Research Projects

Forecasting the evolution of dynamical systems, such as virus spread, brain interaction, social network information, and economic shocks, remains an open problem. Physical models are used to solve these problems, but they often lack the intricacies of real complex contagion dynamics and use ordinary differential equations (ODE). To address this, data-driven models, such as deep neural networks, are proposed. These models can extract information by handling large numbers of parameters, but they often learn structure from time series data and do not learn the inherent nonlinear dynamical behavior. Both physical and data-driven models predict system behavior considering time as a parameter, but space also plays a crucial role in spreading dynamics. This proposal explores the behavior of nonlinear dynamical systems through data-driven AI models, aiming to scale to map real-world situations. The proposed model incorporates partial differential equations (PDE) to the GNN architecture, considering temporal and spatial information. Real-world datasets will be collected to validate the models.