Neural Particle Automata: Learning Self-Organizing Particle Dynamics

2026-01-22

AI Summary

This work proposes a novel framework that generalizes neural cellular automata from static grids to dynamic Lagrangian particle systems, enabling learnable and self-organizing models of cellular behavior. Each particle possesses continuous position coordinates and internal states, updated locally via a shared differentiable neural rule and interacting through differentiable smoothed particle hydrodynamics (SPH) operators to support adaptive neighborhood relations. The approach accommodates heterogeneous dynamics, sparse computation, and end-to-end training, with efficient execution accelerated via CUDA. Demonstrated across tasks including morphogenesis, point cloud classification, and particle-based texture synthesis, the model exhibits self-regeneration capabilities, robustness, and emergent behaviors characteristic of particle systems, thereby validating its effectiveness and scalability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Neuro-Symbolic Learning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production 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.

Problem

• Neural Particle Automata
• self-organizing dynamics
• particle systems
• dynamic neighborhoods
• scalable interaction

Innovation

• Neural Particle Automata
• Smoothed Particle Hydrodynamics
• self-organizing dynamics
• differentiable particle systems
• Lagrangian neural models