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Gamma-Ray Burst Light Curve Reconstruction: A Comparative Machine and Deep Learning Analysis

A. Manchanda, A. Kaushal, M. G. Dainotti, A. Deepu, S. Naqi, J. Felix, N. Indoriya, S. P. Magesh, H. Gupta, K. Gupta, A. Madhan, D. H. Hartmann, A. Pollo, M. Bogdan, J. X. Prochaska, N. Fraija, D. Debnath

TL;DR

This work tackles gaps in gamma-ray burst afterglow light curves by comparing nine machine-learning and statistical approaches against the Willingale model on a large, diverse 521-GRB dataset. It demonstrates that the MLP achieves the best 5-fold CV MSE ($\approx0.0275$) while substantially reducing plateau-parameter uncertainties; the Attention U-Net yields the strongest reduction in $T_a$, $F_a$, and $\alpha$ uncertainties albeit with higher CV error. The results emphasize a trade-off between reconstruction accuracy and uncertainty control, with MLP offering a robust baseline and Attention U-Net excelling at suppressing outliers. These improvements enhance the utility of GRBs as standard candles and cosmological probes, and the framework lays groundwork for extending LC reconstruction to multi-wavelength data and future missions.

Abstract

Gamma-Ray Bursts (GRBs), observed at high-z, are probes of the evolution of the Universe and can be used as cosmological tools. Thus, we need correlations with small dispersion among key parameters. To reduce such a dispersion, we mitigate gaps in light curves (LCs), including the plateau region, key to building the two-dimensional Dainotti relation between the end time of plateau emission (Ta) and its luminosity (La). We reconstruct LCs using nine models: Multi-Layer Perceptron (MLP), Bi-Mamba, Fourier Transform, Gaussian Process-Random Forest Hybrid (GP-RF), Bidirectional Long Short-Term Memory (Bi-LSTM), Conditional GAN (CGAN), SARIMAX-based Kalman filter, Kolmogorov-Arnold Networks (KANs), and Attention U-Net. These methods are compared to the Willingale model (W07) over a sample of 521 GRBs. MLP and Attention U-Net outperform other methods, with MLP reducing the plateau parameter uncertainties by 37.2% for log Ta, 38.0% for log Fa, and 41.2% for alpha (the post-plateau slope in the W07 model), achieving the lowest 5-fold cross-validation (CV) mean squared error (MSE) of 0.0275. Attention U-Net achieved the lowest uncertainty of parameters, a 37.9% reduction in log Ta, a 38.5% reduction in log Fa and a 41.4% reduction in alpha, but with a higher MSE of 0.134. Although Attention U-Net achieves the largest uncertainty reduction, the MLP attains the lowest test MSE while maintaining comparable uncertainty performance, making it the more reliable model. The other methods yield MSE values ranging from 0.0339 to 0.174. These improvements in parameter precision are needed to use GRBs as standard candles, investigate theoretical models, and predict GRB redshifts through machine learning.

Gamma-Ray Burst Light Curve Reconstruction: A Comparative Machine and Deep Learning Analysis

TL;DR

This work tackles gaps in gamma-ray burst afterglow light curves by comparing nine machine-learning and statistical approaches against the Willingale model on a large, diverse 521-GRB dataset. It demonstrates that the MLP achieves the best 5-fold CV MSE () while substantially reducing plateau-parameter uncertainties; the Attention U-Net yields the strongest reduction in , , and uncertainties albeit with higher CV error. The results emphasize a trade-off between reconstruction accuracy and uncertainty control, with MLP offering a robust baseline and Attention U-Net excelling at suppressing outliers. These improvements enhance the utility of GRBs as standard candles and cosmological probes, and the framework lays groundwork for extending LC reconstruction to multi-wavelength data and future missions.

