地震波正演问题的物理信息神经网络算法研究进展  

Research progress of physics-informed neural network in seismic wave modeling

作　　者：邹婧博 刘财[1,2] 赵鹏飞 ZOU JingBo;LIU Cai;ZHAO PengFei(College of Geo-exploration Science and Technology,Jilin University,Changchun 130026,China;Key Laboratory of Geophysical Exploration Equipment,Ministry of Education,Jilin University,Changchun 130026,China)

机构地区：[1]吉林大学地球探测科学与技术学院,长春130026 [2]吉林大学地球信息探测仪器教育部重点实验室,长春130026

出　　处：《地球物理学进展》2023年第1期430-448,共19页Progress in Geophysics

基　　金：国家自然基金项目(41874125);国家重点研发计划课题(2021YFC1523401);自然资源部滨海城市地下空间地质安全重点实验室开放基金课题(BHKF2021Y02)联合资助。

摘　　要：偏微分方程作为一种描述客观物理规律的重要工具,可应用于解决大多数科学问题和工程问题.在地球物理学中,求解波动方程是地震波场数值模拟的重要步骤,对于偏移成像和反演起着至关重要的作用.随着勘探目标复杂化,地震波方程的数学描述也更加复杂,现有的经典地震波数值模拟方法存在一些待完善之处,需要一些新型正演算法的应用.物理信息神经网络(Physics-Informed Neural Network,简称PINN)是一种利用神经网络求解偏微分方程近似解的有效手段,通过自动微分将偏微分方程及其定解条件引入损失函数中,在最小化数据驱动误差的同时,使其满足方程的物理约束条件.本文在分析PINN原理并总结其研究现状的基础上,对其在波动方程正演中已有成果进行归纳和分析,展望了其未来可能的研究方向,并对PINN在一维声波方程正演中的应用进行了探究.Partial differential equations,as important tools to describe objective physical laws,can be applied to solve the most scientific and engineering problems.Solving wave equations is an important part of numerical simulation of seismic wave field in Geophysics,which plays a necessary role in migration imaging and inversion.Based on the complexity of the structure of exploration targets,the mathematical descriptions of seismic wave equations are facing challenges.Classical numerical simulation methods have some pending improvements,and the demand for new orthogonal algorithms has become more vigorous.Physics-Informed Neural Network(PINN)is effective to get approximate solutions of partial differential equations by neural networks.PDEs,initial and boundary conditions will be embedded into loss functions through automatic differentiation to minimize data-driven errors while satisfying the physical constraint conditions of PDEs.Based on the analysis of PINN and the summary of its current research status,this paper summarizes and analyzes its existing study of solving wave equations,looks forward to its possible research directions in the future,and explores the application of PINN in 1D acoustic wave equations.

关 键 词：地震波正演 物理信息神经网络 深度学习 自动微分 

分 类 号：P631[天文地球—地质矿产勘探]