Pith. sign in

REVIEW 4 major objections 6 minor 125 references

PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention

T0 review · 4 major / 6 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 A lightweight CNN whose attention is regularized to follow smooth, peak-centered signal structure aims to improve forecasting accuracy and event-focused performance on cutting-force and blazar-flare time series without annotated…

desk verdict The sparsity regularizer in §4.3.3 is mathematically inert, so the paper's three-part framework reduces to two; otherwise a clearly written applied study with a suggestive blazar result but thin evidence. read the letter →

arxiv 2608.07681 v1 pith:FHE4COFQ submitted 2026-08-07 cs.LG physics.data-an

Amal Saadallah , Julia Tjus , Petra Wiederkeher , Wolfgang Rhode This is my paper · ORCID
classification cs.LGphysics.data-an
keywords timeseriesforecastingphysics-informedneuralnetworksattentionregularizationconvolutionalblazarflarescutting-forcepredictioninterpretability
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

PhysAttNet is a forecasting model built from a lightweight convolutional network plus an attention head, trained so that the attention weights follow smooth, peak-centered temporal profiles derived from the input signal. The paper's central claim is that this physics-informed regularization improves forecasting accuracy, generalization, and performance on structurally important events for two very different physical time series: cutting forces during milling and gamma-ray flares from blazars. The payoff is that the gains are supposed to come from a small differentiable bias rather than from a larger or more complex network, keeping the model cheap enough for real-time monitoring while producing attention maps that concentrate on physically meaningful peaks. If the claim holds, domain knowledge can be injected into forecasting models without hand-labeled explanations or explicit physical equations.

What carries the argument

The central object is the attention vector $\boldsymbol{\alpha}$ over $T'$ downsampled temporal features, produced by a $1\times 1$ convolution followed by softmax normalization, so $\alpha_t \ge 0$ and $\sum_t \alpha_t = 1$. The training objective adds three differentiable penalties to the forecasting MSE: an alignment loss that matches $\boldsymbol{\alpha}$ to Gaussian target profiles centered on peaks detected in the input signal, a smoothness loss penalizing squared differences between consecutive attention weights, and a sparsity loss defined as the mean absolute attention weight. The target profiles make the supervision fully automatic, since they are built from the signal itself rather than from annotations. Because the attention vector is softmax-normalized, the sparsity penalty as written is constant for every possible attention vector; the active learning pressure comes from the alignment and smoothness terms.

What would settle it

Run PhysAttNet twice on identical data and splits, once with $\lambda_{\mathrm{sparse}}$ set to the tuned value and once with it set to zero. If the sparsity term is truly inert, the two runs must have identical losses, gradients, attention weights, and test metrics; any difference would mean the implementation does not follow the stated softmax-normalized attention. A simpler arithmetic check settles the same point: the gradient of $\frac{1}{T'}\sum_t|\alpha_t|$ with respect to $\boldsymbol{\alpha}$ is zero because $\boldsymbol{\alpha}$ is a probability vector.

Watch

Extended reading notes

Core claim

On its own terms, the paper demonstrates that regularizing temporal attention to be peak-aligned and continuous improves forecasting in event-dominated physical signals. In the blazar task, using monthly Fermi-LAT photon flux from 13 sources with a 24-month look-back and a 6-month horizon, PhysAttNet reports the lowest mean RMSE and event-weighted RMSE among all compared models, including N-BEATS, Transformer, DeepAR, and a plain CNN. In the cutting-force task, based on 274 milling experiments aggregated to 0.1 ms resolution with a 10 ms horizon, PhysAttNet lands close to N-BEATS and Transformer while using a substantially simpler CNN backbone. The paper interprets these results as evidence that structural assumptions about localized, continuous, peak-centered dynamics transfer across domains that differ enormously in physical scale and sampling rate.

Load-bearing premise

The method's success rests on the premise that its training penalties actually push the attention weights in a useful direction; since the sparsity penalty is a mathematical constant for any attention weights that are normalized to sum to one, everything the paper attributes to sparsity depends on the other two penalties doing the real work.

Editorial extensions

If this is right

  • On the blazar benchmark, PhysAttNet attains the best mean RMSE and event-weighted RMSE among all compared models, with the largest advantage appearing under the event-weighted metric.
  • On the cutting-force benchmark, PhysAttNet's error is close to N-BEATS and Transformer while its backbone is a lightweight CNN, implying comparable accuracy at much lower architectural cost.
  • Attention maps from PhysAttNet concentrate on high-flux flare intervals and stay suppressed in quiescent phases, whereas an unregularized CNN spreads attention more diffusely, linking the regularizer to more interpretable focus.
  • The regularization pipeline needs no annotated explanations or manual relevance labels, so the same recipe can be applied to any time series where relevant events appear as smooth, localized peaks.
  • The modular regularizers can be redefined—for example, inverted to emphasize trough-centered events—without changing the CNN backbone or the attention head.

