物理信息神经网络驱动的光纤非线性建模  

Nonlinear dynamic modeling of fiber optics driven by physics-informed neural network

作　　者：罗霄 张民[1] 蒋啸天 宋裕琛 张希萌 王丹石[1] Luo Xiao;Zhang Min;Jiang Xiaotian;Song Yuchen;Zhang Ximeng;Wang Danshi(State Key Laboratory of Information Photonics and Optical Communications,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学信息光子学与光通信全国重点实验室,北京100876

出　　处：《红外与激光工程》2023年第12期244-254,共11页Infrared and Laser Engineering

基　　金：国家自然科学基金项目(61975020,62171053)。

摘　　要：近年来,在计算物理领域提出了一种具有变革意义的利用神经网络直接求解微分方程的方案——物理信息神经网络(physics-informed neural network,PINN),引起了广泛关注,并且已经在多个领域的微分方程相关的问题中都得到了成功的验证。着眼于光纤非线性的建模,针对光纤中:光信号传输时受损耗、色散以及非线性等多种物理效应影响而发生演化;受激拉曼散射引起的功率转移;光模场在多种几何结构光纤中的分布与传输这三个场景展开研究。在数学上,这三个场景的控制方程分别为:非线性薛定谔方程、受激拉曼散射常微分方程以及傍轴亥姆霍兹方程,文中先后呈现了利用PINN求解这三个方程的具体实施方案及结果,并与数值方法进行对比分析,二者结果显示出较高的一致性,且PINN具备更低的计算复杂度。PINN作为一种精准、高效的微分方程求解框架,在未来有潜力推进光纤非线性建模的发展。Objective In the field of nonlinear dynamic of fiber optics,various fiber optic effects can be mathematically described by differential equations such as the nonlinear Schrödinger equation(NLSE)that describes the evolution of optical signals due to many physical effects such as loss,dispersion and nonlinearity;Stimulated Raman scattering(SRS)ordinary differential equation describes the power evolution caused by stimulated Raman scattering;And the paraxial Helmholtz equation(PHE)describes the distribution and propagation of optical mode fields in fibers with various geometric structures.For a long time in the past,differential equations,including these three equations,were solved using numerical methods,most of which are based on the idea of difference and microelement,and discretize the computational domain and then obtain the approximate solution of the differential equation through iteration,such as finite difference method(FDM),finite-difference time-domain method(FDTD),finite element method(FEM),spectral method(SM),etc.However,the main problems faced by numerical methods are as follows.In complex scenes(such as high nonlinearity,large scale,high dimension,etc.),in order to obtain stable and accurate results,it is necessary to divide the grid more precisely,and the number of iterations is proportional to the scale of the desired scene.As the complexity of the scene increases,the amount of computation increases Exponential growth,which consumes a lot of computing resources and computing time;The computational resources and time consumed by numerical methods are unbearable,and there is currently no reasonable solution to these problems.Therefore,it is necessary to introduce a new equation solving tool with the properties of efficiency and low complexity to avoid the difficulties faced by numerical methods to meet the needs of accurate modeling of the dynamic process of interest physical quantity in complex scene.In recent years,in the field of computational physics,a revolutionary scheme for directly solving di

关 键 词：光纤非线性 科学计算 物理信息神经网络 非线性薛定谔方程 受激拉曼散射 傍轴亥姆霍兹方程 

分 类 号：TN252[电子电信—物理电子学]