Field Neural Networks

Dynamic interactions are modeled in many ways, from temporal graphs and recurrent state updates to Neural ODEs and physics-based dynamical systems. Inspired by classical field theory, we instead model interactions as the evolution of a latent field. We introduce Field Neural Networks (FNNs), which parameterize simple neural updates with field-equation structure to capture diffusion-like and wave-like dynamics. On controlled simulations, FNNs recover the underlying dynamics across various hidden synthetic topologies and remain robust under long rollouts and sparse observations. On real temporal link-prediction benchmarks, they remain competitive with established temporal graph models while using roughly an order of magnitude fewer parameters. Mechanistic ablations further reveal dataset-dependent reliance on learned dynamical coefficients and velocity state. These results suggest that field equations can serve as compact inductive biases for interaction data, providing a structured way to model how activity enters, propagates through, and persists within relational systems.