Reading between the lines

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

  • Because softmax attention satisfies $\alpha_t \ge 0$ and $\sum_t \alpha_t = 1$, the sparsity penalty $\frac{1}{T'}\sum_t |\alpha_t|$ is identically $1/T'$ for every attention vector and has zero gradient; any reported benefit attributed to sparsity must in fact come from the alignment or smoothness terms.
  • A direct test follows immediately: setting the sparsity weight $\lambda_{\mathrm{sparse}}$ to zero while keeping the other two regularizers should reproduce the reported training curves and test metrics, which would confirm that the three-part formulation reduces to two active constraints.
  • The modular design invites a transfer test beyond peak-centered events: in domains where predictive relevance sits at troughs, change points, or piecewise-constant regimes, redefining the target profile and relaxing smoothness would show whether the inductive bias generalizes or only fits Gaussian-shaped peaks.
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

4 major / 6 minor

Summary. The paper proposes PhysAttNet, a lightweight CNN forecaster augmented with a temporal attention head whose weights are regularized during training by three physics-inspired terms: alignment to Gaussian peak-centered target profiles, smoothness over time, and L1 sparsity. The method is evaluated on two real-world forecasting tasks, Fermi-LAT blazar photon-flux forecasting and high-frequency cutting-force prediction in milling, and compared with classical, tree-based, and deep baselines. The central claims are that the three regularizers improve forecasting accuracy, generalization, and performance on structurally important events, and that this is achieved with a lightweight architecture. The blazar experiments show PhysAttNet with the lowest mean RMSE and wRMSE among the compared models, while on cutting forces N-BEATS and Transformer outperform PhysAttNet on both metrics.

Significance. If the proposed regularization framework were fully effective, it would provide a simple and computationally cheap way to inject domain structure into attention-based time-series forecasting, with potential value for industrial monitoring and astrophysical event prediction. The two application studies are relevant and the underlying intuition, that attention should concentrate on localized, peak-centered and temporally coherent regions, is plausible. The paper is also honest about the cutting-force result, where PhysAttNet is competitive rather than best. However, the significance is undermined by a mathematically inert sparsity term, the absence of ablations that isolate the regularizers, and the lack of statistical significance testing. The reported improvements are therefore more suggestive than established.

major comments (4)
  1. [§4.3.3] The sparsity regularizer is mathematically inert. Because the attention weights satisfy α_t ≥ 0 and Σ_t α_t = 1, the L1 penalty L_sparse = (1/T') Σ_t |α_t| equals 1/T' for every possible attention vector, and its gradient with respect to the pre-softmax scores is identically zero by the softmax normalization. The paragraph in §4.3.3 asserting that this term 'promotes where attention should be concentrated' is therefore incorrect, and the claimed three-part regularizer is actually only two-part. Since no ablation varies λ_sparse independently, any reported benefit cannot be attributed to this term.
  2. [§5.2, Table 1] The headline claim that PhysAttNet 'improves forecasting accuracy' is not supported by the cutting-force results: PhysAttNet's RMSE (0.758 ± 0.055) and wRMSE (0.765 ± 0.071) are worse than those of N-BEATS (0.732 ± 0.087 and 0.744 ± 0.125) and Transformer (0.729 ± 0.071 and 0.737 ± 0.122). Only in the blazar task is PhysAttNet numerically best, and even there the margin over the CNN baseline is small: RMSE 8.19e-08 vs 8.65e-08 and wRMSE 9.79e-08 vs 9.83e-08, with overlapping standard deviations. Without significance tests or confidence intervals, the claimed improvements are not established.
  3. [§5.1.2 and §5.1.3] The experimental design cannot isolate the effect of the proposed physics-informed regularization. The CNN baseline shares the backbone but omits both the attention head and all regularizers, so any difference between CNN and PhysAttNet could come from the attention mechanism alone. There is no ablation with attention but no regularizers, and no independent variation of λ_align, λ_smooth, or λ_sparse. The claim that the regularizers drive the reported gains therefore lacks direct support.
  4. [§4.3.1 and §5.1.3] The event-focused evaluation appears partly circular. The alignment regularizer is constructed from Gaussian target profiles centered at detected peaks in the input, while the wRMSE metric up-weights exactly those time steps where the observed signal exceeds a percentile threshold (95th for blazars, 90th for cutting forces). If the peak detection underlying the alignment target uses the same or correlated thresholds, then the reported wRMSE improvement partly reflects how well the model matches the training-time attention target rather than an independent improvement on physically important events. Please report unweighted RMSE restricted to event windows defined by an independent or annotated event set, or otherwise clarify the relationship between the two peak definitions.
minor comments (6)
  1. [Abstract and §1] There are several typographical and formatting errors, including 'thesesettings' in the abstract and 'Germnay' in the author affiliations, that should be corrected.
  2. [Table 1] The standard deviation for ExpSmooth wRMSE is reported as '± 25525', which is implausible and likely a formatting or data-processing error; please correct or explain this value.
  3. [Table 1] Bold formatting is applied to PhysAttNet in the cutting-force columns even though N-BEATS and Transformer achieve lower RMSE and wRMSE; this is misleading and should be fixed.
  4. [Figures 2 and 5] The y-axis label '1e 7' should be typeset as '×10^7' or similar for clarity.
  5. [References] The citation 'Spiliotis et al., 2022' in §5.1.2 lacks a full reference entry with authors and title; please complete the reference list.
  6. [General] No code, data availability statement, or hyperparameter configuration details are provided. Given that the paper reports no ablations and only aggregate metrics, releasing code and specific hyperparameter settings would substantially strengthen reproducibility.

Circularity Check

3 steps flagged · score 6.0 of 10

The claimed sparsity regularizer is constant by the paper's own softmax definition, and the event-level evaluation is built from the same peak-centered prior used to train the attention, so the three-part mechanism reduces to two active terms and the event-focused claim is partly self-confirming.

  1. self definitional [Section 4.3 (softmax attention definition) and Section 4.3.3 (Attention Sparsity Regularization)]
    "α_t = exp(e_t) / Σ_{k=1}^{T'} exp(e_k), α_t ≥ 0, Σ_{t=1}^{T'} α_t = 1. ... To encourage selective focus, we apply an ℓ1 sparsity penalty: L_sparse = 1/T' Σ_{t=1}^{T'} |α_t|. ... sparsity promotes where attention should be concentrated by discouraging diffuse relevance across time."

