pith. sign in

arxiv: 2606.05910 · v1 · pith:XX5X4C57new · submitted 2026-06-04 · 🌌 astro-ph.HE

Modeling Gamma-Ray Burst Spectra with Convolutional Neural Networks: Fast-Cooling Synchrotron Emission in a Decaying Magnetic Field

Jia-Ming Chen , Ke-Rui Zhu , Shan Chang , Zhao-Yang Peng , Yong-Gang Zheng , Li Zhang This is my paper

Pith reviewed 2026-06-28 00:38 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords gamma-ray burstssynchrotron emissiondecaying magnetic fieldconvolutional neural networksspectral emulatorBayesian inferenceFermi GBMprompt emission
0
0 comments X

The pith

A convolutional neural network emulator makes the decaying magnetic field fast-cooling synchrotron model practical for Bayesian fitting, and this model fits GRB 231020A spectra better than the standard version in most time intervals.

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

The paper trains a convolutional neural network on synthetic spectra to emulate the fast-cooling synchrotron emission produced in a radially decaying magnetic field. This emulator reduces spectral evaluation from expensive numerical integration to milliseconds, allowing full Bayesian analysis of time-resolved Fermi/GBM data. When applied to GRB 231020A, the decaying-field model returns better fits and lower Bayesian information criterion values than the constant-field fast-cooling synchrotron model across most time bins. The result indicates that a radially decaying magnetic field supplies a more physically consistent description of the observed nonthermal spectra.

Core claim

By replacing numerical integration with a trained convolutional neural network, the authors make the fast-cooling synchrotron spectrum in a decaying magnetic field fast enough for routine Bayesian spectral fitting; when this emulator is used on the time-resolved spectra of GRB 231020A, the decaying-field model is statistically preferred over the standard fast-cooling synchrotron model in most intervals.

What carries the argument

Convolutional neural network spectral emulator trained on numerical realizations of fast-cooling synchrotron emission in a decaying magnetic field, which replaces costly integration with millisecond evaluation inside a Bayesian fitting pipeline.

If this is right

  • The decaying-field model becomes feasible for systematic comparison against other prompt-emission mechanisms across large GRB samples.
  • Bayesian information criterion values favor the decaying-field interpretation for GRB 231020A in the majority of time-resolved intervals.
  • The emulator framework can be retrained for other numerically expensive emission models to enable similar statistical tests.
  • A radially decaying magnetic field supplies a concrete physical mechanism that naturally produces the observed spectral shape without additional tuning.

Where Pith is reading between the lines

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

  • The same emulator strategy could be applied to other GRBs to test whether decaying fields are common rather than exceptional.
  • Extending the network to output time-dependent spectra might allow joint fitting of light curves and spectra within one model.
  • If the preference for decaying fields holds in a larger sample, it would tighten constraints on magnetic field evolution in GRB jets.

Load-bearing premise

The convolutional neural network must reproduce the numerical spectra from the decaying magnetic field model with high accuracy across the full range of parameters relevant to real GRB observations.

What would settle it

If re-running the analysis with the actual numerical spectra (without the emulator) reverses the preference and shows the standard model fitting better or equally well in most intervals of GRB 231020A, the central claim is falsified.

Figures

Figures reproduced from arXiv: 2606.05910 by Jia-Ming Chen, Ke-Rui Zhu, Li Zhang, Shan Chang, Yong-Gang Zheng, Zhao-Yang Peng.

