Ou Z. W. 2025. Application of deep learning methods to high-energy astrophysics. Astronomical Techniques and Instruments, 2(1): 44−51. https://doi.org/10.61977/ati2024063.
Citation:
Ou Z. W. 2025. Application of deep learning methods to high-energy astrophysics. Astronomical Techniques and Instruments, 2(1): 44−51. https://doi.org/10.61977/ati2024063.
Ou Z. W. 2025. Application of deep learning methods to high-energy astrophysics. Astronomical Techniques and Instruments, 2(1): 44−51. https://doi.org/10.61977/ati2024063.
Citation:
Ou Z. W. 2025. Application of deep learning methods to high-energy astrophysics. Astronomical Techniques and Instruments, 2(1): 44−51. https://doi.org/10.61977/ati2024063.
High-energy gamma-ray astronomy, at frequencies of 100 MeV to 100 GeV, yields insights into the fields of compact objects, extreme processes, and particle propagation. Thousands of gamma-ray sources have been detected by the Fermi Gamma-ray Space Telescope, many without any known counterpart at other wavelengths or clear identification of the source. Deep learning algorithms have been successfully applied to a variety of problems in astronomy. In this paper, I give some typical examples for classifying Fermi sources with deep learning methods, to show how such techniques can improve capability to unveil the nature of high-energy gamma-ray sources.
High-energy (HE) gamma-rays (100 MeV to 100 GeV) represent the most energetic and extreme non-thermal processes in the Universe. They can be produced by particle acceleration from compact objects and extreme environments, providing insight into the origin and propagation of cosmic rays. The Small Astronomy Satellite 2 (SAS-2)[1], Celestial Observation Satellite B (COS-B)[2] and the Compton Gamma Ray Observatory (CGRO)[3] explore the Universe at sub-GeV and GeV energies. Energetic Gamma-Ray Experiment Telescope (EGRET) performed the first sensitive all-sky survey at gamma-ray frequencies, which yielded many valuable results, such as the first observation that Active Galactic Nuclei (AGN) can emit high-energy gamma-rays. EGRET has also increased the number of known pulsars, and helped to construct models to reveal how they accelerate particles. Since the launch of the Fermi Gamma-ray Space Telescope, HE gamma-ray astronomy has entered a golden age[4]. The Large Area Telescope (LAT), an instrument on board Fermi, covers an energy range from tens of MeV up to several TeV. Fermi Large Area Telescope (Fermi-LAT) surveys the sky in the high-energy regime approximately every 3 hours, performing excellently at monitoring persistent and transient sources with both galactic and extragalactic origins[5,6].
HE gamma-rays are mainly produced by two processes. In the leptonic process, HE electrons and positrons can interact with low-energy photons and boost them to high energies by Inverse Compton scattering. Electrons and positrons interacting with magnetic fields can also produce synchrotron photons. The other process is hadronic, in which the interaction between HE protons or nuclei in compact objects with protons in the dense interstellar medium often produces neutral mesons. Such mesons, resulting from nuclear interactions, quickly decay and produce gamma-rays. It is of key importance to determine whether leptonic or hadronic processes dominate the HE, very-high-energy (VHE, 100 GeV to 100 TeV) and even ultra-high-energy (UHE, above 100 TeV) ranges[7]. Since neutrinos are also the product of proton-proton interactions, hadronic processes are key for multi-messenger astronomy which link gamma-rays and neutrinos. For example, Fermi blazars (i.e. blazars detected by Fermi-LAT) are considered to give an important contribution to the diffuse TeV neutrino flux[8]. Consequently, observing HE gamma-rays from astrophysical sources is crucial to understand particle acceleration in the Universe.
This paper is organized as follows: Section 2 describes HE gamma-ray astronomy, Section 3 briefly describes machine learning (ML) techniques in astronomy, Section 4 elaborates on the identification of gamma-ray sources, and Section 5 gives a summary of this paper.
2.
HE GAMMA-RAY ASTRONOMY
Detection of HE gamma-rays uses the conversion of photons to electron/positron pairs. Such secondary electrons and positrons can be recorded with tracking detectors. Thus, one can reconstruct the arrival direction and energy of primary gamma-rays according to the secondary particles produced, with the energy resolution being affected by fluctuations in the electron/positron cascade which develop in the detector. At several GeV, this technique has a better energy resolution than at other energy range.
