pith. sign in

arxiv: 2605.17369 · v1 · pith:7343GNTCnew · submitted 2026-05-17 · 🌌 astro-ph.SR

The Deep Learning-Based Dual-Branch Multimodal Fusion Model for Solar Flare Prediction

Limin Zhao , Xingyao Chen , Xiaoshuai Zhu , Dong Zhao , and Yihua Yan This is my paper

Pith reviewed 2026-05-19 22:59 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar flare predictiondeep learningmultimodal fusionmagnetogramscross-attentionX-class flaresspace weather
0
0 comments X

The pith

Dual-branch fusion model predicts strong solar flares with TSS of 0.78 for X-class events

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a dual-branch deep learning model designed to predict solar flares 24 hours in advance by combining two types of data. One branch handles magnetogram images while the other processes numerical magnetic parameters, with cross-attention mechanisms allowing the model to fuse complementary information from both. Additional cross-scale interactions help capture features at different sizes, supporting both a simple yes-no prediction for flares at or above C-class and a more detailed classification into C, M, or X classes. Rigorous testing with data splits based on active region numbers and cross-validation shows the model outperforms prior methods especially on rare X-class flares while keeping false alarms low.

Core claim

The dual-branch multimodal fusion model integrates magnetograms and magnetic parameters through cross-attention mechanisms, followed by cross-scale interactions at the feature level to enhance multi-scale representation. It achieves a TSS of 0.661 and an HSS of 0.658 for binary ≥C-class prediction, while notably attaining a TSS of 0.780 and an HSS of 0.775 for X-class flares in the multi-class task, demonstrating superior performance in predicting intense X-class flares, effectively suppressing the false alarm rate, and exhibiting strong generalization capability.

What carries the argument

Dual-branch architecture using cross-attention mechanisms to fuse magnetogram images with magnetic parameters, plus cross-scale feature interactions for multi-scale representation.

If this is right

  • The model provides more reliable forecasts for intense solar flares that can disrupt satellites and power systems.
  • Lower false alarm rates reduce unnecessary preparations by operators.
  • The approach demonstrates better ability to generalize to previously unseen solar active regions.
  • Multi-class output allows for more nuanced space weather alerts tailored to flare strength.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar multimodal fusion techniques might enhance predictions for other solar phenomena such as coronal mass ejections.
  • The success suggests that future models could benefit from incorporating even more data modalities like EUV images or time sequences.
  • Operational deployment could support more precise real-time alerts for space weather impacts on technology.

Load-bearing premise

The splitting-before-sampling strategy based on NOAA active region numbers together with the stratified group five-fold cross-validation scheme fully prevents data leakage and ensures genuine generalization to unseen active regions.

What would settle it

If a test on randomly split data without respecting active region boundaries shows substantially lower TSS and HSS scores for X-class flares, it would suggest that the original results benefited from data leakage.

Figures

Figures reproduced from arXiv: 2605.17369 by and Yihua Yan, Dong Zhao, Limin Zhao, Xiaoshuai Zhu, Xingyao Chen.