Figure 1
Figure 1. Figure 1: presents the complete modeling procedure adopted in this work. In this section, we construct a syn￾thetic spectral data set to train the CNN emulator by sampling physical parameters within reasonable ranges, calling the numerical synchrotron model to generate theoretical photon spectra, and organizing the results into supervised “parameter–spectrum” pairs. Latin Hypercube Sampling 2 × 105 Parameter Sets Ph… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the CNN spectral emulator and the training workflow. Specifically, the input X ∈ R 11 is projected to 128 dimensions through a linear layer followed by a ReLU activation (A. Krizhevsky et al. 2012), yielding h0 ∈ R 128. We reshape h0 into a one-dimensional signal of shape (batch, 1, 128) and stack three 1D convolutional layers (kernel size 3; padding = 1 to preserve the sequence length), with … view at source ↗
Figure 3
Figure 3. Figure 3: Training and validation ℓ1 loss as a function of epoch for the CNN spectral emulator. Both curves decrease rapidly during the initial epochs and then gradually converge, indicating stable optimization and good generalization with no evidence for overfitting. We further evaluate the prediction errors on an independent test set [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Validation statistics of the CNN spectral emulator on the independent test set. Left: distribution of logarithmic residuals, defined as log10(FCNN/Fnum), showing negligible systematic bias and a narrow scatter around zero. Right: distribution of relative errors, with a median of ∼ 2.73% and a 95th-percentile value of ∼ 11.22%. Overall, the training converges fast and remains stable, with consistent perform… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the CNN-emulated photon spectra and the corresponding numerical-model spectra on the fixed Fermi/GBM energy grids. The left and right columns show the NaI and BGO bands, respectively, for three representative epochs (t = 1.0, 3.0, and 5.0 s; colors). The upper panels present N(E) as a function of energy, while the lower panels show the logarithmic residuals (in dex) between the emulator … view at source ↗
Figure 6
Figure 6. Figure 6: Light curve of GRB 231020A. The green dashed vertical lines mark the Bayesian Blocks change points, defining the time intervals used for the time-resolved spectral analysis. become strongly degenerate because the synchrotron peak energy is mainly controlled by their combination. Therefore, the FCSYN magnetic-field parameter should be regarded as an effective constant-field value and should not be directly … view at source ↗
Figure 7
Figure 7. Figure 7: GRB 231020A: representative fitting result for one time bin. Left: corner plot of the posterior distributions for the ME FCSYN CNN model parameters from the Bayesian fit. Right: best-fit forward-folded GBM count spectra and residuals for the same interval. The comparison with the standard fast-cooling synchrotron model yields a consistent trend across all time bins [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the temporal evolution of the empirical spectral parameters and the BIC values of the three models. The Band and CPL fits show clear spectral evolution during the prompt-emission episode. Around the flux peak, the low-energy photon index becomes relatively hard and approaches the synchrotron slow-cooling limit, α = −2/3, [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
read the original abstract

The radiation mechanism of gamma-ray burst (GRB) prompt emission remains uncertain. Although the fast-cooling synchrotron model in a decaying magnetic field can account for the characteristic nonthermal spectral shape, its computational cost has limited its use in systematic observational fitting and statistical model comparison. We develop a convolutional neural network (CNN)-based spectral emulator for this physical model and train it on a large synthetic data set generated over a physically motivated parameter space. The trained network reproduces the numerical spectra with high fidelity while reducing the cost of spectral evaluation to the millisecond level. We then incorporate the emulator into a Bayesian spectral-analysis framework and apply it to the time-resolved spectra of GRB 231020A observed by Fermi/GBM. In most time intervals, the decaying-field fast-cooling synchrotron model provides better fits and smaller Bayesian information criterion values than the standard fast-cooling synchrotron model. These results suggest that a radially decaying magnetic field provides a plausible and more physically motivated interpretation of the prompt-emission spectrum of this burst, while also indicating that the emulator offers a practical route for large-sample Bayesian inference and systematic comparisons of GRB prompt-emission models.

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

2 major / 2 minor

Summary. The manuscript develops a CNN-based emulator for fast-cooling synchrotron spectra in a radially decaying magnetic field, trained on a large grid of synthetic spectra. The emulator is then embedded in a Bayesian fitting pipeline and applied to the time-resolved Fermi/GBM spectra of GRB 231020A, where the decaying-field model is reported to yield better fits and lower BIC values than the standard fast-cooling synchrotron model in most time intervals.

