高分辨率成像技术和基于粒子的模拟方法的最新进展使各种生物和工程活性物质系统中集体动力学的精确微观表征成为可能。并行,用于学习可解释连续体模型的数据驱动算法已显示出从连续体模拟数据中恢复基础偏微分方程(PDE)的潜力。相比之下,直接从实验或粒子模拟中学习活性物质的宏观流体力学方程仍然是一个重大挑战,特别是当连续体模型不知道先验或分析粗粒度失败时,非稀释和异构系统通常是这样。这里,我们提出了一个框架,利用光谱基础表示和稀疏回归算法从微观模拟和实验数据中发现PDE模型,同时结合相关的物理对称性。我们通过一系列应用来说明实际潜力,从模拟不相同的游泳细胞的手性活性颗粒模型到最近的微罗实验和训练鱼。在所有这些情况下,我们的方案学习流体动力学方程,重现自组织的集体动力学在模拟和实验中观察到。该推断框架使得可以并行地并且直接从视频数据测量大量的流体动力学参数。
Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.