Figure 1
Figure 1. Figure 1: The proposed network architecture consists of three main components: the Magnetogram and Magnetic Param￾eter Tokenizer (MMP-tokenizer), the Multi-Head Cross Attention module (MMP-MHCA), and the Multimodal Cross-Scale Interaction Network (MCSI-network). It incorporates M = 3 multimodal transformer encoders, each containing two branches processing magnetogram patches at different scales. Multimodal fusion wi… view at source ↗
Figure 2
Figure 2. Figure 2: The CNN module for extracting features from magnetograms and the structure for converting magnetic parameters into token representations. feature map is reshaped into a sequence of visual tokens only after these spatial features are captured, providing a structured input that can be directly fed into the transformer encoder. The feature extraction process can be formally described as: F1 = σ(W1 ∗ I + b1), … view at source ↗
Figure 3
Figure 3. Figure 3: Architecture of the multi-branch transformer encoder module. end to stabilize the feature distribution. This results in a tensor of parameter tokens Tp ∈ R B×Np×D, where D denotes the target embedding dimension consistent with the visual token space. This tokenization strategy ensures that the parameter tokens are architecturally aligned with visual tokens, enabling effective multimodal interaction in the … view at source ↗
Figure 4
Figure 4. Figure 4: Cross-attention information fusion between different branches. at the 0-th position is extracted as the multimodal CLS token ecls, while the subsequent tokens constitute the spatial patch sequence epatch. As illustrated in [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The curves show the loss dynamics of our proposed model during training and testing. Curves of different colors represent the loss trajectories across epochs for different datasets. Subfigure (a) and (c) depicts the training loss variations for each dataset, while subfigure (b) and (d) shows the corresponding testing loss variations. alization gap, defined as the difference between training and testing los… view at source ↗
Figure 6
Figure 6. Figure 6: The radar charts illustrate the evolution of recall, TSS, HSS,and F1 scores across training epochs on datasets D1 and D2. multiple key evaluation metrics. With TSS, HSS, and F1-score reaching 0.661, 0.658, and 0.827, respectively, our model significantly outperforms the corresponding results reported by R. Tang et al. (2021) and X. Huang et al. (2018). Although N. Nishizuka et al. (2018) reported a recall … view at source ↗
Figure 7
Figure 7. Figure 7: The radar charts illustrate the evolution of TSS, HSS, and F1 scores for C, M, and X-class flares across training epochs under datasets F1–F5. The results are arranged vertically in the figure, with C-class at the top, M-class in the middle, and X-class at the bottom [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of multimodal interaction strategies between magnetograms and physical parameters. specific architectures, all strategies follow a unified design principle: using the magnetogram modality as the primary information stream and incorporating parameter information to enrich feature representation and achieve cross-modal coordination. The corresponding quantitative comparison are summarized in [PIT… view at source ↗
Figure 9
Figure 9. Figure 9: Statistical comparison of feature channel responses across flare classes. The upper and lower panels display the median gradient and total intensity of the feature extraction layer across channels, respectively. Curves of different colors correspond to different flare classes [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Scatter plots illustrate the relationships between the global network median gradient and MEANPOT, TOTPOT, and R VALUE. Black dashed lines indicate linear regression trends with confidence intervals denoted by gray shading. Pearson correlation coefficients are annotated at the top of each panel. Notably, in these key channels, the feature response intensity exhibits a strict hierarchical distribution (i.e… view at source ↗
Figure 11
Figure 11. Figure 11: Spatiotemporal evolution of model attention. Rows illustrate the evolution of model attention within the prediction window for an X-class flare event. Columns from left to right display: (a) the original line-of-sight magnetogram; (b) the model attention heatmap where warm colors indicate high activation; (c) the overlay of the magnetogram and heatmap; and (d) the magnetogram superimposed with features wh… view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
read the original abstract

Solar flares are intense eruptive events caused by the rapid release of magnetic energy, often impacting Earth's space environment through electromagnetic radiation and high-energy particles. Accurate flare prediction is critical for space weather forecasting. However, many existing deep learning approaches often rely on single-modal inputs or shallow feature fusion, limiting their ability to capture complementary information. In this study, we propose a dual-branch multimodal fusion deep learning model for predicting 24-hour solar flares. The model integrates magnetograms and magnetic parameters through cross-attention mechanisms, followed by cross-scale interactions at the feature level to enhance multi-scale representation. It is designed to perform both binary prediction of $\geqslant$ C-class flares and multi-class classification of C, M, and X-class flares. To ensure rigorous evaluation, we employ a stratified group five-fold cross-validation scheme to preserve class representativeness and adopt a splitting-before-sampling strategy based on NOAA active region numbers to prevent data leakage. Experimental results show that the model achieves a TSS of 0.661 and an HSS of 0.658 for binary $\geqslant$ C-class prediction, while notably attaining a TSS of 0.780 and an HSS of 0.775 for X-class flares in the multi-class task. Compared with existing approaches, the model demonstrates superior performance in predicting intense X-class flares, effectively suppresses the false alarm rate, and exhibits strong generalization capability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a dual-branch multimodal deep learning model that fuses solar magnetograms and magnetic parameters via cross-attention mechanisms and cross-scale feature interactions for 24-hour ahead prediction of solar flares. It performs both binary classification of ≥C-class events and multi-class classification into C/M/X flares, reporting TSS = 0.661 and HSS = 0.658 on the binary task and notably higher skill (TSS = 0.780, HSS = 0.775) for X-class events. Evaluation relies on a stratified group 5-fold cross-validation scheme combined with a splitting-before-sampling strategy keyed to NOAA active-region numbers, which the authors state prevents data leakage and supports claims of superior performance and strong generalization relative to prior approaches.