Significance. If the emulator fidelity is demonstrated to be sufficient relative to the data uncertainties, the work supplies both a practical computational tool for testing a physically motivated extension of the synchrotron model and concrete evidence favoring magnetic-field decay in at least one bright GRB. The integration of the emulator into a full Bayesian framework with BIC model comparison is a clear methodological advance for systematic GRB prompt-emission studies.

major comments (2)
  1. [CNN validation section] CNN validation section: The central claim that the decaying-field model produces lower BIC values rests on the assumption that emulator residuals are negligible compared with GBM statistical uncertainties. No quantitative validation metrics (test-set mean fractional error per energy bin, maximum deviation in the 8–1000 keV band, or performance near the best-fit decay index and electron index) are provided, leaving open the possibility that systematic emulation errors contribute to the reported BIC differences.
  2. [Results section on GRB 231020A fits] Results section on GRB 231020A fits: The statement that the decaying-field model is preferred 'in most time intervals' is load-bearing for the physical interpretation. The manuscript should report the exact fraction of intervals, the distribution of ΔBIC values, and whether the improvement persists after accounting for any emulation uncertainty.
minor comments (2)
  1. [Training data generation] The parameter ranges used for the synthetic training grid should be stated explicitly and compared with the posterior ranges recovered from the data to confirm coverage.
  2. [Model description] Notation for the magnetic-field decay index and the electron power-law index should be introduced once and used consistently in both the model description and the emulator output.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate the requested information.

read point-by-point responses

  1. Referee: [CNN validation section] CNN validation section: The central claim that the decaying-field model produces lower BIC values rests on the assumption that emulator residuals are negligible compared with GBM statistical uncertainties. No quantitative validation metrics (test-set mean fractional error per energy bin, maximum deviation in the 8–1000 keV band, or performance near the best-fit decay index and electron index) are provided, leaving open the possibility that systematic emulation errors contribute to the reported BIC differences.

    Authors: We agree that quantitative validation metrics are required to confirm that emulator residuals do not affect the BIC comparisons. In the revised manuscript we add these metrics to the CNN validation section, reporting the test-set mean fractional error per energy bin, the maximum deviation across the 8–1000 keV band, and the performance evaluated at the best-fit decay and electron indices. These additions demonstrate that the emulation errors remain well below the GBM statistical uncertainties. revision: yes

  2. Referee: [Results section on GRB 231020A fits] Results section on GRB 231020A fits: The statement that the decaying-field model is preferred 'in most time intervals' is load-bearing for the physical interpretation. The manuscript should report the exact fraction of intervals, the distribution of ΔBIC values, and whether the improvement persists after accounting for any emulation uncertainty.

    Authors: We acknowledge that the current phrasing requires more precise quantification. The revised Results section now states the exact fraction of time intervals in which the decaying-field model is preferred, presents the distribution of ΔBIC values, and includes a check that the model preference remains after emulation uncertainty is propagated into the likelihood and BIC calculation. revision: yes

Circularity Check

0 steps flagged

No circularity: emulator trained on independent synthetics; BIC comparison uses standard statistics

full rationale

The paper generates a large synthetic dataset from the decaying-field fast-cooling synchrotron model, trains a CNN emulator on it, then applies the emulator to fit real Fermi/GBM time-resolved spectra of GRB 231020A and compares models via BIC. Training data are produced independently of the observational fits; BIC is an external, standard criterion. No equation or step reduces a claimed prediction to a fitted parameter by construction, no self-citation chain bears the central claim, and the derivation remains self-contained against external benchmarks (synthetic spectra and standard model-selection statistics).

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the physical validity of the decaying-field synchrotron model and the numerical fidelity of the CNN approximation; the abstract provides no independent verification of either beyond the reported BIC improvement on one burst.

free parameters (2)
  • magnetic field decay index
    Physical parameter varied in synthetic training data and fitted to observations; its value is not fixed by first principles.
  • electron power-law index
    Physical parameter varied in synthetic training data and fitted to observations.
axioms (1)
  • domain assumption Fast-cooling synchrotron emission in a radially decaying magnetic field produces the observed nonthermal GRB prompt spectra.
    This is the core physical model being emulated and compared; invoked throughout the abstract as the basis for synthetic data generation.

