Latent Field Discovery In Interacting Dynamical Systems With Neural Fields
This addresses the challenge of modeling field effects in complex systems for applications like physics simulation and traffic prediction, representing a novel method rather than an incremental improvement.
The paper tackled the problem of discovering latent force fields in interacting dynamical systems from observed dynamics alone, using a novel graph network that combines equivariant graph networks with neural fields to disentangle local interactions from global field effects. The result was accurate field discovery and effective forecasting in charged particles, traffic scenes, and gravitational n-body problems.
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.