Data assimilation (DA) refers to methodologies which combine data and underlying governing equations to provide an estimation of a complex system. Physics informed neural network (PINN) provides an innovative machine learning technique for solving and discovering the physics in nature. By encoding general nonlinear partial differential equations, which govern different physical systems such as fluid flows, to the deep neural network, PINN can be used as a tool for DA. Due to its nature that neither numerical differential operation nor temporal and spatial discretization is needed, PINN is straightforward for implementation and getting more and more attention in the academia. In this paper, we apply the PINN to several flow problems and explore its potential in fluid physics. Both the mesoscopic Boltzmann equation and the macroscopic Navier-Stokes are considered as physics constraints. We first introduce a discrete Boltzmann equation informed neural network and evaluate it with a one-dimensional propagating wave and two-dimensional lid-driven cavity flow. Such laminar cavity flow is also considered as an example in an incompressible Navier-Stokes equation informed neural network. With parameterized Navier-Stokes, two turbulent flows, one within a C-shape duct and one passing a bump, are studied and accompanying pressure field is obtained. Those examples end with a flow passing through a porous media. Applications in this paper show that PINN provides a new way for intelligent flow inference and identification, ranging from mesoscopic scale to macroscopic scale, and from laminar flow to turbulent flow.

数据同化（DA）是指将数据和基本控制方程式组合以提供对复杂系统的估计的方法。物理信息神经网络（PINN）提供了一种创新的机器学习技术，用于解决和发现自然界的物理问题。通过将控制不同物理系统（例如流体流动）的一般非线性偏微分方程编码到深层神经网络，PINN可以用作DA的工具。由于不需要数值微分运算和时间和空间离散化的性质，PINN易于实现并且在学术界越来越受到关注。在本文中，我们将PINN应用于多个流动问题，并探索其在流体物理学中的潜力。介观的玻尔兹曼方程和宏观的纳维-斯托克斯都被视为物理约束。我们首先介绍一个离散的Boltzmann方程告知神经网络，并使用一维传播波和二维盖驱动腔流动对其进行评估。在不可压缩的Navier-Stokes方程通知的神经网络中，此类层流腔也被视为示例。使用参数化的Navier-Stokes，研究了两种湍流，一种在C形导管内，另一种通过凸点，并获得了相应的压力场。这些示例以流过多孔介质的流结束。本文的应用表明，PINN为智能流推断和识别提供了一种新方法，其范围从介观尺度到宏观尺度，从层流到湍流。