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 NCAs where cells are pinned to pixels or voxels, NPA model each cell as a particle with a continuous position and internal state, both updated by a shared, learnable neural rule. This particle-based formulation yields clear individuation of cells, allows heterogeneous dynamics, and concentrates computation only on regions where activity is present. At the same time, particle systems pose challenges: neighborhoods are dynamic, and a naive implementation of local interactions scale quadratically with the number of particles. We address these challenges by replacing grid-based neighborhood perception with differentiable Smoothed Particle Hydrodynamics (SPH) operators backed by memory-efficient, CUDA-accelerated kernels, enabling scalable end-to-end training. Across a set of tasks -- (i) growing morphologies, (ii) self-classifying point clouds, and (iii) self-organizing particle textures -- we show that NPA inherit hallmark NCA properties such as robustness and self-regeneration, while enabling qualitatively new particle-based behaviors, establishing NPAs as a compact neural model for self-organizing particle systems.