Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Proc Natl Acad Sci U S A. 2023 Feb 14;120(7):e2206994120. doi: 10.1073/pnas.2206994120. Epub 2023 Feb 10.
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.
近年来，高分辨率成像技术和基于粒子的模拟方法的进步使得对各种生物和工程活性物质系统中的集体动力学进行精确的微观特征化成为可能。与此同时，用于学习可解释连续体模型的数据驱动算法显示出了从连续体模拟数据中恢复基础偏微分方程（PDE）的巨大潜力。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动力学方程仍然是一个主要挑战，特别是当连续体模型事先未知或分析粗粒化失败时，这种情况在非稀溶液和非均匀系统中经常发生。在这里，我们提出了一个框架，该框架利用谱基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其实用潜力，从模仿非同质游动细胞的手性活性粒子模型到最近的微辊实验和成群游动的鱼类。在所有这些情况下，我们的方案学习了能够再现模拟和实验中观察到的自组织集体动力学的流体动力学方程。该推理框架使得可以并行且直接从视频数据中测量大量流体动力学参数。
