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REVIEW 4 major objections 4 minor 72 references

Meta-Learning and Knowledge Discovery based Physics-Informed Neural Network for Remaining Useful Life Prediction

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read MKDPINN combines meta-learning with a data-discovered PDE to predict machine remaining life from a few samples.

desk verdict A clever architecture and real industrial data, but the physics term is circular—Eq. (27) lets the PGR learn the identity on d u/dt—so the load-bearing claim that discovered PDEs improve few-shot RUL is not supported. read the letter →

arxiv 2504.13797 v1 pith:GZ4MAMGU submitted 2025-04-18 cs.LG cs.AI

Yu Wang , Shujie Liu , Shuai Lv , Gengshuo Liu This is my paper · ORCID
classification cs.LGcs.AI
keywords remainingusefullifepredictionmeta-learningphysics-informedneuralnetworksPDEdiscoveryfew-shotlearninghiddenstatemappingrotatingmachineryC-MAPSS
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

Remaining useful life (RUL) prediction usually needs large run-to-failure datasets and an explicit model of how machines degrade, neither of which is available for new equipment or new operating conditions. This paper proposes MKDPINN, a framework that trains a network simultaneously to map noisy multi-sensor readings into a smooth hidden degradation state, to discover the partial differential equation that governs that state, and to learn a meta-initialization that adapts to a new task from only a handful of labeled samples. The physics enters through a regularizer: the residual of the discovered PDE is added to the data loss, so predictions are pushed toward physically plausible degradation trends. The paper reports that on industrial slurry-pump data and the C-MAPSS benchmark MKDPINN outperforms data-only, physics-only, and meta-only baselines, achieving the lowest average RMSE (12.71) and SCORE (622.15) among the compared models.

What carries the argument

The load-bearing machinery is the joint regularized objective of three modules. The Hidden State Mapper (HSM) is a self-attention network that converts high-dimensional noisy sensor windows into a low-dimensional smooth hidden state; the RUL predictor is a four-layer network on the concatenation of that state and running time; and the Physics-Guided Regulator (PGR) is a neural network that maps the predicted state and its spatial derivatives to the time derivative, thereby approximating the unknown nonlinear operator $\mathcal{N}$. The physics loss in Eq. (27) is the MSE between the regulator output and the time derivative of the predicted state computed by automatic differentiation, and this term is added to the data loss to form the total loss in Eq. (29). On top of that objective, the meta-update rule in Eq. (33) moves the shared initialization toward the average of the per-task adapted parameters, which the paper shows is an implicit combination of average-loss minimization and in-task gradient alignment without second-order derivatives.

What would settle it

Train MKDPINN on synthetic run-to-failure data generated from a known nonlinear PDE, then inspect whether the PGR recovers the generating equation and whether removing the physics loss changes test error; if accurate predictions persist while the recovered operator is wrong, the physical guidance is not doing the load-bearing work.

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Extended reading notes

Core claim

The paper's central claim is that the unknown dynamics of equipment degradation can be learned as an effective PDE over a hidden state, and that embedding this discovered PDE into a first-order meta-learner improves few-shot RUL prediction beyond using either component alone. The claim is supported by two experimental regimes: cross-life-cycle and cross-machine prediction on real slurry pumps, where MKDPINN reaches RMSE 27.19 and 25.62 respectively, and a 0-shot evaluation on C-MAPSS, where its average RMSE is 12.71. The authors further claim that the model can produce meaningful RUL trends even when the 15 adaptation samples contain no degradation information, and that accuracy improves as more or later-stage samples are added.

Load-bearing premise

The method assumes that the PGR's supervised fit to time derivatives computed from training data has recovered the true PDE of degradation, and that this learned operator carries genuine physical content; if the operator is a poor model of the real dynamics, the physics loss adds little or can degrade prediction.

