We investigate the prospect of reconstructing the ``cosmic distance ladder'' of the Universe using a novel deep learning framework called LADDER - Learning Algorithm for Deep Distance Estimation and Reconstruction. LADDER is trained on the apparent magnitude data from the Pantheon Type Ia supernovae compilation, incorporating the full covariance information among data points, to produce predictions along with corresponding errors. After employing several validation tests with a number of deep learning models, we pick LADDER as the best performing one. We then demonstrate applications of our method in the cosmological context, that include serving as a model-independent tool for consistency checks for other datasets like baryon acoustic oscillations, calibration of high-redshift datasets such as gamma ray bursts, use as a model-independent mock catalog generator for future probes, etc. Our analysis advocates for interesting yet cautious consideration of machine learning applications in these contexts.

翻译：我们研究了一种名为LADDER（学习算法用于深度距离估计与重建）的新型深度学习框架，用于重建宇宙的“距离阶梯”。该框架基于Pantheon Ia型超新星样本的表观星等数据进行训练，融合了数据点间的完整协方差信息，从而生成预测结果及相应误差。经过对多种深度学习模型的多项验证测试后，我们选取LADDER作为性能最优的模型。随后，我们展示了该方法在宇宙学背景下的应用，包括：作为无模型工具对其他数据集（如重子声学振荡）进行一致性检验、校准高红移数据集（如伽马射线暴）、为未来探测任务生成无模型模拟星表等。我们的分析倡导在这一领域以审慎态度积极探索机器学习应用的可能性。