    Under the paper's own softmax definition, α_t ≥ 0 and Σ α_t = 1 for every possible input and parameter setting, so |α_t| = α_t and Σ |α_t| = 1. Hence L_sparse ≡ 1/T' is a constant and ∂L_sparse/∂e_k = (1/T') ∂(Σ α_t)/∂e_k = 0. The term cannot 'promote selective focus' or 'discourage diffuse relevance'; it is inert by construction. The claimed three-part physics-informed objective therefore reduces to L_pred + λ_align L_align + λ_smooth L_smooth, and any reported benefit attributed to sparsity is a definitional artifact rather than an active constraint.

  2. self definitional [Section 4.3.1 (Attention Alignment Regularization) and Section 5.2 / Figure 5]
    "The alignment loss is defined as: L_align = 1/T' Σ_{t=1}^{T'} (α_t − α⋆_t)^2. ... In the training region, PhysAttNet’s attention concentrates on temporally localized high-flux intervals corresponding to flare-like structures ... This indicates that the physics-informed regularization encourages PhysAttNet to prioritize physically meaningful, peak-centered regions rather than distributing importance uniformly."

    Because L_align directly penalizes any deviation of the attention vector α from α⋆, and α⋆ is constructed as Gaussian kernels centered at detected peaks, the model is explicitly trained to place high attention near peaks. Observing concentrated attention near peaks in the training region is therefore the training objective itself, not an emergent or independently verified property. Presenting this imposed localization as evidence that the regularization produces physically meaningful focus is circular: the behavior is entailed by the definition of the loss.

1 more flagged steps
  1. other [Section 4.3.1 (Attention Alignment Regularization) and Section 5.1.3 (Event-Weighted Evaluation Metrics)]
    "we construct a target attention profile α⋆ using Gaussian kernels centered at salient peaks detected in the input signal. ... w_t = 1 + γ·𝕀(y_t > τ), where ... τ denotes a percentile-based threshold identifying events ... errors on flare months count two times as much as baseline months."

    The same peak-centered event prior is used twice: once as the training target for attention (Gaussian kernels at detected peaks) and once as the evaluation weighting (95th-percentile flare months and 90th-percentile force transients). The claimed improvement on 'structurally important events' is therefore measured with a metric constructed from the very property the alignment regularizer is trained to emphasize. The event-level advantage is partly self-confirming rather than independent evidence, although the overall RMSE comparison remains an external benchmark.

full rationale

The main forecasting-accuracy comparison in Table 1 is external and is not derived from the regularizers' definitions, so this is not a fully circular paper; self-citations to Saadallah et al. are contextual and not load-bearing. However, three parts of the argument reduce by construction. First, the ℓ1 sparsity regularizer is constant: with softmax attention, α_t ≥ 0 and Σ α_t = 1 imply Σ |α_t| = 1, so L_sparse = 1/T' with zero gradient; the paper's claimed three-part loss is only two active terms. Second, the attention-localization 'result' is imposed: L_align supervises α to match Gaussian profiles centered on detected peaks, so observing concentrated attention near peaks in training is the objective, not an emergent confirmation. Third, the event-weighted wRMSE metric uses percentile-based event weights that reflect the same peak-centered structure used to build the alignment targets, making the event-level performance claim partly self-confirming. No ablation varying λ_align, λ_smooth, or λ_sparse is provided and no code is released, so the individual contribution of the two active regularizers cannot be isolated; that is a support gap, separate from the definitional collapses identified above.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entity, particle, force, or conserved quantity. Its only invented construct is the Gaussian attention target profile, which is derived from data rather than independently evidenced, and is captured in the axioms and free parameters.

free parameters (8)
  • lambda_align = not reported
    Weight of the alignment loss in the total objective; selected via validation (§4.4).
  • lambda_smooth = not reported
    Weight of the smoothness loss; selected via validation (§4.4).
  • lambda_sparse = not reported
    Weight of the sparsity loss; moot because the term is constant under softmax (§4.3.3).
  • Gaussian target profile parameters (peak detection, width, normalization) = not reported
    The alignment target alpha* is built from Gaussian kernels centered at 'salient peaks detected in the input signal', with no algorithm or widths given (§4.3.1).
  • Event-weighting parameters for wRMSE = gamma_flare=2, gamma_force=3, tau=P95/P90
    These choices define the metric on which the event-focused performance claims rest (§5.1.3).
  • Blazar look-back and horizon = L=24 months, H=6 months
    Task configuration chosen by the authors; different choices change the forecasting problem and results (§5.1.1).
  • Milling aggregation and horizon = 0.1 ms aggregation, 10 ms horizon
    Data preprocessing and task configuration; affects which transients are preserved (§5.1.1).
  • CNN backbone hyperparameters (layers, channels, kernel sizes) = not reported
    The backbone is described only as 'lightweight'; reimplementation requires these choices (§4.2).
assumptions (4)
  • domain assumption Important events manifest as localized, peak-centered structures in the observed time series.
    Used to construct Gaussian attention targets and to justify the alignment loss (§3.3, §4.3.1). The authors concede in §4.5 and §6 that trough-centered or discontinuous dynamics may violate this.
  • domain assumption Peaks in the input window are the right places for attention to focus when forecasting the future.
    The alignment target is built from input-derived peaks; if predictive information lies in quiescent precursors or troughs, this bias will misdirect attention (§4.3.1).
  • ad hoc to paper An L1 penalty applied to softmax-normalized attention weights can induce sparsity.
    Implicit in §4.3.3; mathematically false because the softmax weights are nonnegative and sum to 1, making the penalty constant with zero gradient.
  • domain assumption Attention weights at the reduced temporal resolution can be meaningfully supervised by Gaussian profiles derived from the raw input.
    The mapping from input peaks to the reduced feature dimension T' is not specified; the correctness of the supervision depends on this mapping (§4.3).

