# DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks

arXiv: https://arxiv.org/abs/1810.01483 · HTML: https://mlsanity.com/paper/1810.01483/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2018.

## Built on by (most cited first, 11 of 11)

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- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
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- [Hybrid Neural Representations for Spherical Data](https://mlsanity.com/paper/2402.05965/) (2024)
- [Reconstructing Patchy Reionization with Deep Learning](https://mlsanity.com/paper/2101.01214/) (2021)
- [DeepSZ: Identification of Sunyaev-Zel'dovich Galaxy Clusters using Deep Learning](https://mlsanity.com/paper/2102.13123/) (2021)
- [Reconstructing Cosmic Polarization Rotation with ResUNet-CMB](https://mlsanity.com/paper/2109.09715/) (2021)
- [Datacube segmentation via Deep Spectral Clustering](https://mlsanity.com/paper/2401.17695/) (2024)
- [Bayesian Inference of Primordial Magnetic Field Parameters from CMB with Spherical Graph Neural Networks](https://mlsanity.com/paper/2510.20795/) (2025)
- [Deep Learning for Primordial B-mode Extraction](https://mlsanity.com/paper/2512.19577/) (2025)
- [A Fast Generative Framework for High-dimensional Posterior Sampling: Application to CMB Delensing](https://mlsanity.com/paper/2603.04535/) (2026)

## Abstract (arXiv)

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 performs 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) - ie, 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 CNN provides a few innovations at the intersection of cosmology and machine learning. First, while training and regressing on images, we predict 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. We expect this approach to excel in capturing hard-to-model non-Gaussian astrophysical foreground and noise contributions.