Nonparametric inference of interaction laws in particles/agent systems

Applied and Computational Mathematics Seminar
Monday, December 3, 2018 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Fei Lu – Johns Hopkins University – feilu@math.jhu.edu
Wenjing Liao
Self-interacting systems of particles/agents arise in many areas of science, such as particle systems in physics, flocking and swarming models 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 kernels, and we develop a nonparametric statistic learning theory addressing learnability, consistency and optimal rate of convergence of the estimators. Especially, we show that despite the high-dimensionality of the systems, optimal learning rates can still be achieved.