Weiqi Chu: Learning Interaction Kernels from Mean-Field Models

Consider a complex system of a vast number of interacting agents, which can give rise to emergent collective behaviors such as bird flocking, fish swarming, and opinion formation — phenomena that cannot be obtained by studying individual agents alone. However, high-dimensional systems present significant challenges for inference tasks, particularly when data availability is limited. In this presentation, I will discuss how a mean-field approach can be used to derive mean-field models from agent-based dynamics and to infer interaction kernels with limited data observation. I will also address the PDE-constrained optimization method employed and highlight the identifiability challenges that commonly arise in such inference problems.