Neural Particle Automata: Learning Self-Organizing Particle Dynamics

TL;DR

Neural Particle Automata (NPA) extend Neural Cellular Automata from fixed lattices to dynamic particle systems by modeling each cell as a moving particle with a continuous position $\mathbf{x}$ and internal state $\mathbf{S}$ updated by a shared neural rule. Perception is realized with differentiable Smoothed Particle Hydrodynamics (SPH) operators, providing mesh-free, locally invariant neighborhood features within a radius $\epsilon$, and are implemented via memory-efficient CUDA kernels for scalability. Across morphogenesis, texture synthesis, and self-classifying point clouds, NPA achieve robust, self-organizing behaviors that retain NCA-like properties such as regeneration while enabling particle-specific dynamics and heterogeneous interactions. The approach offers a compact, end-to-end trainable framework for learning self-organizing particle dynamics with potential impact on real-time graphics, simulation, and multi-agent systems. The work also discusses equivariance, stability, and multi-species composition, highlighting both practical benefits and current limitations such as particle merging/splitting and sensitivity to hyperparameters.

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.

Figures (15)

• Figure 1: Neural Particle Automata (NPA) are self-organizing particle dynamical systems driven by a shared, strictly local neural update rule. Three learned rules are shown: (top) growing a morphology from an egg-like seed, (bottom left) RGBA texture formation from a uniform seed, and (bottom right) self-classifying particle digits; numbers denote update steps. Check out our interactive demo available at: https://selforg-npa.github.io/.
• Figure 2: Single update step of Neural Particle Automata.
• Figure 3: Training of Neural Particle Automata.
• Figure 4: Growing 2D Morphology Starting from the same egg-like seed, learned NPA rules self-organize into different emoji targets.
• Figure 5: Growing 3D Morphology A learned NPA rule grows a gaussian-splat representation from a compact seed under 3D multi-view supervision.