During its 16 years of operation, Fermi-LAT has created numerous catalogs including general sources[9-12], hard sources[13-15], solar flares[16], transients[17], gamma-ray bursts[18,19], pulsars[20-22], AGN[23-26], low energy sources[27], flaring sources[28], and supernova remnants[29]. These catalogs have significantly increased the number and variety of known HE gamma-ray sources.
Fermi-LAT revealed that the high-energy gamma-ray sky is dominated by AGN and pulsars, which are prevalent as extragalactic and galactic sources, respectively. AGN emit gamma-rays from collimated jets of charged particles with relativistic speeds[30]. As emissions from extragalactic sources, gamma-rays from AGN suffer attenuation due to the extragalactic background light (EBL) and produce electron/positron pairs[31]. Among AGN, blazars are a sub-class with extreme variability on timescales of seconds to years. Blazars show a spectroscopic structure with two bumps[32], which can be explained by the Doppler beaming effect observed in relativistic jets pointing at the observer, with a small viewing angle. According to emission lines in the optical band, blazars can be subdivided into BL Lacertae and flat spectral radio quasar (FSRQ) varieties. The distribution of photon index for Fermi blazars correlates with the blazar subclass[33].
Pulsar gamma-ray emissions originate from electromagnetic interactions between relativistic charged particles accelerated along magnetic field lines. Pulsars are stable, providing the most luminous gamma-ray sources in our galaxy. Spin-down power can be efficiently converted into gamma-rays via particle acceleration. Two types of magnetosphere models have been proposed to explain gamma-ray emission from pulsars. Polar cap models suggest that gamma-rays arise from cascades of electron/positron pairs, originating in the regions near the neutron star surface. Outer gap models, on the other hand, suggest that gamma-ray emissions originate from the outer part of the neutron star magnetosphere[34]. More than 3130 of the associated or identified the Fermi-LAT Fourth Source Catalog (4FGL) sources are AGN, while 239 are pulsars. However, for the total number of 5064 4FGL sources, 1336 (26.4%) remain unassociated. Most of them are faint sources with test statistics (TS) < 100. Elucidating unidentified sources (UID) may greatly improve understanding of the gamma-ray sky. In addition, some identified sources are still of unknown sub-class. For example, 1312 sources are labeled as blazar candidates of uncertain type (BCU) in Fermi-LAT 4FGL data release 1 (DR1). Consequently, it is also important to identify the sub-class of progenitor AGN.
Identifying gamma-ray sources can yield information on the physical environment of their progenitors. In the extragalactic sky, the origin of the extragalactic gamma-ray background (EGB) is still an open question, and blazars and radio galaxies are thought to be substantial EGB contributors. Considering star formation activity and resulting cosmic ray acceleration, star-forming galaxies are also candidates for the EGB. Therefore, determining the class and number of extragalactic gamma-ray sources is important for resolving prospective components of the EGB[35].
Among galactic sources, pulsars dominate the high-energy range. Pulsar spin-down can be explained by various models[36-38], with wind or outflow expected to contribute to the process. The pulsar wind nebula (PWN) population is a promising contributor to galactic diffuse gamma-ray emissions (DGE). In addition, pulsar halos are recently discovered objects which also contribute to DGE[39]. These depend on the injection rate and injection spectral shape.
A primary strategy to identify UIDs in Fermi-LAT data concerns how to find suspected progenitors like AGN and/or pulsars. The population of UIDs can be assumed to follow the same distribution as associated/identified sources. Research into source identification aims to unveil the nature of UID gamma-ray sources. Classification requires up-to-date knowledge on different kinds of gamma-ray sources.
3.
APPLICATION OF ML IN ASTRONOMY
3.1
ML Algorithms
ML has a long history of application to astronomical researches, such as identifying light curves[40,41], analyzing spectra[42,43], detecting absorbing species in interstellar gas[44] and classification[45,46]. Employing ML techniques improves the efficiency of classification methods by using prediction models based on training data. ML algorithms determine information directly from data rather than depending on predetermined formulation. As the sample size used in ML increases, the algorithm performance improves adaptively. The application of this kind of classification to HE gamma-ray astronomy is discussed in Section 4.
ML can be divided into supervised learning and unsupervised learning. Supervised learning aims to develop a predictive model based on both input and output data, for classification and regression. The relationship between input and output data must be known for optimal model training. The training data include features and labels, with the intention being for ML to determine the connection between these two values. Unsupervised learning aims to group and interpret data based only on input data. Input data provide the feature without the label, which can be applied to more complicated cases such as clustering. The intention is for the machine to learn by itself.