Significance. If the reported metrics are shown to reflect genuine cross-AR generalization rather than residual intra-region correlations, the work would constitute a useful incremental advance in multimodal deep-learning methods for space-weather forecasting. The emphasis on X-class skill and false-alarm suppression addresses a practically important regime, and the adoption of group CV is a constructive step toward more rigorous evaluation standards in the field.

major comments (1)
  1. [Evaluation protocol] Evaluation protocol (abstract and §3): The claim that the stratified group 5-fold CV with NOAA-AR splitting-before-sampling fully prevents leakage is load-bearing for the generalization and superiority assertions. The manuscript does not specify (i) whether every sample belonging to a given AR is forced into a single fold, (ii) how overlapping 24-hour prediction windows within the same AR are assigned, or (iii) whether temporal autocorrelation of magnetic evolution across consecutive samples is mitigated. Without these details the reported TSS/HSS values cannot be confidently interpreted as cross-region generalization.
minor comments (2)
  1. [Figures] Figure captions and architecture diagrams should explicitly label the cross-attention blocks and cross-scale interaction modules so that the dual-branch fusion pathway is immediately traceable.
  2. [Results] The abstract states performance numbers but does not report the number of positive/negative samples per fold or the class-imbalance handling strategy; these statistics belong in the results section or a supplementary table.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our evaluation protocol and for recognizing the potential value of our multimodal approach for X-class flare prediction. We agree that greater specificity is required to support the no-leakage claim and will revise the manuscript to address each sub-point raised.

read point-by-point responses

  1. Referee: whether every sample belonging to a given AR is forced into a single fold

    Authors: Yes. Our stratified group 5-fold procedure first partitions the set of unique NOAA active-region numbers into five disjoint groups. All magnetogram and magnetic-parameter samples associated with any given AR number are then assigned exclusively to the fold corresponding to that group. This group-level assignment occurs before any instance-level sampling. We will add an explicit statement of this rule in the revised §3. revision: yes

  2. Referee: how overlapping 24-hour prediction windows within the same AR are assigned

    Authors: Because the split is performed at the AR-group level prior to sampling, every 24-hour window (including temporally overlapping windows) that belongs to the same active region is automatically placed in the identical fold. Consequently, no training–test leakage can arise from overlapping prediction intervals that share the same AR. We will clarify this assignment rule in the methods section of the revision. revision: yes

  3. Referee: whether temporal autocorrelation of magnetic evolution across consecutive samples is mitigated

    Authors: The protocol prevents cross-AR leakage but does not impose additional temporal gaps or decorrelation steps within an AR; consecutive samples from the same region therefore remain together in one fold. We acknowledge that residual intra-AR temporal autocorrelation may still be present. In the revised manuscript we will explicitly discuss this limitation and its implications for the interpretation of within-fold performance versus cross-region generalization. revision: partial

Circularity Check

0 steps flagged

No significant circularity; performance metrics are empirical evaluations on held-out data

full rationale

The paper's central claims consist of reported TSS/HSS scores obtained via stratified group 5-fold cross-validation after splitting samples by NOAA active region numbers. These metrics are computed directly from model predictions on test folds that are constructed to be disjoint from training data; they do not reduce algebraically to any fitted parameter, self-citation, or ansatz inside the model equations. The dual-branch fusion architecture, cross-attention mechanism, and training procedure are defined independently of the final numerical scores, so the generalization statements rest on external observational benchmarks rather than internal redefinition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The performance claims rest on the domain assumption that magnetograms and magnetic parameters supply complementary predictive signals and on the procedural assumption that the described data partitioning eliminates leakage.

free parameters (1)
  • neural network weights and hyperparameters
    The deep learning model contains numerous trainable parameters and architectural choices that are optimized against the training data to produce the reported skill scores.
axioms (1)
  • domain assumption Magnetograms and magnetic parameters contain complementary information that improves flare prediction when fused via cross-attention
    The model design presupposes that single-modal inputs are insufficient and that the proposed fusion mechanism extracts useful joint representations.