pith-pipeline@v0.9.1-grok · 5753 in / 1467 out tokens · 40149 ms · 2026-06-28T00:38:00.054387+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

73 extracted references · 64 canonical work pages · 37 internal anchors

  1. [1]

    Open Questions in GRB Physics

    Open questions in GRB physics. Comptes Rendus Physique , keywords =. doi:10.1016/j.crhy.2011.03.004 , archivePrefix =. 1104.0932 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.crhy.2011.03.004 2011

  2. [2]

    The Physics of Gamma-Ray Bursts and Relativistic Jets

    The physics of gamma-ray bursts & relativistic jets. , keywords =. doi:10.1016/j.physrep.2014.09.008 , archivePrefix =. 1410.0679 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2014.09.008 2014

  3. [3]

    doi:10.1017/9781139226530 , adsurl =

    The Physics of Gamma-Ray Bursts , year =. doi:10.1017/9781139226530 , publisher =

    work page doi:10.1017/9781139226530

  4. [4]

    BATSE Observations of Gamma-Ray Burst Spectra. I. Spectral Diversity. , keywords =. doi:10.1086/172995 , adsurl =

    work page doi:10.1086/172995

  5. [5]

    The BATSE Gamma-Ray Burst Spectral Catalog. I. High Time Resolution Spectroscopy of Bright Bursts Using High Energy Resolution Data. , keywords =. doi:10.1086/313289 , archivePrefix =. astro-ph/9908119 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/313289

  6. [6]

    The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts

    The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts. , keywords =. doi:10.1086/505911 , archivePrefix =. astro-ph/0601188 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/505911

  7. [7]

    , keywords =

    The Fermi-GBM Gamma-Ray Burst Spectral Catalog: 10 yr of Data. , keywords =. doi:10.3847/1538-4357/abf24d , archivePrefix =. 2103.13528 , primaryClass =

    work page doi:10.3847/1538-4357/abf24d

  8. [8]

    Science , keywords =

    Fermi Observations of High-Energy Gamma-Ray Emission from GRB 080916C. Science , keywords =. doi:10.1126/science.1169101 , adsurl =

    work page doi:10.1126/science.1169101

  9. [9]

    Observations of GRB 990123 by the Compton Gamma-Ray Observatory

    Observations of GRB 990123 by the Compton Gamma Ray Observatory. , keywords =. doi:10.1086/307808 , archivePrefix =. astro-ph/9903247 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/307808

  10. [10]

    Steep Slopes and Preferred Breaks in GRB Spectra: the Role of Photospheres and Comptonization

    Steep Slopes and Preferred Breaks in Gamma-Ray Burst Spectra: The Role of Photospheres and Comptonization. , keywords =. doi:10.1086/308371 , archivePrefix =. astro-ph/9908126 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/308371

  11. [11]

    Monthly Notices of the Royal Astronomical Society , author =

    Collisional mechanism for gamma-ray burst emission. , keywords =. doi:10.1111/j.1365-2966.2010.16770.x , archivePrefix =. 0907.0732 , primaryClass =

    work page doi:10.1111/j.1365-2966.2010.16770.x 2010

  12. [12]

    Photospheric Emission in Gamma-Ray Bursts

    Photospheric emission in gamma-ray bursts. International Journal of Modern Physics D , keywords =. doi:10.1142/S021827181730018X , archivePrefix =. 1603.05058 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s021827181730018x

  13. [13]

    A Theory of Mulicolor Black Body Emission from Relativistically Expanding Plasmas

    A Theory of Multicolor Blackbody Emission from Relativistically Expanding Plasmas. , keywords =. doi:10.1088/0004-637X/732/1/49 , archivePrefix =. 1008.4590 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/732/1/49

  14. [14]

    A theory of photospheric emission from relativistic, collimated outflows

    A theory of photospheric emission from relativistic, collimated outflows. , keywords =. doi:10.1093/mnras/sts219 , archivePrefix =. 1208.2965 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/sts219

  15. [15]

