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Systems of interacting objects often evolve under the influence of fieldeffects that govern their dynamics, yet previous works have abstracted awayfrom such effects, and assume that systems evolve in a vacuum. In this work, wefocus on discovering these fields, and infer them from the observed dynamicsalone, without directly observing them. We theorize the presence of latentforce fields, and propose neural fields to learn them. Since the observeddynamics constitute the net effect of local object interactions and globalfield effects, recently popularized equivariant networks are inapplicable, asthey fail to capture global information. To address this, we propose todisentangle local object interactions -- which are $\mathrm{SE}(n)$ equivariantand depend on relative states -- from external global field effects -- whichdepend on absolute states. We model interactions with equivariant graphnetworks, and combine them with neural fields in a novel graph network thatintegrates field forces. Our experiments show that we can accurately discoverthe underlying fields in charged particles settings, traffic scenes, andgravitational n-body problems, and effectively use them to learn the system andforecast future trajectories.

Latent Field Discovery In Interacting Dynamical Systems With Neural Fields