Editorial extensions

If this is right

  • A machine with no failure history can still receive a useful RUL estimate after a few labeled samples, because the meta-learned initialization encodes degradation priors from source machines.
  • Few-shot adaptation improves predictably with data: in the cross-machine task, RMSE drops from 43.35 at 5-shot to 19.05 at 20-shot, so users can trade labeling effort against accuracy.
  • The framework makes PINN-style constraints available for systems whose governing equations are unknown, since the PDE is discovered rather than hand-derived.
  • Because the meta-update is first-order, adapting to a new task avoids the Hessian-vector products of second-order meta-learning, reducing the computational burden relative to that class of meta-learners.

Reading between the lines

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

  • If the PGR's learned operator does not reflect true degradation physics, the regularizer may still help by acting as a data-dependent smoothing term; the paper's own ablation, where KDPINN without meta-learning raises RMSE above the Base Learner, is consistent with the regularizer being beneficial mainly inside the meta-learning loop.
  • A direct test of the physics claim would be to generate synthetic degradation data from a known nonlinear PDE and check whether the PGR recovers the generating operator; the paper does not inspect the discovered PDE itself.
  • The 0-shot C-MAPSS evaluation measures generalization from large training sets, not the few-shot adaptation regime the method is designed for, so reporting few-shot splits on C-MAPSS would separate the contribution of the meta-initialization from that of the physics term.
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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

4 major / 4 minor

Summary. The paper proposes MKDPINN, a framework for remaining-useful-life (RUL) prediction that combines a hidden-state mapper, a physics-guided regulator (PGR) that learns a PDE from data, an RUL predictor, and a first-order Reptile-style meta-learning loop. The authors claim that the discovered PDE regularizer improves accuracy and generalization in few-shot settings, and they report experiments on an industrial slurry-pump dataset and on C-MAPSS. The central scientific claim is that adding a data-discovered physics constraint to a meta-learner yields better RUL prediction than either component alone.

Significance. If the claims were valid, the paper would make a useful contribution to few-shot RUL prediction by coupling meta-learning with learned physical constraints, and the authors deserve credit for providing source code and a real industrial case study with two full life cycles. However, the central claim is not supported by the manuscript's own evidence: Eq. (27) defines the physics loss so that the PGR can trivially fit the target derivative from an input coordinate, the ablation results in Tables 1 and 2 show that the physics-only variant is worse than the base learner, and the reported C-MAPSS average SCORE claim is contradicted by Table 7. These are load-bearing issues, not presentation problems.

major comments (4)
  1. [Sec. 3.2.3, Eqs. (25)-(27)] As written, the PGR input in Eq. (27) includes the target time derivative ∂û_j/∂t itself, and the loss is the squared difference between the PGR output and that same target. The network can therefore drive L_phys to zero by approximately learning the identity map on that coordinate, so the 'physics' constraint has no independent constraining content. Even if the ∂û_j/∂t coordinate were removed, L_phys would still be a supervised regression to a derivative estimated from the training samples rather than a PDE residual evaluated at independent collocation points, so no external physical information would enter the model.
  2. [Tables 1 and 2] The ablation results contradict the claim that the PINN constraint improves accuracy. In Table 1, KDPINN has RMSE 171.33 and R² 0.13, which is worse than the Base Learner's RMSE 149.39 and R² 0.34; in Table 2, KDPINN again has higher RMSE (140.39 vs. 126.58) and lower R² (0.21 vs. 0.36) than the Base Learner. Consequently, the better performance of MKDPINN relative to the Meta Learner cannot be attributed to the physics-guided regularizer, and the paper's contribution claim that embedding the PGR 'improves' accuracy and generalization is unsupported by its own results.
  3. [Sec. 4.2.3 and Table 7] The statement that 'MKDPINN achieved the lowest average RMSE (12.71) and the lowest average SCORE (622.15) among all the compared models' is false for SCORE: the DAM model in Table 7 reports an average SCORE of 557.75, which is lower than 622.15. The average RMSE claim is arithmetically consistent with the table, but the paper should correct the SCORE claim and re-evaluate any conclusions that rely on it.
  4. [Sec. 3.3.3, Eqs. (34)-(37)] The theoretical analysis of the meta-update direction is derived for SGD, but the actual method uses Adam in the inner loop. The paper asserts that Adam's update 'can be expected' to have a structure similar to the SGD Taylor expansion, but provides no derivation or empirical verification of this equivalence. Since the first-order meta-learning update rule is central to the method, this gap leaves the theoretical justification of Eq. (33) incomplete.
minor comments (4)
  1. [Reference [50]] The arXiv identifier for the Reptile paper is malformed: it reads 'arXiv preprint arXiv:.02999' and should be 'arXiv:1803.02999'.
  2. [Sec. 4.2.2] The C-MAPSS evaluation is described as a 0-shot testing scenario because no target-domain samples are used for adaptation, but the paper elsewhere emphasizes few-shot adaptation; the relationship between the 0-shot C-MAPSS protocol and the few-shot claim should be clarified.
  3. [Eq. (42)] The SCORE formula contains confusing notation in the exponents; the subscripts and superscripts for predicted and true RUL should be cleaned up so the piecewise definition is unambiguous.
  4. [General] Several equations contain apparent OCR errors (for example, the feature vector in Eq. (26) uses ∇_d where the time derivative is presumably intended), and the text would benefit from a careful proofreading pass.

