In this paper, we discuss an artificial intelligence based approach to constrain the redshift of blazars using combined $\gamma$--ray observations from the \emph{Fermi} Large Area Telescope (LAT) and ground based atmospheric Cherenkov telescopes (ACTs) in GeV and \emph{sub} TeV energy regimes respectively. The spectral measurements in GeV and TeV energy bands show a redshift dependent spectral break in the $\gamma$--ray spectra of blazars. We use this observational feature of blazars to constrain their redshift. The observed spectral information of blazars with known redshifts reported in the \emph{Fermi} catalogs (3FGL and 1FHL) and TeV catalog are used to train an Artificial Neural Network (ANN) based algorithm. The training of the ANN methodology is optimized using \emph{Levenberg - Marquardt} algorithm with $\gamma$--ray spectral indices and redshifts of 35 well observed blazars as input and output parameters respectively. After training, we use only observed spectral indices in GeV and sub TeV regimes for 10 blazars as inputs to predict their redshifts. The comparison of predicted redshifts by the ANN with the known redshift suggests that both the values are consistent within $\sim$ 18$\%$ uncertainty. The method proposed in the present work would be helpful in future for constraining or predicting the redshifts of the blazars using only observational $\gamma$--ray spectral informations obtained from the \emph{Fermi}-LAT and current generation IACTs as well as from the next generation Cherenkov Telescope Array (CTA) with improved source statistics.

中文翻译：

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基于人工智能的γ射线观测约束耀变体红移方法

在本文中，我们讨论了一种基于人工智能的方法，使用来自 \emph {Fermi} 大面积望远镜 (LAT) 和地面大气切伦科夫望远镜 (ACT) 的组合 $\gamma$-射线观测来约束耀变体的红移。 GeV 和 \emph {sub} TeV 能量状态分别。GeV 和 TeV 能带中的光谱测量显示了耀变体的 $\gamma$ - 射线光谱中的红移相关光谱中断。我们使用耀变体的这种观察特征来限制它们的红移。在\emph{Fermi} 目录（3FGL 和1FHL）和TeV 目录中报告的具有已知红移的耀变体的观测光谱信息用于训练基于人工神经网络（ANN）的算法。ANN 方法的训练使用 \emph {Levenberg - Marquardt} 算法进行优化，其中 $\gamma$-射线光谱指数和 35 个观测良好的耀变体的红移分别作为输入和输出参数。训练后，我们仅使用 10 个耀变体在 GeV 和亚 TeV 范围内观察到的光谱指数作为输入来预测它们的红移。ANN 预测的红移与已知红移的比较表明，这两个值在 $\sim$ 18$\%$ 不确定性内是一致的。当前工作中提出的方法将有助于在未来仅使用从 \emph {Fermi}-LAT 和当前一代 IACT 获得的观测 $\gamma$-射线光谱信息来约束或预测耀变体的红移来自具有改进源统计数据的下一代切伦科夫望远镜阵列 (CTA)。