Inverse Problem of Nonlinear Schr\"odinger Equation as Learning of Convolutional Neural Network

• URL: http://arxiv.org/abs/2107.08593v1
• Date: Mon, 19 Jul 2021 02:54:37 GMT
• Title: Inverse Problem of Nonlinear Schr\"odinger Equation as Learning of Convolutional Neural Network
• Authors: Yiran Wang, Zhen Li
• Abstract summary: It is shown that one can obtain a relatively accurate estimate of the considered parameters using the proposed method. It provides a natural framework in inverse problems of partial differential equations with deep learning.
• Score: 5.676923179244324
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schr\"odinger 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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