Nonparametric inference of interaction laws in systems of agents from trajectory data

TL;DR

This paper introduces a non-parametric statistical method to infer interaction laws in complex dynamical systems from trajectory data without assuming their analytical form, applicable across diverse disciplines.

Contribution

It presents a novel non-parametric learning approach with theoretical guarantees for estimating interaction laws from observational data.

Findings

Effective in diverse systems including physics and social dynamics

Provides theoretical guarantees for the inference method

Successfully tested on multiple prototypical systems

Abstract

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. 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. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics.