The discovery of governing equations from data is revolutionizing the development of some research fields, where the scientific data are abundant but the well-characterized quantitative descriptions are probably scarce. In this work, we propose to combine the direct simulation Monte Carlo (DSMC) method, which is a popular molecular simulation tool for gas flows, and machine learning to discover the governing equations for fluid dynamics. The DSMC method does not assume any macroscopic governing equations a priori but just relies on the model of molecular interactions at the microscopic level. The data generated by DSMC are utilized to derive the underlying governing equations using a sparse regression method proposed recently. We demonstrate that this strategy is capable of deriving a variety of equations in fluid dynamics, such as the momentum equation, diffusion equation, Fokker–Planck equation and vorticity transport equation. The data-driven discovery not only provides the right forms of the governing equations, but also determines accurate values of the transport coefficients such as viscosity and diffusivity. This work proves that data-driven discovery combined with molecular simulations is a promising and alternative method to derive governing equations in fluid dynamics, and it is expected to pave a new way to establish the governing equations of non-equilibrium flows and complex fluids.

中文翻译：

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基于分子模拟的流体动力学控制方程的数据驱动发现

从数据中发现控制方程正在彻底改变一些研究领域的发展，这些领域的科学数据丰富，但表征良好的定量描述可能很少。在这项工作中，我们建议将直接模拟蒙特卡罗 (DSMC) 方法（一种流行的气体流动分子模拟工具）与机器学习相结合，以发现流体动力学的控制方程。DSMC 方法不假设任何先验的宏观控制方程，而仅依赖于微观水平的分子相互作用模型。DSMC 生成的数据用于使用最近提出的稀疏回归方法推导出基本的控制方程。我们证明了这种策略能够推导出流体动力学中的各种方程，如动量方程、扩散方程、福克-普朗克方程和涡量输运方程。数据驱动的发现不仅提供了正确形式的控制方程，而且还确定了传输系数的准确值，例如粘度和扩散率。这项工作证明数据驱动的发现与分子模拟相结合是一种很有前途的替代方法来推导流体动力学中的控制方程，有望为建立非平衡流动和复杂流体的控制方程铺平道路。