pith-pipeline@v0.9.0 · 5794 in / 1501 out tokens · 50640 ms · 2026-05-19T22:59:02.734691+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages

  1. [1]

    W., Qahwaji, R., Colak, T., et al

    Ahmed, O. W., Qahwaji, R., Colak, T., et al. 2013, Solar Physics, 283, 157

    work page 2013

  2. [2]

    2007, Space Weather, 5

    Barnes, G., Leka, K., Schumer, E., & Della-Rose, D. 2007, Space Weather, 5

    work page 2007

  3. [3]

    2016, The Astrophysical Journal, 829, 89

    Barnes, G., Leka, K., Schrijver, C., et al. 2016, The Astrophysical Journal, 829, 89

    work page 2016

  4. [4]

    Gallagher, P. T. 2012, The Astrophysical Journal Letters, 747, L41

    work page 2012

  5. [5]

    G., & Couvidat, S

    Bobra, M. G., & Couvidat, S. 2015, The Astrophysical Journal, 798, 135

    work page 2015

  6. [6]

    G., Sun, X., Hoeksema, J

    Bobra, M. G., Sun, X., Hoeksema, J. T., et al. 2014, Solar Physics, 289, 3549

    work page 2014

  7. [7]

    E., Al-Ghraibah, A., & McAteer, R

    Boucheron, L. E., Al-Ghraibah, A., & McAteer, R. J. 2015, The Astrophysical Journal, 812, 51

    work page 2015

  8. [8]

    2021, in Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)

    Chen, C.-F., Fan, Q., & Panda, R. 2021, in Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)

    work page 2021

  9. [9]

    2025, Multimedia Tools and Applications, 1

    Chen, R., Gao, C., Tan, Z., et al. 2025, Multimedia Tools and Applications, 1

    work page 2025

  10. [10]

    B., Hero, A

    Chen, Y., Manchester, W. B., Hero, A. O., et al. 2019, Space weather, 17, 1404

    work page 2019

  11. [11]

    2021, The Astrophysical Journal, 915, 38

    Cicogna, D., Berrilli, F., Calchetti, D., et al. 2021, The Astrophysical Journal, 915, 38

    work page 2021

  12. [12]

    2022, The Astrophysical Journal Supplement Series, 260, 9

    Deshmukh, V., Flyer, N., Van der Sande, K., & Berger, T. 2022, The Astrophysical Journal Supplement Series, 260, 9

    work page 2022

  13. [13]

    Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. 2019, in Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers) (Association for Computational Linguistics), 4171–4186

    work page 2019

  14. [14]

    2021, in International Conference on Learning Representations

    Dosovitskiy, A., Beyer, L., Kolesnikov, A., et al. 2021, in International Conference on Learning Representations. https://openreview.net/forum?id=YicbFdNTTy

    work page 2021

  15. [15]

    F., Khazanov, I., & Moore, R

    Falconer, D., Barghouty, A. F., Khazanov, I., & Moore, R. 2011, Space Weather, 9

    work page 2011

  16. [16]

    2018, Solar Physics, 293, 28

    Florios, K., Kontogiannis, I., Park, S.-H., et al. 2018, Solar Physics, 293, 28

    work page 2018

  17. [17]

    Giovanelli, R. G. 1939, Astrophysical Journal, vol. 89, p. 555, 89, 555

    work page 1939

  18. [18]

    D., Royer, A., Blankevoort, T., & Bejnordi, B

    Havtorn, J. D., Royer, A., Blankevoort, T., & Bejnordi, B. E. 2023, in Proceedings of the IEEE/CVF International Conference on Computer Vision, 838–848

    work page 2023

  19. [19]

    2018, The Astrophysical Journal, 856, 7

    Huang, X., Wang, H., Xu, L., et al. 2018, The Astrophysical Journal, 856, 7

    work page 2018

  20. [20]

    2010, Solar Physics, 263, 175

    Huang, X., Yu, D., Hu, Q., Wang, H., & Cui, Y. 2010, Solar Physics, 263, 175

    work page 2010

  21. [21]

    2020, Space weather, 18, e2020SW002440

    Jiao, Z., Sun, H., Wang, X., et al. 2020, Space weather, 18, e2020SW002440

    work page 2020

  22. [22]

    2022, in Proceedings of the Asian Conference on Computer Vision, 1488–1503 Kors´ os, M., Ludmany, A., Erdelyi, R., & Baranyi, T

    Kaneda, K., Wada, Y., Iida, T., et al. 2022, in Proceedings of the Asian Conference on Computer Vision, 1488–1503 Kors´ os, M., Ludmany, A., Erdelyi, R., & Baranyi, T. 2015, The Astrophysical Journal Letters, 802, L21

    work page 2022

  23. [23]

    2012, Solar Physics, 281, 639

    Lee, K., Moon, Y.-J., Lee, J.-Y., Lee, K.-S., & Na, H. 2012, Solar Physics, 281, 639

    work page 2012

  24. [24]

    Lee, Y., Kim, J., Willette, J., & Hwang, S. J. 2022, in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 7287–7296

    work page 2022

  25. [25]

    2003, The Astrophysical Journal, 595, 1296

    Leka, K., & Barnes, G. 2003, The Astrophysical Journal, 595, 1296

    work page 2003

  26. [26]

    2019, The Astrophysical Journal Supplement Series, 243, 36

    Leka, K., Park, S.-H., Kusano, K., et al. 2019, The Astrophysical Journal Supplement Series, 243, 36

    work page 2019

  27. [27]

    2021, Advances in neural information processing systems, 34, 9694

    Li, J., Selvaraju, R., Gotmare, A., et al. 2021, Advances in neural information processing systems, 34, 9694

    work page 2021

  28. [28]

    2013, Research in Astronomy and Astrophysics, 13, 1118

    Li, R., & Zhu, J. 2013, Research in Astronomy and Astrophysics, 13, 1118

    work page 2013

  29. [29]

    2020, The Astrophysical Journal, 891, 10

    Li, X., Zheng, Y., Wang, X., & Wang, L. 2020, The Astrophysical Journal, 891, 10

    work page 2020

  30. [30]

    2024, The Astrophysical Journal Supplement Series, 276, 7

    Li, X., Li, X., Zheng, Y., et al. 2024, The Astrophysical Journal Supplement Series, 276, 7

    work page 2024

  31. [31]

    T., & Wang, H

    Liu, C., Deng, N., Wang, J. T., & Wang, H. 2017, The Astrophysical Journal, 843, 104

    work page 2017

  32. [32]

    Liu, H., Liu, C., Wang, J. T. L., & Wang, H. 2019, The Astrophysical Journal, 877, 121, doi: 10.3847/1538-4357/ab1b3c

    work page doi:10.3847/1538-4357/ab1b3c 2019

  33. [33]

    D., Luhmann, J

    Liu, Y. D., Luhmann, J. G., Kajdiˇ c, P., et al. 2014, Nature Communications, 5, 3481

    work page 2014

  34. [34]

    2019, Advances in neural information processing systems, 32

    Lu, J., Batra, D., Parikh, D., & Lee, S. 2019, Advances in neural information processing systems, 32

    work page 2019

  35. [35]

    E., Gallagher, P

    McCloskey, A. E., Gallagher, P. T., & Bloomfield, D. S. 2018, Journal of Space Weather and Space Climate, 8, A34

    work page 2018

  36. [36]

    L., et al

    Messerotti, M., Zuccarello, F., Guglielmino, S. L., et al. 2009, Space science reviews, 147, 121

    work page 2009

  37. [37]

    2021, Earth, Planets and Space, 73, 1

    Nishizuka, N., Kubo, Y., Sugiura, K., Den, M., & Ishii, M. 2021, Earth, Planets and Space, 73, 1

    work page 2021

  38. [38]

    2018, The Astrophysical Journal, 858, 113

    Nishizuka, N., Sugiura, K., Kubo, Y., Den, M., & Ishii, M. 2018, The Astrophysical Journal, 858, 113

    work page 2018

  39. [39]

    2017, The Astrophysical Journal, 835, 156

    Nishizuka, N., Sugiura, K., Kubo, Y., et al. 2017, The Astrophysical Journal, 835, 156

    work page 2017

  40. [40]

