【摘要】 人工智能时代的来临使得神经网络与深度学习在不同学科领域中得到了应用。本研究提出了一种基于深度神经网络的方法，用物理信息驱动的神经网络解决二维Navier-Stokes方程求解问题，并对整个物理系统进行建模。为了方便传统计算流体力学（Computational Fluid Dynamics,CFD）数值计算，采用推进剂通入稀薄气体空腔这一经典问题来代替真空中的不可压缩气体流动问题，以满足传统CFD方法的连续性介质假设。在本文所提出的方法中，将Navier-Stokes方程与基于物理信息神经网络（Physics-Informed Neural Networks,PINN）相结合，将物理信息嵌入神经网络，使结果更符合物理定律，建模性能更强。另外此研究引入了基于域分解思想的扩展物理信息神经网络（eXtended Physics-Informed Neural Network,XPINN）方法，试图改进PINN建模效果。结果表明本文提出的基于PINN的气体扩散场建模方法有以下优点：1）与传统的CFD方法相比，该方法与FLUENT求解结果误差较小，可以得到比较准确的数值结果；2）比纯数据驱动的神经网络方法建模预测精度和物理一致性；3）可以求解偏微分方程（Partial Differential Equations,PDEs）逆问题；4）基于域分解思想的XPINN的建模性能要比普通PINN方法表现更优秀。更多还原

【Abstract】 [Background] The advent of the Artificial Intelligence(AI) era has led to the application of neural networks and deep learning in different disciplines. [Purpose] This study aims to solve incompressible gas dispersion problem in an electric thruster discharge cavity using deep neural network-based approach with a physical information-driven neural network. [Methods] First of all, the traditional Computational Fluid Dynamics(CFD) numerical calculations were facilitated and the classical problem of propellant passing into a thin gas cavity was used to replace the incompressible gas flow problem in vacuum to satisfy the continuum medium assumption of the traditional CFD method. Then, the Navier-Stokes equations were combined with Physics-Informed Neural Networks(PINN) to embed physical information into the networks to ensure that the results were more consistent with the laws of physics to enhance the modeling performance. Subsequently, based on the idea of domain decomposition, the XPINN method was proposed to improve the modeling effect of PINN. Finally, predicted results of PINN and XPINN were compared with those of FLUENT simulation. [Results] Comparison results show that the method proposed in this paper has the following advantages: 1) Compared with the traditional CFD method, the PINN-based gas diffusion field modeling method has less error with the FLUENT solution results, and more accurate numerical results can be obtained; 2) The predictive accuracy and physical consistency of PINN-based gas diffusion field modeling approach outperform the purely data-driven neural network approach; 3) It can solve the Partial Differential Equations(PDEs) inverse problem; 4) The modeling performance of XPINN based on the idea of domain decomposition is stronger than that of the ordinary PINN method. [Conclusions] This study demonstrates that the results of PINN method are close to those of traditional CFD methods, while the eXtended Physics-Informed Neural Network(XPINN) method based on the idea of domain decomposition improves the solution of the ordinary PINN.更多还原