    Non-thermal Emission from the Photospheres of Gamma-ray Burst Outflows. I. High-Frequency Tails. , keywords =. doi:10.1088/0004-637X/725/1/1137 , archivePrefix =. 1005.4704 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/725/1/1137

  16. [16]

    Unsteady Outflow Models for Cosmological Gamma-Ray Bursts

    Unsteady Outflow Models for Cosmological Gamma-Ray Bursts. , keywords =. doi:10.1086/187446 , archivePrefix =. astro-ph/9404038 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/187446

  17. [17]

    MNRAS , eprint =

    Gamma-ray bursts from internal shocks in a relativistic wind: temporal and spectral properties. , keywords =. doi:10.1046/j.1365-8711.1998.01305.x , archivePrefix =. astro-ph/9801245 , primaryClass =

    work page doi:10.1046/j.1365-8711.1998.01305.x 1998

  18. [18]

    The Internal-Collision-Induced Magnetic Reconnection and Turbulence (ICMART) Model of Gamma-Ray Bursts

    The Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) Model of Gamma-ray Bursts. , keywords =. doi:10.1088/0004-637X/726/2/90 , archivePrefix =. 1011.1197 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/726/2/90

  19. [19]

    Theory of "Jitter" Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks

    Theory of ``Jitter'' Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks. , keywords =. doi:10.1086/309374 , archivePrefix =. astro-ph/0001314 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/309374

  20. [20]

    Gamma-Ray Bursts from Up-Scattered Self-Absorbed Synchrotron Emission

    Gamma-Ray Bursts from Upscattered Self-absorbed Synchrotron Emission. , keywords =. doi:10.1086/317301 , archivePrefix =. astro-ph/0009309 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/317301

  21. [21]

    MNRAS , archivePrefix = "arXiv", eprint =

    A general scheme for modelling -ray burst prompt emission. , keywords =. doi:10.1111/j.1365-2966.2007.12621.x , archivePrefix =. 0802.2704 , primaryClass =

    work page doi:10.1111/j.1365-2966.2007.12621.x 2007

  22. [22]

    Monthly Notices of the Royal Astronomical Society , author =

    Inverse-Compton cooling in Klein-Nishina regime and gamma-ray burst prompt spectrum. , keywords =. doi:10.1111/j.1365-2966.2012.21533.x , archivePrefix =. 1206.4054 , primaryClass =

    work page doi:10.1111/j.1365-2966.2012.21533.x 2012

  23. [23]

    Inverse Compton Scattering Spectra of Gamma-Ray Burst Prompt Emission

    Inverse Compton Scattering Spectra of Gamma-Ray Burst Prompt Emission. , keywords =. doi:10.3847/1538-4357/ab1b10 , archivePrefix =. 1901.05268 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab1b10 1901

  24. [24]

    , keywords =

    Constraints on the emission mechanisms of gamma-ray bursts. , keywords =. doi:10.1046/j.1365-8711.2000.03354.x , archivePrefix =. astro-ph/9912461 , primaryClass =

    work page doi:10.1046/j.1365-8711.2000.03354.x 2000

  25. [25]

    Time-resolved Analysis of Fermi GRBs with Fast and Slow-Cooled Synchrotron Photon Models

    Time-resolved Analysis of Fermi Gamma-Ray Bursts with Fast- and Slow-cooled Synchrotron Photon Models. , keywords =. doi:10.1088/0004-637X/784/1/17 , archivePrefix =. 1304.4628 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/784/1/17

  26. [26]

    Nature Astronomy , keywords =

    Gamma-ray bursts as cool synchrotron sources. Nature Astronomy , keywords =. doi:10.1038/s41550-019-0911-z , archivePrefix =. 1810.06965 , primaryClass =

    work page doi:10.1038/s41550-019-0911-z

  27. [27]

    Nature Astronomy , keywords =

    Synchrotron radiation in -ray bursts prompt emission. Nature Astronomy , keywords =. doi:10.1038/s41550-020-1041-3 , archivePrefix =. 2002.09638 , primaryClass =

    work page doi:10.1038/s41550-020-1041-3 2002

  28. [28]

    Spectral properties of 438 GRBs detected by Fermi/GBM

    Spectral properties of 438 GRBs detected by Fermi/GBM. , keywords =. doi:10.1051/0004-6361/201016270 , archivePrefix =. 1012.2863 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201016270

  29. [29]

    Fast cooling synchrotron radiation in a decaying magnetic field and $\gamma$-ray burst emission mechanism

    Fast-cooling synchrotron radiation in a decaying magnetic field and -ray burst emission mechanism. Nature Physics , keywords =. doi:10.1038/nphys2932 , archivePrefix =. 1303.2704 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/nphys2932

  30. [30]

    Gamma-Ray Burst Spectrum with Decaying Magnetic Field

    Gamma-Ray Burst Spectrum with Decaying Magnetic Field. , keywords =. doi:10.1088/0004-637X/780/1/12 , archivePrefix =. 1310.0551 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/780/1/12

  31. [31]

    Gamma Ray Bursts as Electromagnetic Outflows

    Gamma Ray Bursts as Electromagnetic Outflows. arXiv e-prints , keywords =. doi:10.48550/arXiv.astro-ph/0312347 , archivePrefix =. astro-ph/0312347 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0312347

  32. [32]

    Low-energy Spectra of Gamma-ray Bursts from Cooling Electrons

    Low-energy Spectra of Gamma-Ray Bursts from Cooling Electrons. , keywords =. doi:10.3847/1538-4365/aa9e84 , archivePrefix =. 1709.05899 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4365/aa9e84

  33. [33]

    Synchrotron Origin of the Typical GRB Band Function - A Case Study of GRB 130606B

    Synchrotron Origin of the Typical GRB Band Function A Case Study of GRB 130606B. , keywords =. doi:10.3847/0004-637X/816/2/72 , archivePrefix =. 1505.05858 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/0004-637x/816/2/72

  34. [34]

    , keywords =

    Synchrotron Radiation Dominates the Extremely Bright GRB 221009A. , keywords =. doi:10.3847/2041-8213/acc84b , archivePrefix =. 2303.00898 , primaryClass =

    work page doi:10.3847/2041-8213/acc84b 2041

  35. [35]

    , keywords =

    One Fits All: A Unified Synchrotron Model Explains GRBs with FRED-shape Pulses. , keywords =. doi:10.3847/1538-4357/ad14fb , archivePrefix =. 2308.00772 , primaryClass =

    work page doi:10.3847/1538-4357/ad14fb

  36. [36]

    , keywords =

    Classification and Physical Characteristic Analysis of Fermi-GBM Gamma-Ray Bursts Based on Deep Learning. , keywords =. doi:10.3847/1538-4365/ada0b0 , archivePrefix =. 2412.05564 , primaryClass =

    work page doi:10.3847/1538-4365/ada0b0

  37. [37]

    , keywords =

    Unsupervised machine learning classification of Fermi gamma-ray bursts using spectral parameters. , keywords =. doi:10.1093/mnras/stad3407 , adsurl =

    work page doi:10.1093/mnras/stad3407

  38. [38]

    Modeling Blazar Broadband Emission with Convolutional Neural Networks. II. External Compton Model. , keywords =. doi:10.3847/1538-4357/ad5351 , archivePrefix =. 2402.07495 , primaryClass =

    work page doi:10.3847/1538-4357/ad5351

  39. [39]

    Modeling Blazar Broadband Emission with a Convolutional Neural Network. I. Synchrotron Self-Compton Model. , keywords =. doi:10.3847/1538-4357/ad19cf , archivePrefix =. 2311.02979 , primaryClass =

    work page doi:10.3847/1538-4357/ad19cf

  40. [40]

    , keywords =

    GRB 240619A: Evidence for a Compact Star Merger Origin. , keywords =. doi:10.3847/1538-4357/ae0938 , adsurl =

    work page doi:10.3847/1538-4357/ae0938

  41. [41]

