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

• URL: http://arxiv.org/abs/2208.02758v1
• Date: Thu, 4 Aug 2022 16:31:01 GMT
• Title: Learning Interaction Variables and Kernels from Observations of Agent-Based Systems
• Authors: Jinchao Feng, Mauro Maggioni, Patrick Martin, Ming Zhong
• Abstract summary: We propose a learning technique that, given observations of states and velocities along trajectories of agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data. We demonstrate the learning capability of our method to a variety of first-order interacting systems.
• Score: 14.240266845551488
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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