Latent Field Discovery In Interacting Dynamical Systems With Neural Fields

TL;DR

This work theorizes the presence of latent force fields, and proposes neural fields to learn them, and model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces.

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.

Figures (6)

• Figure 1: N-body system with underlying gravitational field. We uncover fields that underlie interacting systems using only the observed trajectories.
• Figure 2: Two objects in a gravitational field. We only observe the total force exerted at each particle, i.e. the sum of equivariant pairwise particle forces and global field effects.
• Figure 3: The pipeline of our method, Aether. In the latent neural field (a), a graph aggregation module summarizes the input trajectories in a latent variable $\mathbf{z}$. Query states from input trajectories, alongside $\mathbf{z}$, are fed to a neural field that predicts a latent force field. In (b), a graph network integrates predicted forces with input trajectories to predict future trajectories. The graph aggregation module and the FiLM layers exist only in a dynamic field setting.
• Figure 4: Results on (a) electrostatic field, (b) inD, and (c) gravity.
• Figure 5: Learned Field (left) in electrostatic field setting compared to groundtruth (right).