Several ML classification algorithms have been successfully applied to astronomy:
Decision Tree (DT): The features of sample are split according to branch, towards predictors and targets. This model shows decision rules and classification results according to tree shape. As an induction method, disordered and cluttered data are inverted into a model which can be applied to predict unknown data. Classification can deal with either discrete or continuous target values, and is based on the training of historical data.
Logistic Regression (LR): The LR method is a multivariate analysis model which predicts the probability of different classes, based on the values of a predictor. It is mainly used for classification related to dichotomies. The predictor variables do not need to follow a normal distribution. Such algorithms aim to find the best linear separation for input data.
Random Forest (RF): The RF method uses decision trees as building blocks for tasks such as regression and classification. It can be seen as the integration of multiple DTs. Based on a huge number of DTs, RF improves the predictions by gathering them together. RF can deal with nonlinear situations and large samples. The key parameters are the number of DTs and features.
Support Vector Machine (SVM): The SVM produces an optimal hyperlane that classifies new examples from training data. It uses a dichotomous approach to define the linear classifier with largest functional margin.
Boosted Decision Tree (BDT): Based on DT, the BDT classifier works by repeating yes or no to separate positive and negative classes. By changing the weight of training samples to learn multiple classifiers, the capability of these classifiers can be improved.
Convolutional Neural Network (CNN): This is a popularly used ML algorithm which automatically extracts characteristics from high-dimensional data. CNN has been used extensively in image classification, because it learns underlying features from different layers and obtains spatial relations between pixels.
3.2
Deep Learning Method
Deep learning (DL) is a subclass of ML, using a model that consists of multiple processing layers. This allows it to process more complicated data and tasks. Samples used by DL need to be representative, ensuring training data and predicted samples are classified independently. This guarantees generalization ability and good prediction accuracy. DL has performed successfully in several fields in astronomy.
4.
DL in Fermi-LAT Classification
4.1
Classification Method of Fermi-LAT Sources
For training data, the feature of a sample must be known. Therefore, it is important to understand the feature to be used, from the Fermi catalog, such as spectral models. For example, blazar spectra are modeled using a LogParabola relationship, as
dNdE=N0(EEb)−[α+βln(E/Eb)],
(1)
where N0 is the normalization, α is the first index, β is the second index, and Eb is the scale parameter.
Pulsar spectra are modeled using a power law with an exponential cutoff, as
dNdE={N0(EE0)γ0−d2lnEE0−db6ln2EE0−db224ln3EE0 if |blnEE0|<10−2N0(EE0)γ0+d/bexp{db2[1−(EE0)b]} otherwise ,
(2)
where N0 is the prefactor, γ0 is the first spectral index, E0 is the scale parameter, d is the local curvature parameter, and b is the second spectral index.
The gamma-ray spectra of pulsars are more curved than those of AGN. In addition, for the two sub-class of blazar, flat-spectrum radio quasars (FSRQs) peak at a lower energy than BL Lacs. A prominent feature of blazars is variability, which hint at the mass of the supermassive black hole and radiation from jets. Variability in the timescale from radio waves to gamma-rays spans from years to minutes[47]. All these features in different objects can help to classify them. Strong correlation is found between gamma-ray photon index and log L for FSRQ and BL Lacs[48]. 2863 objects (89% of total sources) are located at high Galactic latitudes in 4LAC (|b| > 10°), where AGN comprise almost four-fifths of the 4FGL sources. UID sources in this region share common spectral features with BCUs which suggests that, for the most part, they are AGN.
The number of detected sources has increased greatly because of data gathered by the Fermi Gamma-ray Space Telescope. 4FGL data release 3 (DR3) contains 6658 point sources[49]. However, around one-third of these are unassociated with any counterparts at different wavelengths.
By considering two major classes of gamma-ray emitters, AGN and pulsars, the RF and LR algorithms have been applied to classify Fermi-LAT Third Source Catalog (3FGL) UID[50]. This work further develops the classification of pulsar candidate sub-classes (young and millisecond pulsars). Similarly, RF and extreme gradient boosting (XGBoost) have been used to determine that 34 unassociated Fermi sources at high galactic latitudes may potentially be pulsars[51].
Which parameters to consider in ML algorithms is an important consideration. Because not all 4FGL parameters are related to a special science case, more parameters may not necessarily improve accuracy.
