Federico Vello

Ph.D XL

Supervisor: Federico Fogolari, co-supervisor: Sara Fortuna

Room: Rizzi B1 2

Research Project

Methods for Entropy Estimation for Machine Learning Algorithms

The project focuses on the development and analysis of ML methods for entropy estimation in high-dimensional systems such as molecular dynamics coordinates and genomic data. The central objective is to understand how entropy and entropy variations can be reliably inferred from finite data samples when the underlying probability distributions are unknown or only implicitly defined. The research addresses both theoretical and computational aspects, with particular attention to the interplay between dimensionality, data geometry, and statistical uncertainty. By adopting a unified perspective that bridges mathematical foundations, statistical physics, and data analysis, the project investigates entropy as a quantitative descriptor of structural variability, disorder, and information content. Applications span from molecular and physical systems to abstract data representations e classification, highlighting the role of entropy-based analysis as a general tool for characterizing complexity, comparing states, and identifying meaningful changes in high-dimensional data. The goal is to contribute a coherent framework that clarifies the scope, limitations, and interpretative power of entropy-based methods in modern scientific and data-driven research.