    2024, arXiv preprint ARXIV.2406.11054

    Pandey, C., Adeyeha, T., Hong, J., Angryk, R., & Aydin, B. 2024, arXiv preprint ARXIV.2406.11054

    work page arXiv 2024

  41. [41]

    2018, The Astrophysical Journal, 869, 91

    Park, E., Moon, Y.-J., Shin, S., et al. 2018, The Astrophysical Journal, 869, 91

    work page 2018

  42. [42]

    2017, Space Weather, 15, 704 27

    Park, J., Moon, Y.-J., Choi, S., et al. 2017, Space Weather, 15, 704 27

    work page 2017

  43. [43]

    Raboonik, A., Safari, H., Alipour, N., & Wheatland, M. S. 2016, The Astrophysical Journal, 834, 11

    work page 2016

  44. [44]

    D., Guo, Y., & Wang, R

    Ran, H., Liu, Y. D., Guo, Y., & Wang, R. 2022, The Astrophysical Journal, 937, 43

    work page 2022

  45. [45]

    Ribeiro, F., & Gradvohl, A. L. S. 2021, Astronomy and Computing, 35, 100468

    work page 2021

  46. [46]

    M., & Kosovichev, A

    Sadykov, V. M., & Kosovichev, A. G. 2017, The Astrophysical Journal, 849, 148

    work page 2017

  47. [47]

    H., Bush, R

    Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, Solar Physics, 275, 229

    work page 2012

  48. [48]

    2009, Solar Physics, 254, 101

    Song, H., Tan, C., Jing, J., et al. 2009, Solar Physics, 254, 101

    work page 2009

  49. [49]

    2019, in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 5693–5703

    Sun, K., Xiao, B., Liu, D., & Wang, J. 2019, in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 5693–5703

    work page 2019

  50. [50]

    G., Wang, X., et al

    Sun, Z., Bobra, M. G., Wang, X., et al. 2022, The Astrophysical Journal, 931, 163

    work page 2022

  51. [51]

    2021, The Astrophysical Journal Supplement Series, 257, 50

    Tang, R., Liao, W., Chen, Z., et al. 2021, The Astrophysical Journal Supplement Series, 257, 50

    work page 2021

  52. [52]

    2017, Advances in neural information processing systems, 30

    Vaswani, A., Shazeer, N., Parmar, N., et al. 2017, Advances in neural information processing systems, 30

    work page 2017

  53. [53]

    2019, The Astrophysical Journal, 884, 175

    Wang, J., Liu, S., Ao, X., et al. 2019, The Astrophysical Journal, 884, 175

    work page 2019

  54. [54]

    Wang, J., Zhang, Y., Webber, S. A. H., et al. 2020, The Astrophysical Journal, 892, 140

    work page 2020

  55. [55]

    2020, The Astrophysical Journal, 895, 3

    Wang, X., Chen, Y., Toth, G., et al. 2020, The Astrophysical Journal, 895, 3

    work page 2020

  56. [56]

    2013, The Astrophysical Journal Letters, 774, L27

    Yang, X., Lin, G., Zhang, H., & Mao, X. 2013, The Astrophysical Journal Letters, 774, L27

    work page 2013

  57. [57]

    2023, IEEE transactions on pattern analysis and machine intelligence, 45, 10870

    Yao, T., Li, Y., Pan, Y., et al. 2023, IEEE transactions on pattern analysis and machine intelligence, 45, 10870

    work page 2023

  58. [58]

    2021, The Astrophysical Journal, 910, 8

    Yi, K., Moon, Y.-J., Lim, D., Park, E., & Lee, H. 2021, The Astrophysical Journal, 910, 8

    work page 2021

  59. [59]

    2009, The Astrophysical Journal, 709, 321

    Yu, D., Huang, X., Hu, Q., et al. 2009, The Astrophysical Journal, 709, 321

    work page 2009

  60. [60]

    2021, Monthly Notices of the Royal Astronomical Society, 507, 3519

    Zheng, Y., Li, X., Si, Y., Qin, W., & Tian, H. 2021, Monthly Notices of the Royal Astronomical Society, 507, 3519

    work page 2021

  61. [61]

    2019, The Astrophysical Journal, 885, 73

    Zheng, Y., Li, X., & Wang, X. 2019, The Astrophysical Journal, 885, 73

    work page 2019