Physical-preserving Deep Learning Algorithm For Three Dimensional Convection-diffusion-reaction Problem

In the fields of fluid mechanics,gas dynamics,environmental science,and energy de-velopment,convection-diffusion reaction equation has important theoretical significance and extensive application value.Model's theory and numerical simulation method of this problem have always been the research focus of computational mathematics and computational physics,and many scholars have paid attention to it.In general,the solution of convection-diffusion-reaction equation by analytical method is limited by the dimensional disaster of the higher dimensional region and the geometric complexity of manifold region.Therefore,it is very important to construct a stable and efficient numerical simulation method.The main research of this paper is to design a data-driven deep learning algorithm for solving three dimensional convection-diffusion-reaction problem.The specific research contents and achievements of this paper are as follows:In this paper,the meshless method is combined with the deep neural network with strong nonlinearity.Data containing equation information and physical laws are used to analyze and statistics the data and reveal the information contained therein.Deep learning algorithm for three dimensional convection-diffusion-reaction equation is designed to overcome the high computational cost caused by the mesh division of high dimensional problems.The validity of the proposed method is verified by numerical experiments.Secondly,the flexibility and diversity of the loss function are used to increase the con-straint of the loss function satisfying the extremum principle.To design a deep learning al-gorithm that preserves physical properties to solve high dimensional convection-diffusion-reaction problem,Overcomes the defect that the traditional finite element method can not guar-antee the extremum principle when solving the parabolic problem.The numerical simulation results verify the reliability and the preservation property of the algorithm.Finally,the strong nonlinearity of deep neural network is used to effectively reduce the nu-merical oscillation caused by three dimensional steady convection-dominated diffusion prob-lem.By using nonlinear activation functions and increasing the depth of the neural network and the number of neurons,To improve the nonlinear expression ability of deep neural network.It can be used to approximate the complex nonlinear function and reduce the numerical oscilla-tion caused by the traditional standard finite element method.The stability and efficiency of the proposed method are verified by numerical simulation of three dimensional steady convection-diffusion-reaction problem.