EPSRC-FAPESP predicting critical transitions in complex dynamical networks: reduction and learning

• Grant number: 23/13706-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: September 01, 2024
• End date: August 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Tiago Pereira da Silva
• Principal researcher abroad: Jeroen Steven Willibrord Lamb
• Institution abroad: Imperial College London, England
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Pesquisadores principais: Edson de Faria
• Associated researchers: Thomas Kaue Dal Maso Peron

Abstract

This grant addresses challenges posed by real-world complex systems described as networks of interconnected dynamical elements. These systems feature in diverse fields such as ecology, biology, and physics. Changes in the interaction structure have far-reaching effects. Indeed, disorders like Parkinson's disease, schizophrenia, and epilepsy are believed to be linked to abnormal interaction patterns among neurons. Predicting disturbances and anticipating their consequences is crucial for averting disasters.While applied studies over the last fifty years have enhanced the understanding of network structures, a lack of mathematical understanding of emergent behaviours is hindering necessary progress in the field. Firstly, dynamical systems have focussed on understanding dynamics at the long time limit, rather than on the intricate finite-time dynamical behaviour of interacting elements, which is crucial to understand triggers to changes in complex systems. Moreover, pertinent phenomena such as collective behaviour cannot be deduced from local information and perturbation theory, which are at the heart of modern theory.This proposal is timely and carried by a strong team with an excellent long-term collaborative track record. Our unique contributions at the interface between pure and applied mathematics have given rise to important breakthroughs in understanding collective behaviour in network dynamics. Central to this project, our pioneering dimension reduction adopts a probabilistic perspective, describing global dynamics over finite time scales for an ensemble of networks and a large set of initial conditions. By disregarding pathological behaviours that arise only in asymptotic time and are highly unlikely to be seen in experiments or everyday situations, we were able to prove results that appear otherwise too challenging and unattainable, such as mechanism responsible for hub synchronization, breaking new ground in mathematics for the analysis of complex high-dimensional systems. Our results have proven relevant to data science, in particular for learning microscopic isolated node dynamics and connectivity, from time series data.Our proposal aims to harness the predictive powers of our reduction principles to develop recovery algorithms to predict abrupt changes in complex systems, known as critical transitions. Such transitions arise in various settings, such as society, ecology, neuroscience, medicine, and technology. (AU)