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.

翻译：我们提出了神经粒子自动机（NPA），这是神经细胞自动机（NCA）从静态晶格到动态粒子系统的拉格朗日推广。与经典欧拉式NCA（其细胞被固定在像素或体素上）不同，NPA将每个细胞建模为一个具有连续位置和内部状态的粒子，两者均由一个共享的、可学习的神经规则更新。这种基于粒子的表述实现了细胞的清晰个体化，允许异质动力学，并且仅将计算集中在存在活动的区域。与此同时，粒子系统也带来了挑战：邻域是动态的，而局部交互的朴素实现会随粒子数量呈二次方增长。我们通过用可微分的平滑粒子流体动力学（SPH）算子替代基于网格的邻域感知来解决这些挑战，该算子由内存高效、CUDA加速的内核支持，从而实现了可扩展的端到端训练。在包括形态发生、点云分类和基于粒子的纹理合成等任务中，我们展示了NPA保留了NCA的关键行为，如鲁棒性和自我再生能力，同时实现了粒子系统特有的新行为。总之，这些结果确立了NPA作为一种用于学习自组织粒子动力学的紧凑神经模型。