how reviews work

0 comments
Cite this review

Pith. "Pith review of PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention." pith.science (2026). https://pith.science/paper/FHE4COFQ

@misc{pith2026260807681,
  author       = {Pith},
  title        = {Pith review of: PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FHE4COFQ}},
  note         = {Machine review of arXiv:2608.07681}
}
read the original abstract

Accurate and robust time series forecasting is essential in many applications involving physical processes, such as manufacturing monitoring and astrophysical event detection. In these settings, predictive models must remain reliable under noise, variability, and measurement uncertainty while capturing temporally localized structures corresponding to physically meaningful events. Convolutional neural networks (CNNs) are widely used for such tasks due to their computational efficiency and strong representational capacity. However, their learned temporal representations often exhibit unstable or physically inconsistent attention patterns, reducing robustness, generalization, and interpretability. This paper introduces PhysAttNet, a physics-informed attention framework for time series forecasting. PhysAttNet augments a lightweight CNN forecaster with an attention head guided by domain-informed regularization reflecting the structural properties of physical signals. Specifically, three complementary constraints are imposed during training: an alignment regularization that encourages attention to follow smooth, peak-centered temporal structures derived from the input signal, a smoothness regularization that enforces continuous temporal evolution, and a sparsity regularization that promotes selective focus on informative intervals. These differentiable regularization terms introduce physics-guided inductive bias without requiring annotated explanations or manual supervision. Experiments on two distinct applications, namely predicting cutting forces during milling and forecasting flares in blazar time series, demonstrate that PhysAttNet improves forecasting accuracy, generalization, and prediction performance on structurally important events.

Figures

Figures reproduced from arXiv: 2608.07681 by the authors.

Figure 1
Figure 1. Conceptual illustration of the physical processes leading to gamma-ray flares in blazar jets. Shock interactions and particle acceleration within the relativistic jet can produce localized bursts of high-energy emission that appear as flares in the observed gamma-ray time series. 2008 2010 2012 2014 2016 2018 2020 2022 2024 Date (UTC) 0 1 2 3 4 5 6 7 8 Photon Flux 1e 7 Observed Photon Flux Smoothed Signal Flare Wind… view at source ↗
Figure 2
Figure 2. Photon flux of the bright 𝛾-ray source 4FGL J1048.4+7143 observed by Fermi-LAT as a function of time, illustrating the occurrence of localized flare events in the light curve [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Illustration of the NC milling process. A rotating milling tool removes material from the workpiece, generating cutting forces that are measured during machining. First Author et al.: Preprint submitted to Elsevier Page 14 of 13 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Progression of cutting forces on zoomed time intervals. 2008 2010 2012 2014 2016 2018 2020 2022 2024 Time (Months) 0 1 2 3 4 5 6 7 8 Photon Flux 1e 7 Physics-Informed Attention vs Standard CNN Observed PhysAttNet Forecast Standard CNN Forecast Train/Test Split PhysAttN…
Figure 5
Figure 5. Figure 5: Comparison of performance and attention distribution between PhysAttNet and standard CNN for blazar photon￾flux forecasting. First Author et al.: Preprint submitted to Elsevier Page 15 of 13 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

125 extracted references · 63 canonical work pages

  1. [1]

    , title =

    Fortunato, S. , title =. Phys. Rep.-Rev. Sec. Phys. Lett. , volume =. 2010 , pages =

    2010

  2. [2]

    Newman, M. E. J. and Girvan, M. , title =. Phys. Rev. E. , volume =. 2004 , pages =

    2004

  3. [3]

    and Reinhardt, T

    Vehlow, C. and Reinhardt, T. and Weiskopf, D. , title =. IEEE Trans. Vis. Comput. Graph. , volume =. 2013 , pages =

    2013

  4. [4]

    and Albert, R

    Raghavan, U. and Albert, R. and Kumara, S. , title =. Phys. Rev E. , volume =. 2007 , pages =

    2007

  5. [5]

    2011 , pages =

    Robust network community detection using balanced propagation , journal =. 2011 , pages =

    2011

  6. [6]

    and Li, S

    Lou, H. and Li, S. and Zhao, Y. , title =. Physica A. , volume =. 2013 , pages =

    2013

  7. [7]

    and Newman, M

    Clauset, A. and Newman, M. E. J. and Moore, C. , title =. Phys. Rev. E. , volume =. 2004 , pages =

    2004

  8. [8]

    Blondel, V. D. and Guillaume, J. L. and Lambiotte, R. and Lefebvre, E. , title =. J. Stat. Mech.-Theory Exp. , volume =. 2008 , pages =

    2008

Show all 125 references
  1. [9]

    and Campari, R

    Sobolevsky, S. and Campari, R. , title =. Phys. Rev. E. , volume =. 2014 , pages =

    2014

  2. [10]

    and Barthelemy, M

    Fortunato, S. and Barthelemy, M. , title =. Proc. Natl. Acad. Sci. U. S. A. , volume =. 2007 , pages =

    2007

  3. [11]

    2011 , pages =

    Unfolding communities in large complex networks: Combining defensive and offensive label propagation for core extraction , journal =. 2011 , pages =

