【信息学院】Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations

ON2022-06-03文章来源 信息科学与技术学院CATEGORY活动

Speaker:    Ling Guo, Shanghai Normal University

Time:         10:00-11:00 , June 07

Location:   Tencent Meeting,Meeting ID369-359-909,Linkhttps://meeting.tencent.com/dm/BEBsOyBEnJC9

Host:          Yue Qiu

 

Abstract:

In this talk, the speaker will introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed neural networks (PINNs), their method relies on deep neural network surrogates in addition to a stochastic approximation strategy for computing the fractional derivatives of the DNN outputs, which can yield less overall computational cost compared to fPINNs and thus provide an opportunity for solving high dimensional fractional PDEs. They demonstrate the performance of MC-PINNs method via several examples that include high dimensional integral fractional Laplacian equations, parametric identification of time-space fractional PDEs, and fractional diffusion equation with random inputs.

 

Bio:

Ling Guo obtained her PhD degree of mathematics from Shanghai Jiaotong University in 2010. Afterwards she worked at Shanghai Normal University as assistant professor, associate professor and professor. She holds several visiting professorship positions worldwide, such as Brown University. Her research interest focuses on uncertainty quantification, scientific machine learning. Her research output has been published in SIAM Rev., SIAM J. Sci. Comp., Journal of Comp. Phy. et al.