Inferring the laws of interaction of particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We start from data consisting of trajectories of interacting agents, which is in many cases abundant, and propose a non-parametric statistical learning approach to extract the governing laws of interaction. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines, with homogeneous and heterogeneous agents systems, ranging from fundamental physical interactions between particles to systems-level interactions, with such as social influence on people's opinion, prey-predator dynamics, flocking and swarming, and cell dynamics.
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