A new method has been proposed, which directly trains on energy- and time-dependent photon fluxes from the 4FGL-DR2 catalog, rather than relying on specific or hand-crafted features[52]. This is a novel technique that uses a recurrent neutral network to give good performance classifying gamma-ray sources, yielding results that are different to but compatible with a previous study related to human-crafted features. This aims to address sample selection bias, and can be applied to multi-wavelength data acquired from different facilities. Most pulsar candidates are distributed in the galactic plane, as shown in Fig. 1. However, AGN candidates have a more random distribution than pulsars. As the variability-curvature plot illustrates, AGN and pulsars cluster to different regions, and pulsars tend to be non-variable while having spectra with significant curvature. The distribution of AGN and pulsar candidates cluster in the variability-curvature plot, confirming that the neural network extracts realistic features from spectra.
Figure
1.
Space and parameter distribution of AGN and pulsars (PSR) from the 4FGL-DR2 catalog[52].
(A) Galactic latitude distribution of AGN among 4FGL-DR2 sources. (B) Galactic latitude distribution of pulsars among 4FGL-DR2 sources. The distribution of AGN and pulsars labeled in the 4FGL catalogue are shown together with the distribution of source candidates as derived by deep neural networks and recurrent neural networks. (C) Variability-curvature plot for labeled AGN and pulsars in 4FGL catalogue. The distribution of AGN and pulsar candidate obtained from deep neural networks is overlaid.
As blazars are the largest population among Fermi sources, there are still many blazar candidates of uncertain type (BCU). These objects display similar flat radio spectra with multi-wavelength spectral energy distributions (SEDs) showing the same two-humped shape as blazars. However, optical association is lacking to confirm their nature. Gradient-boosted decision trees have been used as BCU classifiers, because of the small set of available data[53]. Comparing the distribution of power law (PL) photon indices, it is clear that BL Lacs (2.03 ± 0.21) spectra are harder than those of FSRQs (2.47 ± 0.20), shown in Fig. 2. The PL photon index of BL Lacs (2.09 ± 0.21) and FSRQ (2.57 ± 0.14) candidates show good agreement with known BL Lacs and FSRQs. The alternative plot for the difference in PL photon index between BL Lacs and FSRQs shows photon index versus luminosity. There is a clear correlation between photon index and probability. In this figure, the orange and blue dashed lines show the classification threshold defined for FSRQs and BL Lacs. Furthermore, the plot of PL photon index versus flux shows that different blazar classes are comparable.
Figure
2.
Power law photon index of BL Lacs and FSRQs[53].
(A) The PL photon index distribution of BL Lacs in the 4FGL catalogue. (B) The PL photon index distribution of FSRQs in the 4FGL catalogue. Both confirmed sources and candidates classified with a boosting decision tree are shown. (C) PL photon index versus probability. (D) PL photon index versus energy flux above 100 MeV. The curved black line is the decision boundary corresponding to the separation of the two classes.
The sources in most ML classification tasks for Fermi-LAT UIDs are primarily those with high significance, but it is doubtful that this frame can be applied to all sources. While most UIDs are located at low Galactic latitude, confirmed AGN are mainly dominated by high galactic latitude sources. Because of the diffuse gamma-ray background and the difference between galactic and extragalactic source distribution at different latitudes, care should be taken over the application of training models. Therefore, different classification models (Fig. 3) were established for low and high galactic latitude regions[54].
(A) From top to bottom, the spectral index distribution of Bayesian-Gaussian (BG) parameters for low-latitude associated AGNs, AGN-like candidates, and both. The gray line, red region and blue region represent all sources, sources with low confidence from BG evaluation, and the remaining samples, respectively. (B) From top to bottom, analysis results of AGN-like, pulsar-like, and other sources. The gray, red and blue lines show unassociated sources, associated sources, and candidates for other categories identified by ML, respectively.
Based on the training set with 10 selected parameters, the performance of different ML models can be compared[55]. The parameter correlation coefficients are given in Fig. 4A. The average significance, flux, and energy flux show a strong correlation with each other. These three parameters reflect the features of gamma-ray radiation. Average significance, flux, and energy flux are also strongly correlated. Photon index is the most important feature for RF, as shown in Fig. 4B.
Figure
4.
Estimation of parameter space in ML models[55].
(A) Correlation coefficients of parameters. (B) Parameter importance estimated by the RF algorithm.
Pulsars detected by Fermi arise from the First Fermi-LAT Catalog of Gamma-Ray Pulsars (1PC, 46 pulsars), the Second Fermi-LAT Catalog of Gamma-Ray Pulsars (2PC, 132 pulsars), and the Third Fermi-LAT Catalog of Gamma-Ray Pulsars (3PC, 294 pulsars). Observing gamma-ray pulses from radio pulsars may help with supplementation of multi-wavelength features in pulsars. On the other hand, gamma-ray blind searches of unidentified sources can find more radio-quiet pulsars. The development of pulsation detection techniques can further increase the number of known gamma-ray pulsars. Although more than 3000 pulsars are shown in the Australia Telescope National Facility (ATNF) Pulsar Catalog, less than 300 gamma-ray pulsars have been found by Fermi-LAT.
In the 3FGL era, ML techniques were applied to classify 3FGL sources[50]. The same techniques can also be applied to a sub-sample of gamma-ray pulsars, which includes young and millisecond pulsars. The "outlyingness" with respect to pulsar and AGN classes reveals the nature of the observed source (the definition of outlyingness can be found in Reference [50]). As can be seen, most AGN have large values of pulsar outlyingness. Similarly, most pulsars have large values of AGN outlyingness. For those with a large value of both pulsar and AGN outlyingness, they should be non-pulsar and non-AGN sources, which are shown in Fig. 5.
Figure
5.
Outlyingness with AGN and pulsar classes of all 3FGL sources calculated by the RF algorithm [50].
Aims on searching pulsars in 3FHL, it is useful to label pulsar and non-pulsar to supervise classification methods[56]. As discussed above, gamma-ray flux variability is a crucial feature for distinguishing AGN from pulsars. Such variability features are included in the 4FGL catalog, but not in 3FHL. Therefore, this work employs an automatic algorithm to select features to determine the nature of the sample using recursive feature elimination (RFE). This is a backward selection approach which eliminates unimportant features. As Fig. 6 shows, for this ML technique, patterns and quality of selected data are ignored. This is owing to the limited knowledge available to be emphasized.
Figure
6.
Parameter space for selected features with highly ranked scores[56].
(A) Correlation between power law index and flux density error. (B) Correlation between flux density error and pivot energy. (C) Correlation between power law index and pivot energy.
Here, the flux density error, power law index and pivot energy parameters are ranked, suggesting that the hardness of gamma-rays is important for distinguishing pulsars from other sources. Since a softer gamma-ray source has a smaller pivot energy, it anti-correlates with power law index. Fig. 6 shows two-dimensional projections of the parameter space for highly ranked parameters. This suggests that the hardness (ratio of soft to hard photons) is an important factor for identifying pulsar candidates.
5.
SUMMARY
DL algorithms are applied in HE gamma-ray astronomy for the classification of Fermi-LAT sources and their sub-classes. The application of DL has increased the efficiency of gamma-ray source classification, compared with previous techniques. Such automatic analysis shortens the time cycle required to identify the nature of sources. Several examples mentioned in this review have been corroborated by subsequent multi-wavelength observations. However, current progress on classification is mainly based on observational properties. An increasing number of new kinds of astrophysical objects have also been found in the HE gamma-ray band. Furthermore, DL techniques are computationally intensive, owing to complicated model design. Future classification methods will require a greater number of physical parameters related to different theories and/or new populations.
ACKNOWLEDGMENTS
This work was supported by the Natural Science Foundation of China (12393853).
Derdeyn, S. M., Ehrmann, C. H., Fichtel, C. E., et al. 1972. SAS-B digitized spark chamber gamma ray telescope. Nuclear Instrumentation and Methods, 98: 557−566. doi: 10.1016/0029-554X(72)90243-1
[2]
Bignami, G. F., Boella, G., Burger, J. J., et al. 1975. The COS-B experiment for gamma-ray astronomy. Space Science Instrumentation, 1: 245−268.
