Computational Cosmology Projects

Social Service Project

Cosmología Observacional a través del Cómputo Científico (UNAM)

This section summarizes the academic work carried out during my Social Service at the Instituto de Ciencias Físicas (ICF–UNAM), as documented in the official final report. The project focused on the study and application of modern computational and statistical tools for the analysis of physical and cosmological data.

📄 Full report (PDF):
Informe final de Servicio Social – Notes and Results

Project Overview

The main objective was to develop a solid theoretical and practical understanding of how data-driven methods and machine learning techniques can be integrated with concepts from statistical physics and signal processing to model complex, high-dimensional physical systems.

The work emphasizes interpretability, multiscale analysis, and statistical consistency, particularly in contexts relevant to cosmology.

Topics Covered

• Probabilistic Modeling of Physical Systems
  • Gibbs distributions and Boltzmann statistics
  • Energy-based models and maximum entropy principles
  • Learning effective statistical descriptions from data
• High-Dimensional Data Analysis
  • Curse of dimensionality
  • Multiscale and collective descriptions of physical systems
  • Dimensionality reduction through Principal Component Analysis (PCA)
• Neural Networks
  • Feedforward, convolutional, and residual neural networks
  • Attention mechanisms (Squeeze-and-Excitation blocks)
  • Connections between deep learning architectures and renormalization ideas
• Image Super-Resolution
  • Classical interpolation methods (nearest neighbor, bilinear, bicubic)
  • Deep learning–based super-resolution techniques
  • Evaluation metrics and their limitations for non-natural images, including cosmological data
• Wavelet-Based Multiscale Analysis
  • Continuous and discrete wavelet transforms
  • Wavelet representations for images
  • Wavelet Scattering Transform (WST) and its statistical properties
  • Modeling non-Gaussian fields and long-range correlations using scattering statistics

Academic Outcome

The service resulted in a comprehensive technical report integrating theoretical foundations, mathematical derivations, and practical implementations. The document serves both as an educational resource and as a basis for future research in computational cosmology, super-resolution, and statistical modeling of complex physical fields.