【作者】 张琪；

【导师】 闫伟；

【作者基本信息】 东北师范大学 ， 计算数学， 2020， 硕士

【摘要】 近些年来,深度学习作为机器学习领域的一个新的研究方向,深度学习在智能搜索,智能机器人,人脸识别,语言处理,语音识别音乐新闻推荐等技术获得了很多进步成果,并且已开始大量应用于各类工程问题。在计算流体力学领域,基础模型复杂、运算量大、难以集成等瓶颈长期存在,从而具备了应用深度学习方法的发展条件。本研究应用深度学习的方法来求解流体力学问题。本文首先介绍了机器学习与深度学习的基本概念,展示了二者在工程领域以及交叉学科的广泛应用。因此我们引入了基于物理知识的神经网络,训练出这种神经网络来求解偏微分方程,具体给出了在对流体力学的方程中的应用。本文主要应用是学习基于物理的神经网络,使用神经网络来求偏微分方程的解。我们预测了对流方程与Burgers方程的解,并与精确比较。通过控制神经网络层数、每层神经元个数、训练数据量等变量,观察预测解与准确解之间的误差。进一步考虑了粘性项系数对Burgers方程的影响。最后结合图像,给出了流体力学欧拉方程的预测解与精确解的比较。更多还原

【Abstract】 In recent years,deep learning has become a new research direction in the field of machine learning.Deep learning has achieved many advancements in technologies such as intelligent search,intelligent robots,face recognition,language processing,and voice recognition music news recommendation,and has begun to a large number of Applied to various engineering problems.In the field of computational fluid mechanics,bottlenecks such as complex basic models,large amount of calculation,and difficulty in integration have existed for a long time,and thus have the development conditions for applying deep learning methods.Therefore,this study applies deep learning methods to solve fluid mechanics problems.This article first introduces the basic concepts of machine learning and deep learning,and shows the wide application of the two in the field of engineering and interdisciplinary.Therefore,we introduced a neural network based on physical knowledge,trained this neural network to solve partial differential equations,and specifically given the application in the equations of fluid mechanics.The main application of this article is to learn the physics-based neural network,and use the neural network to solve partial differential equations.We predicted the solutions of the convection equation and the Burgers equation and compared them with the exact ones.By controlling the number of neural network layers,the number of neurons in each layer,the amount of training data and other variables,observe the error between the predicted and accurate solutions.The effect of the coefficient of the viscosity term on the Burgers equation is further considered.Finally,combining the images,the predicted and exact solutions of the Euler equations in fluid mechanics are compared.更多还原