[3]
Kanbach, G., Bertsch, D. L., Fichtel, C. E., et al. 1989. The project EGRET (energetic gamma-ray experiment telescope) on NASA's Gamma-Ray Observatory (GRO). Space Science Reviews, 49(1/2): 69−84. doi: 10.1007/BF00173744
[4]
Spandre, G., GLAST Collaboration. 2007. The γ-ray large-area space telescope: An astro-particle mission to explore the high-energy γ-ray sky. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 572(1): 500−502. doi: 10.1016/j.nima.2006.10.192
[5]
Cai, Y. Z., Pastorello, A., Fraser, M., et al. 2018. AT 2017be-a new member of the class of intermediate-luminosity red transients. Monthly Notices of the Royal Astronomical Society, 480(3): 3424−3445. doi: 10.1093/mnras/sty2070
[6]
Cai, Y. Z., Pastorello, A., Fraser, M., et al. 2019. The transitional gap transient AT 2018hso: new insights into the luminous red nova phenomenon. Astronomy & Astrophysics, 632: L6−L14. doi: 10.1051/0004-6361/201936749
[7]
Cao, Z., Chen, S., Liu, R., et al. 2023. Ultra-high-energy gamma-ray astronomy. Annual Review of Nuclear and Particle Science, 73: 341−363. doi: 10.1146/annurev-nucl-112822-025357
[8]
Aartsen, M. G., Abraham, K., Ackermann, M., et al. 2017. The contribution of Fermi-2LAC blazars to diffuse TeV-PeV neutrino flux. The Astrophysical Journal, 835(1): 45−61. doi: 10.3847/1538-4357/835/1/45
[9]
Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010. Fermi Large Area Telescope first source catalog. The Astrophysical Journal Supplement Series, 188(2): 405−436. doi: 10.1088/0067-0049/188/2/405
[10]
Nolan, P. L., Abdo, A. A., Ackermann, M., et al. 2012. Fermi Large Area Telescope second source catalog. The Astrophysical Journal Supplement Series, 199(2): 31−76. doi: 10.1088/0067-0049/199/2/31
[11]
Acero, F., Ackermann, M., Ajello, M., et al. 2015. Fermi Large Area Telescope third source catalog. The Astrophysical Journal Supplement Series, 218(2): 23−63. doi: 10.1088/0067-0049/218/2/23
[12]
Abdollahi, S., Acero, F., Ackermann, M., et al. 2020. Fermi Large Area Telescope fourth source catalog. The Astrophysical Journal Supplement Series, 247(1): 33−69. doi: 10.3847/1538-4365/ab6bcb
[13]
Ackermann, M., Ajello, M., Allafort, A., et al. 2013. The first Fermi-LAT catalog of sources above 10 GeV. The Astrophysical Journal Supplement Series, 209(2): 34−67. doi: 10.1088/0067-0049/209/2/34
[14]
Ackermann, M., Ajello, M., Atwood, W. B., et al. 2016. 2FHL: The second catalog of hard Fermi-LAT sources. The Astrophysical Journal Supplement Series, 222(1): 5−23. doi: 10.3847/0067-0049/222/1/5
[15]
Ajello, M., Atwood, W. B., Baldini, L., et al. 2017. 3FHL: The third catalog of hard Fermi-LAT sources. The Astrophysical Journal Supplement Series, 232(2): 18−41. doi: 10.3847/1538-4365/aa8221
[16]
Ajello, M., Baldini, L., Bastieri, D., et al. 2021. First Fermi-LAT solar flare catalog. The Astrophysical Journal Supplement Series, 252(2): 13−43. doi: 10.3847/1538-4365/abd32e
[17]
Baldini, L., Ballet, J., Bastieri, D., et al. 2021. Catalog of long-term transient sources in the first 10 yr of Fermi-LAT data. The Astrophysical Journal Supplement Series, 256(1): 13−39. doi: 10.3847/1538-4365/ac072a
[18]
Ackermann, M., Ajello, M., Asano, K., et al. 2013. The first Fermi-LAT gamma-ray burst catalog. The Astrophysical Journal Supplement Series, 209(1): 11−100. doi: 10.1088/0067-0049/209/1/11
[19]
Ajello, M., Arimoto, M., Axelsson, M., et al. 2019. A decade of gamma-ray bursts observed by Fermi-LAT: The second GRB catalog. The Astrophysical Journal, 878(1): 52−112. doi: 10.3847/1538-4357/ab1d4e
[20]
Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010. The first Fermi Large Area Telescope catalog of gamma-ray pulsars. The Astrophysical Journal Supplement Series, 187(2): 460−494. doi: 10.1088/0067-0049/187/2/460
[21]
Abdo, A. A., Ajello, M., Allafort, A., et al. 2013. The second Fermi Large Area Telescope catalog of gamma-Ray pulsars. The Astrophysical Journal Supplement Series, 208(2): 17−76. doi: 10.1088/0067-0049/208/2/17
[22]
