Latent Field Discovery In Interacting Dynamical Systems With Neural Fields

TL;DR

This paper introduces a method to discover and model latent global field effects in interacting dynamical systems using neural fields and equivariant graph networks, enabling better understanding and prediction of complex systems.

Contribution

It proposes a novel neural field approach combined with equivariant graph networks to infer latent global fields from observed dynamics, addressing limitations of previous models.

Findings

Successfully discovers underlying fields in charged particles, traffic, and gravitational systems.

Improves system modeling and trajectory forecasting accuracy.

Demonstrates effectiveness of disentangling local interactions from global fields.

Abstract

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are $\mathrm{SE}(n)$ equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.