    GRB Coordinates Network , year = 2023, month = oct, volume =

    GRB 231020A: Fermi GBM Final Real-time Localization. GRB Coordinates Network , year = 2023, month = oct, volume =

    2023

  42. [42]

    The Multi-Mission Maximum Likelihood framework (3ML)

    The Multi-Mission Maximum Likelihood framework (3ML). arXiv e-prints , keywords =. doi:10.48550/arXiv.1507.08343 , archivePrefix =. 1507.08343 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1507.08343

  43. [43]

    , keywords =

    GRB 231129C: Another Thermal Emission Dominated Gamma-Ray Burst. , keywords =. doi:10.3847/1538-4357/ad5f93 , adsurl =

    work page doi:10.3847/1538-4357/ad5f93

  44. [44]

    , keywords =

    Spectral Properties and Hybrid Jet Model Constraints of Fermi GRB 210610B. , keywords =. doi:10.3847/1538-4357/ac6c2a , adsurl =

    work page doi:10.3847/1538-4357/ac6c2a

  45. [45]

    Large scale magnetic fields and their dissipation in GRB fireballs

    Large scale magnetic fields and their dissipation in GRB fireballs. , keywords =. doi:10.1051/0004-6361:20010131 , archivePrefix =. astro-ph/0004274 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20010131

  46. [46]

    , keywords =

    Bayesian Time-resolved Spectroscopy of GRB Pulses. , keywords =. doi:10.3847/1538-4357/ab488a , archivePrefix =. 1810.07313 , primaryClass =

    work page doi:10.3847/1538-4357/ab488a

  47. [47]

    Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations. , keywords =. doi:10.1088/0004-637X/764/2/167 , archivePrefix =. 1207.5578 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/764/2/167

  48. [48]

    Loss Functions for Image Restoration With Neural Networks , year=

    Zhao, Hang and Gallo, Orazio and Frosio, Iuri and Kautz, Jan , journal=. Loss Functions for Image Restoration With Neural Networks , year=

  49. [49]

    Robust Estimation of a Location Parameter

    Huber, Peter J. Robust Estimation of a Location Parameter. Breakthroughs in Statistics: Methodology and Distribution. 1992. doi:10.1007/978-1-4612-4380-9_35

    work page doi:10.1007/978-1-4612-4380-9_35 1992

  50. [50]

    Constructive approximation , volume=

    On early stopping in gradient descent learning , author=. Constructive approximation , volume=. 2007 , publisher=

    2007

  51. [51]

    2017 , eprint=

    Adam: A Method for Stochastic Optimization , author=. 2017 , eprint=

    2017

  52. [52]

    High Energy Astrophysics

  53. [53]

    ImageNet Classification with Deep Convolutional Neural Networks , url =

    Krizhevsky, Alex and Sutskever, Ilya and Hinton, Geoffrey E , booktitle =. ImageNet Classification with Deep Convolutional Neural Networks , url =

  54. [54]

    Planck 2018 results. VI. Cosmological parameters. , keywords =. doi:10.1051/0004-6361/201833910 , archivePrefix =. 1807.06209 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833910 2018

  55. [55]

    Hunter, Comput

    Matplotlib: A 2D Graphics Environment. Computing in Science and Engineering , keywords =. doi:10.1109/MCSE.2007.55 , adsurl =

    work page doi:10.1109/mcse.2007.55 2007

  56. [56]

    Array Programming with NumPy

    Array programming with NumPy. , keywords =. doi:10.1038/s41586-020-2649-2 , archivePrefix =. 2006.10256 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41586-020-2649-2 2006

  57. [57]

    SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python

    SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature Methods , keywords =. doi:10.1038/s41592-019-0686-2 , archivePrefix =. 1907.10121 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/s41592-019-0686-2 1907

  58. [58]

    and Varoquaux, G

    Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E. , journal=. Scikit-learn: Machine Learning in

  59. [59]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library , url =

    Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Kopf, Andreas and Yang, Edward and DeVito, Zachary and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu an...