    2011

  4. [12]

    and Li, J

    Wang, X. and Li, J. , title =. Physica A. , volume =. 2013 , pages =

    2013

  5. [13]

    and Wang, X

    Li, J. and Wang, X. and Eustace, J. , title =. Physica A. , volume =. 2013 , pages =

    2013

  6. [14]

    Fabio, D. R. and Fabio, D. and Carlo, P. , title =. Sci. Rep. , volume =. 2013 , pages =

    2013

  7. [15]

    and Wu, T

    Chen, Q. and Wu, T. T. and Fang, M. , title =. Physica A. , volume =. 2013 , pages =

    2013

  8. [16]

    and Wang, R

    Zhang, S. and Wang, R. and Zhang, X. , title =. Physica A. , volume =. 2007 , pages =

    2007

  9. [17]

    and Petr\'oczi, A

    Nepusz, T. and Petr\'oczi, A. and N\'egyessy, L. and Bazs\'o, F. , title =. Phys. Rev. E. , volume =. 2008 , pages =

    2008

  10. [18]

    and Liang, Z

    Fabricio, B. and Liang, Z. , title =. Soft Comput. , volume =. 2013 , pages =

    2013

  11. [19]

    and Gao, L

    Sun, P. and Gao, L. and Han, S. , title =. Inf. Sci. , volume =. 2011 , pages =

    2011

  12. [20]

    and Liu, D

    Wang, W. and Liu, D. and Liu, X. and Pan, L. , title =. Physica A. , volume =. 2013 , pages =

    2013

  13. [21]

    and Roberts, S

    Psorakis, I. and Roberts, S. and Ebden, M. and Sheldon, B. , title =. Phys. Rev. E. , volume =. 2011 , pages =

    2011

  14. [22]

    and Yeung, D

    Zhang, Y. and Yeung, D. , title =. In Proc. ACM SIGKDD Conf. , year =

  15. [23]

    , title =

    Liu, J. , title =. Eur. Phys. J. B. , volume =. 2010 , pages =

    2010

  16. [24]

    Havens, T. C. and Bezdek, J. C. and Leckie, C. and Ramamohanarao, K. and Palaniswami, M. , title =. IEEE Trans. Fuzzy Syst. , volume =. 2013 , pages =

    2013

  17. [25]

    Newman, M. E. J. , title =

  18. [26]

    2012 , pages =

    Ubiquitousness of link-density and link-pattern communities in real-world networks , journal =. 2012 , pages =

    2012

  19. [27]

    and Fortunato, S

    Lancichinetti, A. and Fortunato, S. and Radicchi, F. , title =. Phys. Rev. E. , volume =. 2008 , pages =

    2008

  20. [28]

    and Pellegrini, M

    Liu, W. and Pellegrini, M. and Wang, X. , title =. Sci. Rep. , volume =. 2014 , pages =

    2014

  21. [29]

    and Diaz-Guilera, A

    Danon, L. and Diaz-Guilera, A. and Duch, J. and Arenas, A. , title =. J. Stat. Mech.-Theory Exp. , volume =. 2005 , pages =

    2005

  22. [30]

    , title =

    Gregory, S. , title =. J. Stat. Mech.-Theory Exp. , volume =. 2011 , pages =

    2011

  23. [31]

    and Fortunato, S

    Lancichinetti, A. and Fortunato, S. , title =. Phys. Rev. E. , volume =. 2009 , pages =

    2009

  24. [32]

    and Rifqi, M

    Hullermeier, E. and Rifqi, M. , title =. in Proc. IFSA/EUSFLAT Conf. , year =

  25. [33]

    Machine Learning , volume=

    Explainable online ensemble of deep neural network pruning for time series forecasting , author=. Machine Learning , volume=. 2022 , publisher=

    2022

  26. [34]

    2000 , publisher=

    Time-series forecasting , author=. 2000 , publisher=

    2000

  27. [35]

    Joint European conference on machine learning and knowledge discovery in databases , pages=

    A drift-based dynamic ensemble members selection using clustering for time series forecasting , author=. Joint European conference on machine learning and knowledge discovery in databases , pages=. 2019 , organization=

    2019

  28. [36]

    Procedia CIRP , volume=

    Stability prediction in milling processes using a simulation-based Machine Learning approach , author=. Procedia CIRP , volume=. 2018 , publisher=

    2018

  29. [37]

    Engineering Applications of Artificial Intelligence , volume=

    Real-time prediction of process forces in milling operations using synchronized data fusion of simulation and sensor data , author=. Engineering Applications of Artificial Intelligence , volume=. 2020 , publisher=

    2020

  30. [38]

    Galaxies , volume=

    Monitoring the extragalactic high energy sky , author=. Galaxies , volume=. 2019 , publisher=

    2019

  31. [39]

    Journal of Space Weather and Space Climate , volume=

    The flare likelihood and region eruption forecasting (FLARECAST) project: flare forecasting in the big data & machine learning era , author=. Journal of Space Weather and Space Climate , volume=. 2021 , publisher=

    2021

  32. [40]

    Time Series Analysis: Data, Methods, and Applications , volume=

    CNN Approaches for Time Series , author=. Time Series Analysis: Data, Methods, and Applications , volume=. 2019 , publisher=

    2019

  33. [41]

    Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages=

    Explainable online deep neural network selection using adaptive saliency maps for time series forecasting , author=. Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages=. 2021 , organization=

    2021

  34. [42]

    Knowledge-Based Systems , pages=

    Multivariate time series forecasting based on time-frequency transform mixed convolution , author=. Knowledge-Based Systems , pages=. 2025 , publisher=

