Learning Interaction Kernels in Interacting Particle Systems

Learn how to infer interaction laws in systems of interacting agents or particles from observed trajectory data in this mathematical lecture. Explore the inverse problem of learning interaction kernels without assuming specific functional forms, covering cases where interactions depend on pairwise distances in Euclidean spaces, manifolds, or networks. Discover when this inference problem is well-posed and examine estimators with proven statistical and computational properties. Understand the fundamental role of underlying space geometry across different contexts including unknown network structures. Delve into extensions covering second-order systems, generalized interaction kernels, and stochastic systems, with applications spanning multiple scientific disciplines where agent-based modeling is essential.