Circularity Check

2 steps flagged · score 8.0 of 10

Physics constraint is tautological: ∂u/∂t is both the operator input and the regression target in Eqs. (22) and (27).

  1. self definitional [Section 3.2.3, Eq. (22)]
    "the dynamic evolution of the equipment degradation process can be expressed as the following PDE form: ∂u(h,t)/∂t − N(u, ∂u/∂t, ∇_h u, ∇_h^2 u, …, ∇_h^k u) = 0, h ∈ Ω, t ∈ [0,T] (22)"

    The claimed PDE has ∂u/∂t both as the left-hand side and as an argument of the operator N. For any trajectory, the equation is satisfied by choosing N to return its ∂u/∂t argument. The 'discovered physical law' is therefore a tautology: it imposes no independent constraint on the hidden-state evolution or on the RUL prediction.

  2. fitted input called prediction [Section 3.2.3, Eq. (27)]
    "L_phys(θ) = 1/M Σ (P_θ(u_j, ∂u_j/∂t, ∇_h u_j, ∇_h^2 u_j, …, ∇_h^k u_j) − ∂u_j/∂t)^2 (27)"

    The physics loss is defined as the squared error between P_θ's output and ∂u/∂t, while ∂u/∂t is also one of P_θ's listed inputs. Thus P_θ can drive L_phys to zero by learning the identity map on that coordinate. The 'physics constraint' is a supervised fit to the same data-derived derivative used as the target, not a PDE residual evaluated at independent collocation points, so no independent physical information enters the model.

full rationale

The paper's central novelty is the Physics-Guided Regulator discovering a PDE that then constrains RUL prediction. That chain is circular at both the formulation and loss levels. Eq. (22) writes ∂u/∂t − N(u, ∂u/∂t, ∇_h u, …)=0, so the PDE is satisfiable for any trajectory by letting N copy its ∂u/∂t argument. Eq. (27) then defines L_phys as the MSE between P_θ's output and ∂u/∂t while ∂u/∂t is listed among P_θ's inputs, so the physics loss can be minimized to zero by learning the identity on that coordinate. The 'discovered' operator is thus a supervised fit to the same data derivative, not an independent PDE residual at collocation points; it cannot supply the physical information the paper claims. Consistent with this, the ablation KDPINN (PGR without meta-learning) has higher RMSE than the Base Learner in Tables 1 and 2. The empirical C-MAPSS comparisons are external benchmarks and are not themselves circular, but the physics-discipline contribution claimed in the abstract and Section 4.1.3 reduces to a mathematical tautology. Self-citations [15] and [35] are present but not load-bearing because the meta-update is attributed to Reptile [50].

