In 1933, Fritz Zwicky's famous investigations of the mass of the Coma cluster led him to infer the existence of dark matter¹. His fundamental discoveries have proven to be foundational to modern cosmology; as we now know, such dark matter makes up 85% of the matter and 25% of the mass–energy content in the universe. Galaxy clusters like Coma are massive, complex systems of dark matter, hot ionized gas and thousands of galaxies, and serve as excellent probes of the dark matter distribution. However, empirical studies show that the total mass of such systems remains elusive and difficult to precisely constrain. Here we present new estimates for the dynamical mass of the Coma cluster based on Bayesian deep learning methodologies developed in recent years. Using our novel data-driven approach, we predict Coma's M_200c mass to be 10^15.10±0.15 h⁻¹ M_⊙ within a radius of 1.78 ± 0.03 h⁻¹ Mpc of its centre. We show that our predictions are rigorous across multiple training datasets and statistically consistent with historical estimates of Coma's mass. This measurement reinforces our understanding of the dynamical state of the Coma cluster and advances rigorous analyses and verification methods for empirical applications of machine learning in astronomy.

1933 年，Fritz Zwicky 对彗发星团质量的著名调查使他推断出暗物质¹的存在。他的基本发现已被证明是现代宇宙学的基础。正如我们现在所知，这种暗物质构成了宇宙中物质的 85% 和质能的 25%。像昏迷这样的星系团是由暗物质、热电离气体和数千个星系组成的庞大而复杂的系统，是暗物质分布的绝佳探测器。然而，实证研究表明，此类系统的总质量仍然难以捉摸，难以精确约束。在这里，我们提出了基于近年来开发的贝叶斯深度学习方法对昏迷星团动态质量的新估计。使用我们新颖的数据驱动方法，我们预测 Coma 的M _200c质量为 10 ^15.10±0.15  h ^-1  M _⊙在其中心的 1.78 ± 0.03  h ^-1  Mpc 半径内。我们表明，我们的预测在多个训练数据集上是严格的，并且在统计上与昏迷质量的历史估计一致。这一测量加强了我们对昏迷星团动态状态的理解，并为机器学习在天文学中的经验应用推进了严格的分析和验证方法。