  60. [60]

    Galaxies , keywords =

    The Low-Energy Spectral Index of Gamma-Ray Burst Prompt Emission from Internal Shocks. Galaxies , keywords =. doi:10.3390/galaxies9030068 , archivePrefix =. 2109.07681 , primaryClass =

    work page doi:10.3390/galaxies9030068

  61. [61]

    , keywords =

    Gamma-Ray Burst Spectrum with a Time-dependent Injection Rate of High-energy Electrons. , keywords =. doi:10.3847/2041-8213/ab838e , archivePrefix =. 2003.12231 , primaryClass =

    work page doi:10.3847/2041-8213/ab838e 2041

  62. [62]

    , keywords =

    The Soft X-Ray Aspect of Gamma-Ray Bursts in the Einstein Probe Era. , keywords =. doi:10.3847/1538-4357/adceb1 , archivePrefix =. 2410.21687 , primaryClass =

    work page doi:10.3847/1538-4357/adceb1

  63. [63]

    Gamma-Ray Burst Spectral Evolution Through Crosscorrelations of Discriminator Light Curves

    Gamma-Ray Burst Spectral Evolution through Cross-Correlations of Discriminator Light Curves. , keywords =. doi:10.1086/304566 , archivePrefix =. astro-ph/9704206 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/304566

  64. [64]

    The Fermi GBM Gamma-Ray Burst Spectral Catalog: Four Years Of Data

    The Fermi GBM Gamma-Ray Burst Spectral Catalog: Four Years of Data. , keywords =. doi:10.1088/0067-0049/211/1/12 , archivePrefix =. 1401.5069 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0067-0049/211/1/12

  65. [65]

    , keywords =

    GRB 180720B: A GRB with Interesting Spectral Characteristics. , keywords =. doi:10.3847/1538-4357/ac14b8 , adsurl =

    work page doi:10.3847/1538-4357/ac14b8

  66. [66]

    Constraints on the Synchrotron Emission Mechanism in GRBs

    Constraints on the Synchrotron Emission Mechanism in Gamma-Ray Bursts. , keywords =. doi:10.1088/0004-637X/769/1/69 , archivePrefix =. 1301.5575 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/769/1/69

  67. [67]

    The emission mechanism in magnetically dominated GRB outflows

    The emission mechanism in magnetically dominated gamma-ray burst outflows. , keywords =. doi:10.1093/mnras/stu2032 , archivePrefix =. 1402.4113 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stu2032

  68. [68]

    Radiation from a Relativistic Poynting Jet: some general considerations

    Radiation from a relativistic Poynting jet: some general considerations. , keywords =. doi:10.1093/mnras/stv1696 , archivePrefix =. 1509.00479 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stv1696

  69. [69]

    Prompt high-energy emission from gamma-ray bursts in the internal shock model

    Prompt high-energy emission from gamma-ray bursts in the internal shock model. , keywords =. doi:10.1051/0004-6361/200811375 , archivePrefix =. 0811.2956 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/200811375

  70. [70]

    Reconciling observed GRB prompt spectra with synchrotron radiation ?

    Reconciling observed gamma-ray burst prompt spectra with synchrotron radiation?. , keywords =. doi:10.1051/0004-6361/201015457 , archivePrefix =. 1009.2636 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201015457

  71. [71]

    Evidence of an initially magnetically dominated outflow in GRB 080916C

    Evidence of an Initially Magnetically Dominated Outflow in GRB 080916C. , keywords =. doi:10.1088/0004-637X/700/2/L65 , archivePrefix =. 0904.2943 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/700/2/l65

  72. [72]

    Synchrotron emission in small scale magnetic field as possible explanation for prompt emission spectra of gamma-ray bursts

    Synchrotron Emission in Small-Scale Magnetic Fields as a Possible Explanation for Prompt Emission Spectra of Gamma-Ray Bursts. , keywords =. doi:10.1086/508681 , archivePrefix =. astro-ph/0605641 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/508681

  73. [73]

    Statistics and computing , volume=

    Uncertainty quantification and propagation in surrogate-based Bayesian inference , author=. Statistics and computing , volume=. 2025 , publisher=

    2025