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central claim rests on a learned PDE that is fitted to the data it regulates, a latent state with no independent grounding, and several unreported hyperparameters. These are inputs the paper did not pay for externally, so the contribution is mostly the engineering combination.

free parameters (4)
  • PGR network weights (learned PDE operator) = not reported
    The PDE in Eq. (30) is the trained PGR; its weights are fitted to the same data used for RUL prediction, so the physics term is not independent.
  • Hidden state dimension d_h = not specified
    The dimensionality of the latent degradation state in the HSM is chosen by the authors but never stated, and the central derivation depends on it.
  • Order of derivatives k in PGR input = not specified
    Eq. (26) includes derivatives up to order k, but k is never reported; it is a design choice affecting the learned operator.
  • Loss weights w_d and w_p = implicitly 1 and 1
    Eq. (2) defines weighted losses but Section 3.2.3 uses an unweighted sum (Eq. 29); the balance between data and physics terms is set ad hoc.
assumptions (4)
  • domain assumption The degradation process can be represented by a PDE in a low-dimensional hidden state (Eq. 22).
    Section 3.2.3 posits the PDE form without derivation or validation on the actual equipment.
  • domain assumption The PGR neural network can approximate the true differential operator accurately enough for the residual to be a useful constraint.
    Section 3.2.3 relies on the PGR approximation, but no error bound or verification of the learned PDE is provided.
  • ad hoc to paper Adam inner-loop updates behave similarly to SGD for the Taylor expansion in Section 3.3.3.
    The theoretical analysis is derived for SGD (Eq. 34) and then extended to Adam with the sentence 'it can be expected' rather than a proof.
  • domain assumption Source-domain meta-tasks and target-domain tasks share enough structure for Reptile-style adaptation to transfer.
    The meta-learning objective (Eq. 31) assumes a common task distribution; the paper does not test this assumption across different fault modes or operating regimes beyond the two case studies.
invented entities (1)
  • Low-dimensional hidden state h
    purpose: Latent representation of equipment degradation used as input to the PGR and RUL predictor.
    The hidden state is produced by the HSM from data; it has no independent measurement or falsifiable prediction, and its dimension is unspecified.

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Cite this review

Pith. "Pith review of Meta-Learning and Knowledge Discovery based Physics-Informed Neural Network for Remaining Useful Life Prediction." pith.science (2026). https://pith.science/paper/GZ4MAMGU

@misc{pith2026250413797,
  author       = {Pith},
  title        = {Pith review of: Meta-Learning and Knowledge Discovery based Physics-Informed Neural Network for Remaining Useful Life Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GZ4MAMGU}},
  note         = {Machine review of arXiv:2504.13797}
}
read the original abstract

Predicting the remaining useful life (RUL) of rotating machinery is critical for industrial safety and maintenance, but existing methods struggle with scarce target-domain data and unclear degradation dynamics. We propose a Meta-Learning and Knowledge Discovery-based Physics-Informed Neural Network (MKDPINN) to address these challenges. The method first maps noisy sensor data to a low-dimensional hidden state space via a Hidden State Mapper (HSM). A Physics-Guided Regulator (PGR) then learns unknown nonlinear PDEs governing degradation evolution, embedding these physical constraints into the PINN framework. This integrates data-driven and physics-based approaches. The framework uses meta-learning, optimizing across source-domain meta-tasks to enable few-shot adaptation to new target tasks. Experiments on industrial data and the C-MAPSS benchmark show MKDPINN outperforms baselines in generalization and accuracy, proving its effectiveness for RUL prediction under data scarcity

Figures

Figures reproduced from arXiv: 2504.13797 by the authors.

