Learning Interaction Variables and Kernels from Observations of Agent-Based Systems
This addresses the challenge of modeling complex emergent behaviors in dynamical systems for researchers in fields like physics and biology, though it appears incremental as it builds on existing learning techniques for such systems.
The authors tackled the problem of learning interaction rules in agent-based systems from observed trajectories, proposing a nonparametric method that identifies both the interaction variables and the kernel, achieving effective dimension reduction to avoid the curse of dimensionality.
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems.