用可学习的粒子规则模拟自组织动力学，实现高效动态系统建模。
Neural Particle Automata: Learning Self-Organizing Particle Dynamics
- 将神经元细胞自动机推广到可动粒子系统，用神经网络统一更新粒子位置与状态。
- 通过可微分SPH算子实现高效局部交互，计算复杂度不再随粒子数平方增长。
- 适用于形态发生、点云分类等任务，兼具鲁棒性与自修复能力，适合动态系统研究者。
我们提出神经粒子自动机（NPA），是神经细胞自动机（NCA）从静态网格到动态粒子系统的拉格朗日推广。与传统欧拉型NCA中单元固定于像素或体素不同，NPA将每个单元建模为具有连续位置和内部状态的粒子，二者均由共享的可学习神经规则更新。该粒子化框架实现了单元的清晰区分，支持异质动力学，并仅在活动区域集中计算。同时，粒子系统带来挑战：邻域动态变化，朴素的局部交互随粒子数呈二次增长。为此，我们以可微分平滑粒子流体动力学（SPH）算子替代网格邻域感知，结合内存高效的CUDA加速内核，实现可扩展的端到端训练。在形态发生、点云分类及基于粒子的纹理生成等任务中，我们证明了NPA保留了经典NCA的鲁棒性和自再生特性，同时展现出粒子系统特有的新行为。这些结果表明，NPA是一种紧凑的神经模型，适用于学习自组织粒子动力学。
原文摘要 · Abstract (English)
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.
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