Solving Traveltime Tomography with Deep Learning

作     者：Yuwei Fan Lexing Ying 

作者机构：Department of MathematicsStanford UniversityStanfordCA 94305USA 

出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)

年 卷 期：2023年第11卷第1期

页      面：3-19页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：partially supported by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Scientific Discovery through Advanced Computing(SciDAC)program partially supported by the National Science Foundation under award DMS-1818449 

主　　题：Traveltime tomography Eikonal equation Inverse problem Neural networks Convolutional neural network 

摘      要：This paper introduces a neural network approach for solving two-dimensional traveltime tomography(TT)problems based on the eikonal *** mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the *** inverse map is high-dimensional and *** the circular tomography geometry,a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular *** by this and filtered backprojection,we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net,with weights learned from training *** results demonstrate the efficiency of the proposed neural networks.