PI-VEGAN:Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations

作     者：Ruisong Gao Yufeng Wang Min Yang Chuanjun Chen 

作者机构：School of Mathematics and Information SciencesYantai UniversityYantaiChina 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2023年第16卷第4期

页      面：931-953页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11771257,12271468) the Natural Science Foundation of Shandong Province(Grant Nos.ZR2021MA010,ZR2021ZD03) 

主　　题：Stochastic differential equations physics-informed variational inference generative adversarial networks inverse problems 

摘      要：We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network(PI-VEGAN),that effectively tackles the forward,inverse,and mixed problems of stochastic differential *** these scenarios,the governing equations are known,but only a limited number of sensor measurements of the system parameters are *** integrate the governing physical laws into PI-VEGAN with automatic differentiation,while introducing a variational encoder for approximating the latent variables of the actual distribution of the *** latent variables are integrated into the generator to facilitate accurate learning of the characteristics of the stochastic partial *** model consists of three components,namely the encoder,generator,and discriminator,each of which is updated alternatively employing the stochastic gradient descent *** evaluate the effectiveness of PI-VEGAN in addressing forward,inverse,and mixed problems that require the concurrent calculation of system parameters and *** results demonstrate that the proposed method achieves satisfactory stability and accuracy in comparison with the previous physics-informed generative adversarial network(PI-WGAN).