Abstract

Gamma-Ray Bursts (GRBs), observed at high-z, are probes of the evolution of the Universe and can be used as cosmological tools. Thus, we need correlations with small dispersion among key parameters. To reduce such a dispersion, we mitigate gaps in light curves (LCs), including the plateau region, key to building the two-dimensional Dainotti relation between the end time of plateau emission (Ta) and its luminosity (La). We reconstruct LCs using nine models: Multi-Layer Perceptron (MLP), Bi-Mamba, Fourier Transform, Gaussian Process-Random Forest Hybrid (GP-RF), Bidirectional Long Short-Term Memory (Bi-LSTM), Conditional GAN (CGAN), SARIMAX-based Kalman filter, Kolmogorov-Arnold Networks (KANs), and Attention U-Net. These methods are compared to the Willingale model (W07) over a sample of 521 GRBs. MLP and Attention U-Net outperform other methods, with MLP reducing the plateau parameter uncertainties by 37.2% for log Ta, 38.0% for log Fa, and 41.2% for alpha (the post-plateau slope in the W07 model), achieving the lowest 5-fold cross-validation (CV) mean squared error (MSE) of 0.0275. Attention U-Net achieved the lowest uncertainty of parameters, a 37.9% reduction in log Ta, a 38.5% reduction in log Fa and a 41.4% reduction in alpha, but with a higher MSE of 0.134. Although Attention U-Net achieves the largest uncertainty reduction, the MLP attains the lowest test MSE while maintaining comparable uncertainty performance, making it the more reliable model. The other methods yield MSE values ranging from 0.0339 to 0.174. These improvements in parameter precision are needed to use GRBs as standard candles, investigate theoretical models, and predict GRB redshifts through machine learning.
Paper Structure (28 sections, 37 equations, 10 figures, 4 tables)

This paper contains 28 sections, 37 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Dataset and the Willingale model
  4. Reconstruction with the Willingale model
  5. The Machine-Learning Approach
  6. Gaussian Process
  7. Multi-layer Perceptron Model
  8. Attention U-Net
  9. Long Short Term Memory Neural Network
  10. Bi-Mamba Model
  11. Gaussian Process - Random Forest Model
  12. Conditional Generative Adversarial Networks
  13. Kolmogorov-Arnold Networks
  14. The statistical approach
  15. Fourier Transform
  16. ...and 13 more sections

Figures (10)

  • Figure 1: Row 1 and Row 2 describe the GRB LCs divided into four classes depending on the afterglow feature: i) Good GRBs (Row 1, left); ii) GRB LCs with a break towards the end (Row 1, right); iii) Flares or Bumps in the afterglow (Row 2, left); iv) Flares or Bumps with a Double Break towards the end of the LC (Row 3, right). Row 3's left plot shows the LC of GRB050822, starting from the plateau emission, and the best-fit W07 model is shown in red. The Row 3 right plot shows the log(flux) residual histogram, and the best-fit Gaussian distribution is displayed in black.
  • Figure 2: Comparison of LCs before and after hyperparameter tuning.
  • Figure 3: Architecture of nine models shown from top left to bottom right in each row: (a) MLP, (b) Attention U-Net, (c) Bi-LSTM, (d) Bi-MAMBA, (e) GP-RF, (f) CGAN, (g) KAN, (h) Fourier Transform, (i) SARIMAX-based Kalman . Architectures of Bi-Mamba, MLP, KAN, and Attention U-Net are actual representations of the models utilized.
  • Figure 4: Reconstruction of LCs using the W07 function. Row 1 shows the reconstructed LCs at 10% noise level and Row 2 shows the reconstructed LCs at 20% noise level for all four classes: i) Good GRBs (Column 1); ii) a break towards the end of the GRB LC (Column 2); iii) flares or bumps in the afterglow (Column 3); iv) flares or bumps with a double break towards the end of the LC (Column 4).
  • Figure 5: Reconstruction of LCs for all four varieties of GRBs are shown in a grid with four types of GRBs (left to right): i) Good GRBs (Column 1); ii) a GRB LC with a break towards the end (Column 2); iii) flares or bumps in the afterglow (Column 3); iv) flares or bumps with a double break towards the end of the LC (Column 4) and the models (top to bottom): i) GP (Row 1); ii) Bi-Mamba Model (Row 2); iii) MLP model (Row 3); iv) Fourier Transform (Row 4); v) GP+RF model (Row 5).
  • ...and 5 more figures