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.

翻译：交互物体系统通常在支配其动力学的场效应影响下演化，然而先前的研究忽略了此类效应，并假设系统在真空中演化。本研究聚焦于发现这些场，并仅从观测到的动力学中推断它们，无需直接观测场本身。我们理论化潜藏力场的存在，并提出使用神经场来学习它们。由于观测到的动力学是局部物体交互与全局场效应的净结果，近期流行的等变网络并不适用，因为它们未能捕捉全局信息。为此，我们提出将局部物体交互（具有$\mathrm{SE}(n)$等变性且依赖于相对状态）与外部全局场效应（依赖于绝对状态）进行解耦。我们使用等变图网络对交互进行建模，并将其与神经场结合，形成一种集成场力的新型图网络。实验表明，我们能够在带电粒子场景、交通场景以及引力n体问题中准确发现底层场，并有效利用这些场来学习系统动态并预测未来轨迹。