Machine Learning-Driven Analysis of kSZ Maps to Predict CMB Optical Depth $\tau$

TL;DR

This paper develops a machine learning framework using swin transformers and Laplace Approximation to accurately extract the CMB optical depth $ au$ from simulated kSZ maps, aiding future CMB survey analyses.

Contribution

It introduces a novel ML approach with uncertainty quantification for estimating $ au$ from kSZ maps, improving robustness and reliability over previous methods.

Findings

Effective extraction of $ au$ from simulated data.

Comparison of post-hoc and online Laplace Approximation modes.

Framework suitable for upcoming CMB survey data.

Abstract

Upcoming measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect, which results from Cosmic Microwave Background (CMB) photons scattering off moving electrons, offer a powerful probe of the Epoch of Reionization (EoR). The kSZ signal contains key information about the timing, duration, and spatial structure of the EoR. A precise measurement of the CMB optical depth $\tau$, a key parameter that characterizes the universe's integrated electron density, would significantly constrain models of early structure formation. However, the weak kSZ signal is difficult to extract from CMB observations due to significant contamination from astrophysical foregrounds. We present a machine learning approach to extract $\tau$ from simulated kSZ maps. We train advanced machine learning models, including swin transformers, on high-resolution seminumeric simulations of the kSZ signal. To robustly quantify prediction uncertainties of $\tau$, we employ the Laplace Approximation (LA). This approach provides an efficient and principled Gaussian approximation to the posterior distribution over the model's weights, allowing for reliable error estimation. We investigate and compare two distinct application modes: a post-hoc LA applied to a pre-trained model, and an online LA where model weights and hyperparameters are optimized jointly by maximizing the marginal likelihood. This approach provides a framework for robustly constraining $\tau$ and its associated uncertainty, which can enhance the analysis of upcoming CMB surveys like the Simons Observatory and CMB-S4.