Smith, D., Abdollahi, S., Ajello, M., et al. 2023. The third Fermi Large Area Telescope catalog of gamma-ray pulsars. The Astrophysical Journal, 958(2): 191−262. doi: 10.3847/1538-4357/acee67
[23]
Abdo, A. A. Ackermann, M., Ajello, M., et al. 2010. The first catalog of active galactic nuclei detected by the Fermi Large Area Telescope. The Astrophysical Journal, 715(1): 429−457. doi: 10.1088/0004-637X/715/1/429
[24]
Ackermann, M., Ajello, M., Allafort, A., et al. 2011. The second catalog of active galactic nuclei detected by the Fermi Large Area Telescope. The Astrophysical Journal, 743(2): 171−207. doi: 10.1088/0004-637X/743/2/171
[25]
Ackermann, M., Ajello, M., Atwood, W. B., et al. 2015. The third catalog of active galactic nuclei detected by the Fermi Large Area Telescope. The Astrophysical Journal, 810(1): 14−47. doi: 10.1088/0004-637X/810/1/14
[26]
Ajello, M., Angioni, R., Axelsson, M., et al. 2020. The fourth catalog of active galactic nuclei detected by the Fermi Large Area Telescope. The Astrophysical Journal, 892(2): 105−127. doi: 10.3847/1538-4357/ab791e
[27]
Principe, G., Malyshev, D., Ballet, J., et al. 2018. The first catalog of Fermi-LAT sources below 100 MeV. Astronomy & Astrophysics, 618: A22−34. doi: 10.1051/0004-6361/201833116
[28]
Abdollahi, S., Ackermann, M., Ajello, M., et al. 2017. The second catalog of flaring gamma-ray sources from the Fermi All-sky variability analysis. The Astrophysical Journal, 846(1): 34−48. doi: 10.3847/1538-4357/aa8092
[29]
Acero, F., Ackermann, M., Ajello, M., et al. 2016. The first Fermi LAT supernova remnant catalog. The Astrophysical Journal Supplement Series, 224(1): 8−57. doi: 10.3847/0067-0049/224/1/8
[30]
Marscher, A. P., Jorstad, S. G., D’Arcangelo, F. D., et al. 2008. The inner jet of an active galactic nucleus as revealed by a radio-to-γ-ray outburst. Nature, 452: 966−969. doi: 10.1038/nature06895
[31]
Biteau, J., Williams, D. A. 2015. The extragalactic background light, the Hubble constant, and anomalies: Conclusions from 20 years of TeV gamma-ray observations. The Astrophysical Journal, 812(1): 60−85. doi: 10.1088/0004-637X/812/1/60
[32]
Abdo, A. A., Ackermann, M., Agudo, I., et al. 2010. The spectral energy distribution of Fermi bright blazars. The Astrophysical Journal, 716: 30−70. doi: 10.1088/0004-637X/716/1/30
[33]
Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010. Spectral properties of bright Fermi-detected blazars in the gamma-ray band. The Astrophysical Journal, 710(2): 1271−1285. doi: 10.1088/0004-637X/710/2/1271
[34]
Cheng, K. S., Ruderman, M., Zhang, L. 2000. A three-dimensional outer magnetospheric gap model for gamma-ray pulsars: Geometry, pair production, emission morphologies, and phase-resolved spectra. The Astrophysical Journal, 537(2): 964−976. doi: 10.1086/309051
[35]
Di Mauro, M., Mancosi, S., Zechlin, H. S., et al. 2018. Deriving the contribution of blazars to the Fermi-LAT extragalactic γ-ray background at E > 10 GeV with efficiency corrections and photon statistics. The Astrophysical Journal, 856(2): 106−117. doi: 10.3847/1538-4357/aab3e5
[36]
Ou, Z. W., Tong, H., Kou, F. F., et al. 2016. Fluctuating neutron star magnetosphere: braking indices of eight pulsars, frequency second derivatives of 222 pulsars and 15 magnetars. Monthly Notices of the Royal Astronomical Society, 457(4): 3922−3933. doi: 10.1093/mnras/stw227
[37]
Tong, H., Kou, F. F. 2017. Possible evolution of the pulsar braking index from larger than three to about one. The Astrophysical Journal, 837(2): 117−122. doi: 10.3847/1538-4357/aa60c6
[38]
Gao, Z. F., Wang, N., Shan, H., et al. 2017. The Dipole magnetic field and spin-down evolutions of the high braking index pulsar PSR J1640-4631. The Astrophysical Journal, 849(1): 19−30. doi: 10.3847/1538-4357/aa8f49
[39]
Yan, K., Liu, R.Y. 2023. Constraints on the e± pair injection of pulsar halos: Implications from the Galactic diffuse multi-TeV gamma-ray emission. Physical Review D, 107(10): 103028. doi: 10.1103/PhysRevD.107.103028
[40]
