Neural Particle Automata: Learning Self-Organizing Particle Dynamics

We introduce Neural Particle Automata (NPA), a Lagrangian generalization of Neural Cellular Automata (NCA) from static lattices to dynamic particle systems. Unlike classical Eulerian NCA where cells are fixed to pixels or voxels, NPA represent each cell as a particle with a continuous position and an internal state, both updated by a shared learnable neural rule. This particle-based formulation yields clear individuation of cells, allows heterogeneous dynamics, and focuses computation on regions where activity is present. However, particle systems introduce two challenges: neighborhoods are dynamic, and a naive implementation of local interactions scales quadratically with the number of particles. We address these issues by replacing grid-based perception with differentiable Smoothed Particle Hydrodynamics (SPH) operators, backed by memory-efficient CUDA kernels for scalable end-to-end training. Across tasks including morphogenesis, point-cloud classification, and particle-based texture synthesis, we show that NPA retain key NCA behaviors such as robustness and regeneration, while enabling new behaviors specific to particle systems. These results position NPA as a compact neural model for learning self-organizing particle systems.