Reconstruction of sparse network dynamics from data

• Autor(a) principal: Santos, Edmilson Roque dos
• Data de Publicação: 2024
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-21032024-191639/
• topic: Dinâmica de redes; Dynamical systems; Ergodic theory; Métodos de recuperação esparsa; Network dynamics; Redes esparsas; Sistemas dinâmicos; Sparse networks; Sparse recovery methods; Teoria ergódica

Complex network dynamics are prevalent in various natural systems, spanning from physics to neuroscience. These networks feature sparse interaction structures, where only a fraction of all possible connections exist. This interaction structure provides valuable insights into network dynamics. For instance, disruptions in neuronal networks often arise from issues related to connectivity. However, in experimental settings, we typically have access to multivariate time series data rather than the network itself. Our primary goal is to develop methods for predicting and anticipating potential new behaviors within the system. This thesis is dedicated to reconstructing governing equations that describe the dynamics of sparse networks from data. We merge dynamical systems theory and ergodic theory with sparse recovery methods to ensure exact and unique reconstruction. To begin, we introduce a method called Ergodic Basis Pursuit (EBP). This method minimizes the required measurement data, guaranteeing exact reconstruction while robustly identifying the interaction structure from experimental data, thereby revealing the original network structure. Subsequently, we demonstrate the applicability of this method to clustered networks. By leveraging cluster information within the network, EBP adopts a divideand- conquer reconstruction approach. The network reconstruction is divided into subproblems, each restricted to a specific cluster and solved independently. The solutions are then combined to reveal the complete network structure. Finally, we employ sparse recovery methods to reconstruct governing equations from the dynamics of bursting networks.