Webb, S., Lochner, M., Muthukrishna, D., et al. 2020. Unsupervised machine learning for transient discovery in deeper, wider, faster light curves. Monthly Notices of the Royal Astronomical Society, 498(3): 3077−3094. doi: 10.1093/mnras/staa2395
[41]
Cui, K. M., Liu, J. J., Feng, F. B., et al. 2022. Idenfity light-curve signals with deep learning based object detection algorithm. I. Transit detection. The Astronomical Journal, 163(1): 23−32. doi: 10.3847/1538-3881/ac3482
[42]
Bu, Y. D., Zeng, J. J., Lei, Z. X., et al. 2019. Searching for hot subdwarf stars from the LAMOST spectra III. classification of hot subdwarf stars in the fourth data release of LAMOST using a deep learning method. The Astrophysical Journal, 886(2): 128−137. doi: 10.3847/1538-4357/ab4c47
[43]
Wang, B., Zou, J. Q., Cai, Z., et al. 2022. Deep learning of dark energy spectroscopic instrument mock spectra to find damped Lyα systems. The Astrophysical Journal Supplement Series, 259(1): 28−47. doi: 10.3847/1538-4365/ac4504
[44]
Ge, J., Willis, K., Chao, K. X., et al. 2024. Detecting rare neutral atomic-carbon absorbers with a deep neural network. Monthly Notices of the Royal Astronomical Society, 531(1): 387−402. doi: 10.1093/mnras/stae799
[45]
Zhang, Y. X., Zhao, Y. H., Wu, X. B. 2021. Classification of 4XMM-DR9 sources by machine learning. Monthly Notices of the Royal Astronomical Society, 503(4): 5263−5273. doi: 10.1093/mnras/stab744
[46]
Kang, S. J., Li, E. Z., Ou, W. J., et al. 2019. Evaluating the classification of Fermi BCUs from the 4FGL catalog using machine learning. The Astrophysical Journal, 887(2): 134−143. doi: 10.3847/1538-4357/ab558b
[47]
Biteau, J., Meyer, M. 2022. Gamma-ray cosmology and tests of fundamental physics. Galaxies, 10(2): 39. doi: 10.3390/galaxies10020039
[48]
Wang, G., Xiao, H. B., Fan, J. H., et al. 2024. GeV variability properties of TeV blazars detected by Fermi-LAT. The Astrophysical Journal Supplement Series, 270(2): 22−39. doi: 10.3847/1538-4365/ad0e08
[49]
Abdollahi, S., Acero, F., Baldini, L., et al. 2022. Incremental Fermi Large Area Telescope fourth source catalog. The Astrophysical Journal Supplement Series, 260(2): 53−76. doi: 10.3847/1538-4365/ac6751
[50]
Saz Parkinson, P. M., Xu, H., Yu, P. L. H., et al. 2016. Classification and ranking of Fermi LAT gamma-ray sources from the 3FGL catalog using machine learning techniques. The Astrophysical Journal, 820(1): 8−27. doi: 10.3847/0004-637X/820/1/8
[51]
Mirabal, N., Charles, E., Ferrara, E. C., et al. 2016. 3FGL demographics outside the galactic plane using supervised machine learning: Pulsar and dark matter subhalo interpretations. The Astrophysical Journal, 825(1): 69−76. doi: 10.3847/0004-637X/825/1/69
[52]
Finke, T., Kramer, M., Manconi, S. 2021. Classification of Fermi-LAT sources with deep learning using energy and time spectra. Monthly Notices of the Royal Astronomical Society, 507(3): 4061−4073. doi: 10.1093/mnras/stab2389
[53]
Sahakyan, N., Vardanyan, V., Khachatryan, M. 2023. Gradient boosting decision trees classification of blazars of uncertain type in the fourth Fermi-LAT catalogue. Monthly Notices of the Royal Astronomical Society, 519(2): 3000−3010. doi: 10.1093/mnras/stac3701
[54]
Zhu, K. R., Chen, J. M., Zheng, Y. G., et al. 2024. Classifications of Fermi-LAT unassociated sources in multiple machine learning methods. Monthly Notices of the Royal Astronomical Society, 527(2): 1794−1812. doi: 10.1093/mnras/stad2813
[55]
Ding, J. C., Huang, Y. L., Li, X. D., et al. 2023. Hybrid deep learning for blazar classification and correlation search with neutrinos. Monthly Notices of the Royal Astronomical Society, 523(3): 4120−4135. doi: 10.1093/mnras/stad1683
[56]
Hui, C. Y., Lee, J. S., Li, K. L., et al. 2020. Searches for pulsar-like candidates from unidentified objects in the third catalog of hard Fermi-LAT sources with machine learning techniques. Monthly Notices of the Royal Astronomical Society, 495(1): 1093−1109. doi: 10.1093/mnras/staa1113
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