We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate, and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, like asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.

翻译：我们结合无监督聚类与稀疏促进推断算法，学习自组织活性粒子系统中解释宏观图案形成的局部主导力平衡。自驱动粒子微观相互作用自组织形成宏观图案的现象在自然界中普遍存在。尽管流体动力学理论有助于我们更好地理解这一现象的物理基础，但识别出塑造、调控并维持活性粒子系统自组织结构所需的充分局部相互作用仍具挑战性。我们研究了一个经典的自驱动粒子流体动力学模型，该模型能产生从星形结构到移动密度带等多种图案。我们的数据驱动分析表明：传播密度带由密度梯度驱动的局部对齐相互作用形成，而稳态星形结构则源于强粒子相互作用导致的展向负压缩机制。该方法还揭示了粒子速度受局部密度影响的系统中图案形成的类似物理原理，展示了其跨模型揭示物理共性的能力。从数据中推断出的物理机制与分析标度律及实验观测结果高度吻合。