Connell, Rose Yu, Kamyar Azizzadenesheli, Animashree Anandkumar, Yisong Yue, and Soon-Jo Chung

URL https://arxiv.org/abs/2103.04490. Guanya Shi, Xichen Shi, Michael O’Connell, Rose Yu, Kamyar Azizzadenesheli, Animashree Anandkumar, Yisong Yue, and Soon-Jo Chung. Neural lander: Stable drone landing control using learned dynamics. In 2019 International Conference on Robot...

2019 arXiv
[2022]

Lennart Ljung

doi: 10.1109/TPAMI.2021.3079209. Lennart Ljung. System Identification , pages 163–173. Birkh ¨auser Boston, Boston, MA,

2021

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [10]

doi: 10.1126/scirobotics.abm6597

ISSN 2470-9476. doi: 10.1126/scirobotics.abm6597. URL http://dx.doi.org/ 10.1126/scirobotics.abm6597. M. Raissi, P. Perdikaris, and G.E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics , 378:686–707,

doi:10.1126/scirobotics.abm6597

[2] [11]

doi: https://doi.org/10

ISSN 0021-9991. doi: https://doi.org/10. 1016/j.jcp.2018.10.045. URL https://www.sciencedirect.com/science/article/pii/ S0021999118307125. 11 SINGH MUKHERJEE Spencer M. Richards, Navid Azizan, Jean-Jacques Slotine, and Marco Pavone. Adaptive-control-oriented meta-learning for nonlinear systems,

work page 2018

[3] [13]

URL https://doi.org/10.1109/ICRA.2019.8794351

doi: 10.1109/ICRA.2019.8794351. URL https://doi.org/10.1109/ICRA.2019.8794351. Guanya Shi, Wolfgang H ¨onig, Yisong Yue, and Soon-Jo Chung. Neural-swarm: Decentralized close- proximity multirotor control using learned interactions,

arXiv 2019

[4] [14]

Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions

URL https://arxiv.org/abs/ 2003.02992. Russ Tedrake. Underactuated Robotics

work page Pith review arXiv 2003

[5] [1980]

URL https://digital-library

doi: 10.1049/ip-d.1980.0047. URL https://digital-library. 10 LEARNABLE BASIS FUNCTIONS FOR SYSTEM IDENTIFICATION theiet.org/doi/abs/10.1049/ip-d.1980.0047. 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 Scien...

work page arXiv 1980

[6] [1990]

Michael O’Connell, Guanya Shi, Xichen Shi, Kamyar Azizzadenesheli, Anima Anandkumar, Yisong Yue, and Soon-Jo Chung

doi: 10.1109/72.80202. Michael O’Connell, Guanya Shi, Xichen Shi, Kamyar Azizzadenesheli, Anima Anandkumar, Yisong Yue, and Soon-Jo Chung. Neural-fly enables rapid learning for agile flight in strong winds. Science Robotics, 7(66), May

doi:10.1109/72.80202

[7] [1996]

URL http://www.jstor.org/ stable/2346178

ISSN 00359246. URL http://www.jstor.org/ stable/2346178. Vladimir N Vapnik. The Nature of Statistical Learning Theory. Springer,

arXiv

[8] [1998]

doi: 10.1007/978-1-4612-1768-8

ISBN 978-1-4612-1768-8. doi: 10.1007/978-1-4612-1768-8

doi:10.1007/978-1-4612-1768-8