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

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.

CMA-ES with Radial Basis Function Surrogate for Black-Box Optimization

Evolutionary optimization algorithms often face defects and limitations that complicate the evolution processes or even prevent them from reaching the global optimum. A notable constraint pertains to the considerable quantity of function evaluations required to achieve the intended solution. This concern assumes heightened significance when addressing costly optimization problems. However, recent research has shown that integrating machine learning methods, specifically surrogate models, with evolutionary optimization can enhance various aspects of these algorithms. Among the evolutionary algorithms, the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is particularly favored. This preference is due to its use of Gaussian distribution for calculating evolution and its ability to adapt optimization parameters, which reduces the need for user intervention in adjusting initial parameters. In this research endeavor, we propose the adoption of surrogate models within the CMA-ES framework called CMA-SAO to develop an initial surrogate model that facilitates the adaptation of optimization parameters through the acquisition of pertinent information derived from the associated surrogate model. Empirical validation reveals that CMA-SAO algorithm markedly diminishes the number of function evaluations in comparison to prevailing algorithms, thereby providing a significant enhancement in operational efficiency.