Show HN: Neural Particle Automata

Unlike existing Neural Cellular Automata (NCA), which operate on a fixed lattice, Neural Particle Automata (NPA) are based on a dynamic particle system (Lagrangian system) with continuous positions.

Each particle has its own position and internal state, and is updated by a shared, learnable rule. This provides the following advantages:

• Individual particle identification: Enables dynamics implemented at the level of individual particles, unconstrained by a lattice
• Computational efficiency: Concentrates computation only on regions with activity, enabling efficient computation
• Heterogeneous dynamics: Different dynamical properties can be assigned to each particle

To address the neighbor-search complexity problem that is a chronic issue in particle systems, the model introduces a differentiable Smoothed Particle Hydrodynamics (SPH) operator and memory-efficient CUDA kernels, designed to enable large-scale training.

Across tasks such as morphogenesis, point cloud classification, and particle-based texture synthesis, this model successfully demonstrated behavior unique to particle systems, while retaining the robustness and regeneration capabilities that are the strengths of NCA.