    2025

  35. [43]

    Journal of big Data , volume=

    Time-series analysis with smoothed Convolutional Neural Network , author=. Journal of big Data , volume=. 2022 , publisher=

    2022

  36. [44]

    2019 International joint conference on neural networks (IJCNN) , pages=

    Adversarial attacks on deep neural networks for time series classification , author=. 2019 International joint conference on neural networks (IJCNN) , pages=. 2019 , organization=

    2019

  37. [45]

    arXiv preprint arXiv:1711.11561 , year=

    Measuring the tendency of cnns to learn surface statistical regularities , author=. arXiv preprint arXiv:1711.11561 , year=

    arXiv

  38. [46]

    Data mining and knowledge discovery , volume=

    Deep learning for time series classification: a review , author=. Data mining and knowledge discovery , volume=. 2019 , publisher=

    2019

  39. [47]

    Structural Health Monitoring , volume=

    An integrated deep neural network model combining 1D CNN and LSTM for structural health monitoring utilizing multisensor time-series data , author=. Structural Health Monitoring , volume=. 2025 , publisher=

    2025

  40. [48]

    Journal of Intelligent Manufacturing , volume=

    State identification of a 5-axis ultra-precision CNC machine tool using energy consumption data assisted by multi-output densely connected 1D-CNN model , author=. Journal of Intelligent Manufacturing , volume=. 2024 , publisher=

    2024

  41. [49]

    ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages=

    1-D convolutional neural networks for signal processing applications , author=. ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages=. 2019 , organization=

    2019

  42. [50]

    Logic Journal of the IGPL , volume=

    Detection of transiting exoplanets and phase-folding their host star’s light curves from K2 data with 1D-CNN , author=. Logic Journal of the IGPL , volume=. 2025 , publisher=

    2025

  43. [51]

    IEEE access , volume=

    A dilated CNN model for image classification , author=. IEEE access , volume=. 2019 , publisher=

    2019

  44. [52]

    6th FIRST 2022 International Conference (FIRST-ESCSI-22) , pages=

    Enhancing deeper layers with residual network on CNN architecture: A review , author=. 6th FIRST 2022 International Conference (FIRST-ESCSI-22) , pages=. 2023 , organization=

    2022

  45. [53]

    arXiv preprint arXiv:1603.06995 , year=

    Multi-scale convolutional neural networks for time series classification , author=. arXiv preprint arXiv:1603.06995 , year=

    arXiv

  46. [54]

    International Journal of Conceptions on Computing and Information Technology , volume=

    An analysis of early stopping and dropout regularization in deep learning , author=. International Journal of Conceptions on Computing and Information Technology , volume=. 2017 , publisher=

    2017

  47. [55]

    arXiv preprint arXiv:1711.05101 , volume=

    Fixing weight decay regularization in adam , author=. arXiv preprint arXiv:1711.05101 , volume=

    arXiv

  48. [56]

    arXiv preprint arXiv:2405.19652 , year=

    Dual sparse training framework: inducing activation map sparsity via Transformed l1-regularization , author=. arXiv preprint arXiv:2405.19652 , year=

    arXiv

  49. [57]

    Neurocomputing , volume=

    Group sparse regularization for deep neural networks , author=. Neurocomputing , volume=. 2017 , publisher=

    2017

  50. [58]

    Frontiers in applied mathematics and statistics , volume=

    Structured sparsity of convolutional neural networks via nonconvex sparse group regularization , author=. Frontiers in applied mathematics and statistics , volume=. 2021 , publisher=

    2021

  51. [59]

    , author=

    Improving Deep Neural Network Sparsity through Decorrelation Regularization. , author=. Ijcai , volume=

  52. [60]

    Neural Computing and Applications , volume=

    CondenseNet with exclusive lasso regularization , author=. Neural Computing and Applications , volume=. 2021 , publisher=

    2021

  53. [61]

    Machine Learning , volume=

    Improving interpretability via regularization of neural activation sensitivity , author=. Machine Learning , volume=. 2024 , publisher=

    2024

  54. [62]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

    Single-frame regularization for temporally stable cnns , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

  55. [63]

    Low-Rank and Temporal Smoothness Regularization on Value-Based Deep Reinforcement Learning , author=

  56. [64]

    arXiv preprint arXiv:2309.09045 , year=

    Temporal smoothness regularisers for neural link predictors , author=. arXiv preprint arXiv:2309.09045 , year=

  57. [65]

    2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) , pages=

    Deep generative storm model for dynamic imaging , author=. 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI) , pages=. 2021 , organization=

    2021

  58. [66]

    ACM Computing Surveys , volume=

    A survey of explainable artificial intelligence (XAI) in financial time series forecasting , author=. ACM Computing Surveys , volume=. 2025 , publisher=

    2025

  59. [67]

    arXiv preprint arXiv:1611.07450 , year=

    Grad-CAM: Why did you say that? , author=. arXiv preprint arXiv:1611.07450 , year=

    arXiv

  60. [68]

    , author=

    Explainable deep neural networks for multivariate time series predictions. , author=. IJCAI , pages=. 2019 , organization=

    2019

  61. [69]

    arXiv preprint arXiv:2304.07136 , year=

    One Explanation Does Not Fit XIL , author=. arXiv preprint arXiv:2304.07136 , year=

    arXiv

  62. [70]

    Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society , pages=

    Explanatory interactive machine learning , author=. Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society , pages=

    2019

  63. [71]

