Learning Interaction Variables and Kernels from Observations of Agent-Based Systems

TL;DR

This paper introduces a nonparametric learning method to identify interaction variables and kernels in agent-based dynamical systems, enabling effective dimension reduction and capturing complex emergent behaviors from observational data.

Contribution

The paper presents a novel technique to learn both the interaction variables and kernels directly from observational data, reducing dimensionality and improving understanding of agent interactions.

Findings

Successfully learns interaction kernels from data

Reduces dimensionality in high-dimensional systems

Captures complex emergent behaviors

Abstract

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.