Inverse Problem of Nonlinear Schrödinger Equation as Learning of Convolutional Neural Network

2021/07/19 by Yiran Wang, Zhen Li, Wang, Yiran +1 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #cs.LG #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2107.08593

25 pages

arxiv created 2021/07/19 · arxiv updated 2021/07/20

Abstract

In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schrödinger equation, which is widely used in fiber-optic communications. The landscape and minimizers of the non-convex loss function of the learning problem are studied empirically. It provides a guidance for choosing hyper-parameters of the method. The estimation error of the optimal solution is discussed in terms of expressive power of the NLS-Net and data. Besides, we compare the performance of several training algorithms that are popular in deep learning. It is shown that one can obtain a relatively accurate estimate of the considered parameters using the proposed method. The study provides a natural framework of solving inverse problems of nonlinear partial differential equations with deep learning.

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