Inverse Problem of Nonlinear Schr"odinger Equation as Learning of Convolutional Neural Network
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 23 of its 59 references that are in the map. First posted on arXiv 19 Jul 2021.
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11 more
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