Neural Integral Equations: Modeling Real-World Systems

This lecture introduces integral equations (IEs) as functional equations used to model various real-world systems, such as particle physics, brain dynamics, and tissue biology. The instructor explains the significance of IEs in integrating signals over time and space domains, highlighting their non-local nature and complex dynamics. The lecture covers the learning of IEs from data using Neural Integral Equations (NIE) and the advantages of IE solvers over traditional ODE/PDE solvers. Attentional Neural Integral Equations are also discussed, showcasing their speed, interpretability, and scalability. The lecture concludes with applications of ANIE in modeling dynamical systems, brain dynamics, and tissue biology.