Self-interacting systems of particles/agents arise in many areas of science, such as particle systems in physics, flocking and swarming in biology, and opinion dynamics in social science. An interesting question is to learn the laws of interaction between the particles/agents from data consisting of trajectories. In the case of distance-based interaction laws, we present efficient regression algorithms to estimate the interaction functions, and we develop a systematic nonparametric statistical learning theory addressing identifiability, consistency and optimal rate of convergence of the estimators. In particular, we use the theory to guide the design of the regression algorithms, quantification of the uncertainty in estimations, and criteria for statistical model selection. (Joint work with Mauro Maggioni, Sui Tang and Ming Zhong).

Bio:
Fei Lu is an Assistant Professor at the Department of Mathematics of Johns Hopkins University. He graduated from the University of Kansas in 2013, and he was Postdoctoral Fellow at Lawrence Berkeley National Lab and the University of California, Berkeley in 2013-2017. His current research focuses on learning dynamics from data, including applications as well as the mathematical foundations. In particular, he is working on the nonparametric inference of interaction functions in systems of interacting particles/agents, and on model reduction for complex multi-scale systems along with applications in data assimilation and Monte Carlo sampling.