    British Journal of Educational Technology , volume=

    Explanatory learner models: Why machine learning (alone) is not the answer , author=. British Journal of Educational Technology , volume=. 2019 , publisher=

    2019

  64. [72]

    Journal of Manufacturing and Materials Processing , volume=

    Online tool wear classification during dry machining using real time cutting force measurements and a CNN approach , author=. Journal of Manufacturing and Materials Processing , volume=. 2018 , publisher=

    2018

  65. [73]

    The International Journal of Advanced Manufacturing Technology , volume=

    A review on deep learning in machining and tool monitoring: methods, opportunities, and challenges , author=. The International Journal of Advanced Manufacturing Technology , volume=. 2021 , publisher=

    2021

  66. [74]

    Procedia Cirp , volume=

    A hybrid approach using machine learning to predict the cutting forces under consideration of the tool wear , author=. Procedia Cirp , volume=. 2019 , publisher=

    2019

  67. [75]

    Procedia CIRP , volume=

    In-process tool wear prediction system based on machine learning techniques and force analysis , author=. Procedia CIRP , volume=. 2018 , publisher=

    2018

  68. [76]

    Advanced Engineering Informatics , volume=

    Deep-learning-driven intelligent tool wear identification of high-precision machining with multi-scale CNN-BiLSTM-GCN , author=. Advanced Engineering Informatics , volume=. 2025 , publisher=

    2025

  69. [77]

    The Astrophysical Journal , volume=

    Early Detection of Multiwavelength Blazar Variability , author=. The Astrophysical Journal , volume=. 2025 , publisher=

    2025

  70. [78]

    Monthly Notices of the Royal Astronomical Society , volume=

    Deep learning Blazar classification based on multifrequency spectral energy distribution data , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2021 , publisher=

    2021

  71. [79]

    Monthly Notices of the Royal Astronomical Society , volume=

    Insights from leptohadronic modelling of the brightest blazar flare , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2025 , publisher=

    2025

  72. [80]

    Monthly Notices of the Royal Astronomical Society , volume=

    Machine learning applied to multifrequency data in astrophysics: blazar classification , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2020 , publisher=

    2020

  73. [81]

    Pattern Recognition , volume=

    Explainable boosted linear regression for time series forecasting , author=. Pattern Recognition , volume=. 2021 , publisher=

    2021

  74. [82]

    Trusted Artificial Intelligence in Manufacturing: A Review of the Emerging Wave of Ethical and Human Centric AI Technologies for Smart Production , pages=

    A review of explainable artificial intelligence in manufacturing , author=. Trusted Artificial Intelligence in Manufacturing: A Review of the Emerging Wave of Ethical and Human Centric AI Technologies for Smart Production , pages=. 2021 , publisher=

    2021

  75. [83]

    Journal of Industrial Information Integration , volume=

    Interpreting learning models in manufacturing processes: towards explainable AI methods to improve trust in classifier predictions , author=. Journal of Industrial Information Integration , volume=. 2023 , publisher=

    2023

  76. [84]

    Advances in Mechanical Engineering , volume=

    The relationships between cutting parameters, tool wear, cutting force and vibration , author=. Advances in Mechanical Engineering , volume=. 2018 , publisher=

    2018

  77. [85]

    Universe , volume=

    A Comprehensive Guide to Interpretable AI-Powered Discoveries in Astronomy , author=. Universe , volume=. 2025 , publisher=

    2025

  78. [86]

    The Astrophysical Journal , volume=

    Gamma-ray light curves and variability of bright Fermi-detected blazars , author=. The Astrophysical Journal , volume=. 2010 , publisher=

    2010

  79. [87]

    The Astrophysical Journal Supplement Series , volume=

    Exploring -Ray Flares in the Long-term Light Curves of CTA 102 at GeV Energies , author=. The Astrophysical Journal Supplement Series , volume=. 2022 , publisher=

    2022

  80. [88]

    Engineering Applications of Artificial Intelligence , volume=

    An analysis of explainability methods for convolutional neural networks , author=. Engineering Applications of Artificial Intelligence , volume=. 2023 , publisher=

    2023

  81. [89]

    Advances in neural information processing systems , volume=

    Sanity checks for saliency maps , author=. Advances in neural information processing systems , volume=

  82. [90]

    arXiv preprint arXiv:2004.14243 , year=

    Towards transparent and explainable attention models , author=. arXiv preprint arXiv:2004.14243 , year=

    2004 arXiv

  83. [91]

    Artificial Intelligence Review , volume=

    Physics-informed neural networks for PDE problems: A comprehensive review , author=. Artificial Intelligence Review , volume=. 2025 , publisher=

    2025

  84. [92]

    Preprints

    Embedding Physics into Deep Learning: A Structured Review of Physics-Informed Neural Networks , author=. Preprints. org , year=

  85. [93]

    arXiv preprint arXiv:2401.04986 , year=

    Structure-preserving physics-informed neural networks with energy or lyapunov structure , author=. arXiv preprint arXiv:2401.04986 , year=

    arXiv

  86. [94]

    arXiv preprint arXiv:2410.17445 , year=

    Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks , author=. arXiv preprint arXiv:2410.17445 , year=

    arXiv

  87. [95]

    Results in Engineering , volume=

    Forecasting energy consumption demand of customers in smart grid using Temporal Fusion Transformer (TFT) , author=. Results in Engineering , volume=. 2023 , publisher=

    2023

  88. [96]

    Energy , volume=

    Short-term wind power forecasting model based on temporal convolutional network and Informer , author=. Energy , volume=. 2023 , publisher=

    2023

  89. [97]

