Next-generation cosmic microwave background (CMB) experiments will have lower noise and therefore increased sensitivity, enabling improved constraints on fundamental physics parameters such as the sum of neutrino masses and the tensor-to-scalar ratio $r$. Achieving competitive constraints on these parameters requires high signal-to-noise extraction of the projected gravitational potential from the CMB maps. Standard methods for reconstructing the lensing potential employ the quadratic estimator (QE). However, the QE is known to perform suboptimally at the low noise levels expected in upcoming experiments. Other methods, like maximum likelihood estimators (MLE), are under active development. In this work, we demonstrate reconstruction of the CMB lensing potential with deep convolutional neural networks (CNN) — i.e., a ResUNet. The network is trained and tested on simulated data, and otherwise has no physical parametrization related to the physical processes of the CMB and gravitational lensing. We show that, over a wide range of angular scales, ResUNets recover the input gravitational potential with a higher signal-to-noise ratio than the QE method, reaching levels comparable to analytic approximations of MLE methods. We demonstrate that the network outputs quantifiably different lensing maps when given input CMB maps generated with different cosmologies. We also show we can use the reconstructed lensing map for cosmological parameter estimation. This application of CNNs provides a few innovations at the intersection of cosmology and machine learning. First, while training and regressing on images, this application predicts a continuous-variable field rather than discrete classes. Second, we are able to establish uncertainty measures for the network output that are analogous to standard methods. Beyond this first demonstration, we expect this approach to excel in capturing hard-to-model non-Gaussian astrophysical foreground and noise contributions.

下一代宇宙微波背景（CMB）实验将降低噪声，从而提高灵敏度，从而改善对基本物理参数（例如中微子质量总和和张量与标量比）的约束 $\mathrm{[R}$。要在这些参数上达到竞争性约束，就需要从CMB映射中高信噪比提取出预计的引力。用于重建透镜潜力的标准方法采用二次估计器（QE）。但是，已知QE在即将进行的实验中所期望的低噪声水平下表现欠佳。其他方法，如最大似然估计器（MLE），正在积极开发中。在这项工作中，我们展示了使用深卷积神经网络（CNN）（即ResUNet）重建CMB镜头的潜力。该网络是在模拟数据上进行训练和测试的，否则就没有与CMB和重力透镜的物理过程相关的物理参数化。我们表明，在各种角度范围内，ResUNets以比QE方法更高的信噪比恢复输入重力势，达到了与MLE方法的解析近似值相当的水平。我们证明，当使用不同的宇宙学生成给定的输入CMB图时，网络可输出的量化的镜头图也不同。我们还展示了我们可以使用重建的透镜图进行宇宙学参数估计。CNN的这种应用在宇宙学和机器学习的交汇处提供了一些创新。首先，在对图像进行训练和回归时，此应用程序会预测连续变量字段而不是离散类。其次，我们能够建立类似于标准方法的网络输出不确定性度量。除了第一次示范，