# Neural Particle Automata: Learning Self-Organizing Particle Dynamics

arXiv: https://arxiv.org/abs/2601.16096 · HTML: https://mlsanity.com/paper/2601.16096/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Style Transfer by Relaxed Optimal Transport and Self-Similarity](https://mlsanity.com/paper/1904.12785/) (2019)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [Med-NCA: Robust and Lightweight Segmentation with Neural Cellular Automata](https://mlsanity.com/paper/2302.03473/) (2023)
- [Growing Isotropic Neural Cellular Automata](https://mlsanity.com/paper/2205.01681/) (2022)
- [DyNCA: Real-time Dynamic Texture Synthesis Using Neural Cellular Automata](https://mlsanity.com/paper/2211.11417/) (2022)
- [Mesh Neural Cellular Automata](https://mlsanity.com/paper/2311.02820/) (2023)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [NoiseNCA: Noisy Seed Improves Spatio-Temporal Continuity of Neural Cellular Automata](https://mlsanity.com/paper/2404.06279/) (2024)
- [Differentiable Programming of Reaction-Diffusion Patterns](https://mlsanity.com/paper/2107.06862/) (2021)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Neural Cellular Automata: From Cells to Pixels](https://mlsanity.com/paper/2506.22899/) (2025)
- [DeepLABNet: End-to-end Learning of Deep Radial Basis Networks with Fully Learnable Basis Functions](https://mlsanity.com/paper/1911.09257/) (2019)

## Built on by (most cited first, 2 of 2)

- [On Growth and Form, and Function: Reusable Regulatory Handles Control Phenotypic Variation](https://mlsanity.com/paper/2609.29755/) (2026)
- [Reasoning with Neural Cellular Automata](https://mlsanity.com/paper/2609.36126/) (2026)

## Abstract (arXiv)

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.