    Energy , pages=

    A novel CNN-LSTM-based forecasting model for household electricity load by merging mode decomposition, self-attention and autoencoder , author=. Energy , pages=. 2025 , publisher=

    2025

  90. [98]

    Energy and Buildings , volume=

    Interpretable deep learning model for building energy consumption prediction based on attention mechanism , author=. Energy and Buildings , volume=. 2021 , publisher=

    2021

  91. [99]

    IEEE access , volume=

    Toward practical usage of the attention mechanism as a tool for interpretability , author=. IEEE access , volume=. 2022 , publisher=

    2022

  92. [100]

    Joint European conference on machine learning and knowledge discovery in databases , pages=

    Online adaptive multivariate time series forecasting , author=. Joint European conference on machine learning and knowledge discovery in databases , pages=. 2022 , organization=

    2022

  93. [101]

    arXiv preprint arXiv:1902.10186 , year=

    Attention is not explanation , author=. arXiv preprint arXiv:1902.10186 , year=

    1902 arXiv

  94. [102]

    arXiv preprint arXiv:2507.20453 , year=

    Your Attention Matters: to Improve Model Robustness to Noise and Spurious Correlations , author=. arXiv preprint arXiv:2507.20453 , year=

    arXiv

  95. [103]

    2023 IEEE International Conference on Data Mining (ICDM) , pages=

    Explainable adaptive tree-based model selection for time-series forecasting , author=. 2023 IEEE International Conference on Data Mining (ICDM) , pages=. 2023 , organization=

    2023

  96. [104]

    World conference on explainable artificial intelligence , pages=

    A deep dive into perturbations as evaluation technique for time series XAI , author=. World conference on explainable artificial intelligence , pages=. 2023 , organization=

    2023

  97. [105]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

    Casting your model: Learning to localize improves self-supervised representations , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

  98. [106]

    Information , volume=

    ProtoPGTN: A Scalable Prototype-Based Gated Transformer Network for Interpretable Time Series Classification , author=. Information , volume=. 2025 , publisher=

    2025

  99. [107]

    Procedia Manufacturing , volume=

    Virtual machining: capabilities and challenges of process simulations in the aerospace industry , author=. Procedia Manufacturing , volume=. 2016 , publisher=

    2016

  100. [108]

    Journal of forecasting , volume=

    ARMA models and the Box--Jenkins methodology , author=. Journal of forecasting , volume=. 1997 , publisher=

    1997

  101. [109]

    International journal of forecasting , volume=

    Exponential smoothing model selection for forecasting , author=. International journal of forecasting , volume=. 2006 , publisher=

    2006

  102. [110]

    Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages=

    Right on time: Revising time series models by constraining their explanations , author=. Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages=. 2025 , organization=

    2025

  103. [111]

    Foresight , volume=

    Decision trees for time-series forecasting , author=. Foresight , volume=

  104. [112]

    Machine learning , volume=

    Random forests , author=. Machine learning , volume=. 2001 , publisher=

    2001

  105. [113]

    Ieee Access , volume=

    Hybrid CNN-LSTM model for short-term individual household load forecasting , author=. Ieee Access , volume=. 2020 , publisher=

    2020

  106. [114]

    International journal of forecasting , volume=

    DeepAR: Probabilistic forecasting with autoregressive recurrent networks , author=. International journal of forecasting , volume=. 2020 , publisher=

    2020

  107. [115]

    arXiv preprint arXiv:1905.10437 , year=

    N-BEATS: Neural basis expansion analysis for interpretable time series forecasting , author=. arXiv preprint arXiv:1905.10437 , year=

    1905 arXiv

  108. [116]

    Energies , volume=

    Transformer-based model for electrical load forecasting , author=. Energies , volume=. 2022 , publisher=

    2022

  109. [117]

    KDD , year=

    Generic and scalable framework for automated time-series anomaly detection , author=. KDD , year=

  110. [118]

    International journal of forecasting , volume=

    Another look at measures of forecast accuracy , author=. International journal of forecasting , volume=. 2006 , publisher=

    2006

  111. [119]

    Advances in data science and information engineering: proceedings from ICDATA 2020 and IKE 2020 , pages=

    A brief review of domain adaptation , author=. Advances in data science and information engineering: proceedings from ICDATA 2020 and IKE 2020 , pages=. 2021 , publisher=

    2020

  112. [120]

    arXiv preprint arXiv:2105.06643 , year=

    Monash time series forecasting archive , author=. arXiv preprint arXiv:2105.06643 , year=

    arXiv

  113. [121]

    Computer Methods and Programs in Biomedicine , volume=

    Concept-based AI interpretability in physiological time-series data: Example of abnormality detection in electroencephalography , author=. Computer Methods and Programs in Biomedicine , volume=. 2024 , publisher=

    2024

  114. [122]

    Frontiers in Artificial Intelligence , volume=

    Human-annotated rationales and explainable text classification: a survey , author=. Frontiers in Artificial Intelligence , volume=. 2024 , publisher=

    2024

  115. [123]

    The Astrophysical Journal Supplement Series , volume=

    Fermi large area telescope fourth source catalog , author=. The Astrophysical Journal Supplement Series , volume=. 2020 , publisher=

    2020

  116. [124]

    The Astrophysical Journal , volume=

    Multimessenger Picture of J1048+ 7143 , author=. The Astrophysical Journal , volume=. 2022 , publisher=

    2022

  117. [125]

    2026 , eprint=

    A Meta-Knowledge-Augmented LLM Framework for Hyperparameter Optimization in Time-Series Forecasting , author=. 2026 , eprint=

    2026

Pith tools

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