Neural Particle Automata: Learning Self-Organizing Particle Dynamics

TL;DR

Neural Particle Automata (NPA) extend Neural Cellular Automata to dynamic particles, enabling scalable, learnable, self-organizing systems with applications in morphogenesis, classification, and texture synthesis.

Contribution

We introduce NPA, a particle-based neural automaton framework that overcomes scalability challenges of dynamic neighborhoods using differentiable SPH operators.

Findings

NPA retains robustness and self-regeneration properties of NCA.

NPA enables new particle-specific behaviors.

Scalable end-to-end training of particle systems.

Abstract

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 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 tasks including morphogenesis, point-cloud classification, and particle-based texture synthesis, we show that NPA retain key NCA behaviors such as robustness and self-regeneration, while enabling new behaviors specific to particle systems. Together, these results position NPA as a compact neural model for learning self-organizing particle dynamics.