
doi: 10.3390/math14132269
handle: 11268/17258 , 20.500.14352/138276
The cosmic microwave background (CMB) contains key information about the early Universe, particularly through its polarization structure. This work proposes a Fuzzy and Explainable Artificial Intelligence framework (FAS-XAI) for the regional analysis of CMB polarization using Planck SMICA data. From the Stokes components Q and U, the polarization amplitude P and the scalar polarization modes E and B are derived. Regional features are then extracted over a HEALPix grid, considering only polarization-valid regions defined by the Planck polarization mask. Fuzzy C-Means identifies four interpretable polarization regimes: high-polarization structured regions, E-dominated medium-polarization regions, B-enhanced medium-polarization regions, and low-polarization regions. An XGBoost-SHAP layer is used to explain the resulting fuzzy memberships. XGBoost accurately reproduces the memberships, with R2>0.98 for all clusters, while SHAP confirms the physical relevance of amplitude-related features and the log(B/E) balance. Finally, controlled perturbations in P and log(B/E) reveal a globally robust fuzzy structure with localized sensitivity. The proposed framework provides an interpretable methodology for studying regional CMB polarization patterns and their stability under controlled perturbations.
Astrofísica, cosmic microwave background, Estadística matemática (Matemáticas), 519.237, 1102.08 Lógica Matemática, Análisis estadístico, CMB Polarization, explainable AI, Astronomía (Física), Cosmic Microwave Background, Inteligencia artificial (Informática), Goal 4: Quality education, Computación y tecnología, HEALPix, 524.8, Goal 9: Build resilient infrastructure, promote sustainable industrialization and foster innovation, Inteligencia artificial, Fuzzy C-Means, 1203.04 Inteligencia Artificial, SHAP, Explainable AI, 2101 Cosmología y Cosmogonía, CMB polarization, perturbation analysis, 004.8, Perturbation Analysis
Astrofísica, cosmic microwave background, Estadística matemática (Matemáticas), 519.237, 1102.08 Lógica Matemática, Análisis estadístico, CMB Polarization, explainable AI, Astronomía (Física), Cosmic Microwave Background, Inteligencia artificial (Informática), Goal 4: Quality education, Computación y tecnología, HEALPix, 524.8, Goal 9: Build resilient infrastructure, promote sustainable industrialization and foster innovation, Inteligencia artificial, Fuzzy C-Means, 1203.04 Inteligencia Artificial, SHAP, Explainable AI, 2101 Cosmología y Cosmogonía, CMB polarization, perturbation analysis, 004.8, Perturbation Analysis
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