Figure 1
Figure 1. The Overall Process of the Proposed MKDPINN [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 1
Figure 1. First, the monitoring [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Structure of the Knowledge Discovery based Physics [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figures from the paper (18 more)
Figure 3
Figure 3. Figure 3: intuitively depicts the update process of the first-order optimization-based meta￾parameters 𝜱𝜱 in the proposed MKDPINN framework, which includes two core stages: meta￾training and rapid adaptation. In the meta-training stage, the goal is to learn a set of optimized me…
Figure 4
Figure 4. Figure 4: Operational Status and Vibration Data Acquisition of Slurry Pump [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Wear condition of the pump casing [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Vibration Signals of Pump #1 during Two Life Cycles: (a) Cycle 1, (b) Cycle 2 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Visualization of correlation analysis results [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Task 1 RUL Prediction Results: (a) Base Learner, (b)KDPINN, (c) Meta Learner, (d) MKDPINN. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Task 1: RUL Prediction Metric Comparison [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: shows the wear condition of the pump casing of pump No. 2 used for Task 2. Its wear characteristics are manifested as local damage. A clear penetrating hole can be seen in the left image (outer wall perspective). The right image (inner wall perspective) reveals a larg…
Figure 11
Figure 11. Figure 11: Vibration Signals of Pump #2 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: Task 2 RUL Prediction Results: (a) Base Learner, (b) KDPINN, (c) Meta Learner, (d) MKDPINN. [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: Task 2: RUL Prediction Metric Comparison [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: RUL Prediction Results of MKDPINN in 15-shot Scenario Using Samples from Different Degradation Stages. (a) Using samples from normal operation (no degradation samples); (b) Using samples randomly selected from the first 20% of degradation samples; (c) Using samples ra…
Figure 15
Figure 15. Figure 15: Performance of MKDPINN for RUL Prediction in 15 [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]
Figure 16
Figure 16. Figure 16: RUL Prediction Results of MKDPINN for Cross-Machine RUL Prediction Tasks with Different Shot Sizes. (a) 5 shot; (b) 10 shot; (c) 15 shot; (d) 20 shot [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]
Figure 17
Figure 17. Figure 17: Performance Metrics of MKDPINN for Cross [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]
Figure 18
Figure 18. Figure 18: Standardized Values of P30, Nc, and BPR Sensors: (a) Global Standardization, (b) [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]
Figure 19
Figure 19. Figure 19: MKDPINN RUL Prediction Results on C-MAPSS Dataset: (a) FD001, (b) FD002, (c) FD003, (d) FD004 [PITH_FULL_IMAGE:figures/full_fig_p028_19.png]
Figure 20
Figure 20. Figure 20: Engine RUL Predictions on C-MAPSS Sub-datasets [PITH_FULL_IMAGE:figures/full_fig_p029_20.png]

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Reference graph

Works this paper leans on

72 extracted references · 37 canonical work pages

  1. [1]

    We propose a hierarchical learning framework consisting of an HSM and a PGR, where the HSM is responsible for extracting smooth hidden states from raw sensor data, and the PGR can adaptively learn the non-linear PDE dynamics equation followed by the latent states

    work page

  2. [2]

    We embed the PGR as a physical constraint into the PINN framework, guiding the training of the neural network through a regularized loss function, realizing the collaborative optimization of data-driven and physics knowledge, and improving the generalization ability of the model and its compliance with physical rules

    work page

  3. [3]

    The model is further extended into a meta-learning framework, enabling it to quickly adjust model parameters with only a small amount of data from new equipment or new working conditions, achieving accurate prediction of new tasks, and avoiding the calculation of second-order derivatives based on MAML

    work page

  4. [4]

    Comprehensive experimental validation is performed on real industrial scenarios and the publicly available CMAPSS dataset. The results show that MKDPINN exhibits superior performance in predicting RUL of the same equipment in different life cycles and across different equipment in the scenario of scarce target domain samples, verifying the effectiveness a...

    work page

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    Learning to Learn,

    Problem Formulation 2.1 Physics-Informed Neural Networks PINNs are a deep learning framework that embeds prior physical knowledge into neural networks, providing a promising approach to address the problem of missing physics -informed information during model training[38] . The core idea of PINNs is to incorporate PDEs that govern the behavior of control ...

