Reduction Techniques in Complex Networks

• Grant number: 25/09758-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2025
• End date: August 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Bella Rocxane Martins Figliaggi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 23/13706-0 - EPSRC-FAPESP predicting critical transitions in complex dynamical networks: reduction and learning, AP.TEM

Abstract

This project develops mathematical techniques for reducing the dimensionality of complex networks to enable the prediction of their dynamical evolution. Such networks arise in fields like neuroscience, ecology, and technology, where global behaviors emerge from intricate local interactions. Traditional methods often fail to capture these dynamics over finite time scales.By combining tools from ergodic theory, random dynamical systems, and probabilistic analysis, we construct reduced models that remain faithful to the full system while being analytically tractable. These models allow for the reconstruction of network dynamics from limited time-series data and provide early-warning signals for critical transitions.The project is part of the international FAPESP-UKRI initiative "Predicting Critical Transitions in Complex Dynamical Networks: Reduction and Learning," and contributes to establishing a rigorous framework for forecasting the behavior of large-scale heterogeneous networks. (AU)