    work page

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    Proposed method 3.1 Overall framework of the proposed method The overall workflow of the proposed MKDPINN is shown in Figure 1. First, the monitoring data during the equipment operation process is preprocessed, and a set of meta-tasks is constructed: the complete life -cycle data of each equipment is divided into multiple subsequences, and each subsequenc...

    work page

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    Task Batch Sampling: Randomly sample a mini -batch containing 𝐵𝐵 tasks from the source domain task distribution 𝑃𝑃(𝒯𝒯): {𝒯𝒯𝑝𝑝}𝑝𝑝=1 𝐵𝐵

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    Initialize task parameters: 𝜽𝜽𝒑𝒑 (𝟎𝟎) = 𝜱𝜱 (using the latest meta-parameters)

    Parallel Inner Loop Adaptation: For each task 𝒯𝒯𝑝𝑝(𝑝𝑝 = 1, … , 𝐵𝐵) in the batch, independently perform the following operations: ( a. Initialize task parameters: 𝜽𝜽𝒑𝒑 (𝟎𝟎) = 𝜱𝜱 (using the latest meta-parameters). ( b. Use the Adam optimizer (with a learning rate of α) to perform 𝑘𝑘 steps of updates on the training data 𝒟𝒟𝑝𝑝 𝑑𝑑𝑡𝑡 of task 𝒯𝒯𝑝𝑝 to minimize t...

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    task update vector

    Outer Loop Meta -Parameter Update: Based on the adaptation results of all tasks in the batch, calculate the update amount of the meta-parameter 𝜱𝜱. The update rule is: 𝜱𝜱𝒏𝒏𝒏𝒏𝒏𝒏 = 𝜱𝜱𝒐𝒐𝒐𝒐𝒅𝒅 + 𝜂𝜂 1 𝐵𝐵 � �𝜽𝜽𝒑𝒑 (𝒌𝒌) − 𝜱𝜱𝒐𝒐𝒐𝒐𝒅𝒅� 𝐵𝐵 𝑝𝑝=1������������� Average update direction Δ𝜱𝜱 �33�...

  2. [10]

    The experimental objects are two 150ZJ -I-A65 type slurry pumps, which have a rated power of 178kW, a designed head of 63.2m, a rated flow of 470m³/h, and a working speed of 980rpm

    Experiment 4.1 Case study 1: Real Industrial Scenarios To validate the proposed RUL prediction methodology in a relevant industrial setting, experiments were conducted on critical assets within a large- scale iron ore processing system (an iron ore concentrator). The experimen...

  3. [11]

    1, and the target domain data is the second life cycle of the pump

    Task 1 (Cross -Life Cycle RUL Prediction): The source domain data comes from the first life cycle of pump No. 1, and the target domain data is the second life cycle of the pump

  4. [12]

    The source domain data also comes from the first life cycle of pump No

    Task 2 (Cross -Machine Few-Shot RUL Prediction): This task represents a more challenging scenario and evaluates the model's RUL prediction performance for completely new equipment. The source domain data also comes from the first life cycle of pump No. 1, but the target domain...

  5. [13]

    Its performance represents the baseline level of relying solely on data -driven learning

    Base Learner: Serves as the basic model and adopts the same core network architecture and parameter configuration as MKDPINN, but does not integrate the PINN framework or the meta- learning strategy. Its performance represents the baseline level of relying solely on data -driv...

  6. [14]

    By comparing it with the Base Learner, the effect of PINN constraints on improving prediction accuracy can be evaluated

    KDPINN: This model introduces the knowledge discovery -based PINN framework on the basis of the Base Learner. By comparing it with the Base Learner, the effect of PINN constraints on improving prediction accuracy can be evaluated

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    run -to-failure

    Meta Learner: This model applies our proposed meta -learning framework on the Base Learner architecture, but omits the PINN part. Comparing it with the Base Learner and MKDPINN can reveal the contribution of the meta -learning strategy in improving the m odel's adaptability an...

    2022

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.