利用物理信息神经网络求解多模非线性Schrödinger方程

IF 0.5 4区 数学 Q3 MATHEMATICS
I. A. Chuprov, J. Gao, D. S. Efremenko, F. A. Buzaev, V. V. Zemlyakov
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引用次数: 0

摘要

单模光纤(SMFs)已成为现代通信系统的基础。然而,它们的容量预计将在不久的将来达到理论极限。多模光纤(MMF)的使用被认为是解决这一容量不足的最有希望的解决方案之一。描述光在MMF中传播的多模非线性Schrödinger方程(MMNLSE)比SMF方程要复杂得多,这使得基于MMF的系统的数值模拟在大多数实际情况下计算成本高昂且不切实际。在本文中,我们应用物理通知神经网络(pinn)来解决MMNLSE问题。我们证明了pin n的简单实现不会产生令人满意的结果。我们研究了PINN的收敛性,并提出了一种新的零阶色散系数的缩放变换,该变换允许PINN考虑所有重要的物理效应。对于长度达几百米的光纤,我们的计算结果与分步傅里叶(SSF)方法很好地吻合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solution of the Multimode Nonlinear Schrödinger Equation Using Physics-Informed Neural Networks

Single-mode optical fibers (SMFs) have become the foundation of modern communication systems. However, their capacity is expected to reach its theoretical limit in the near future. The use of multimode fibers (MMF) is seen as one of the most promising solutions to address this capacity deficit. The multimode nonlinear Schrödinger equation (MMNLSE) describing light propagation in MMF is significantly more complex than the equations for SMF, making numerical simulations of MMF-based systems computationally costly and impractical for most realistic scenarios. In this paper, we apply physics-informed neural networks (PINNs) to solve the MMNLSE. We show that a simple implementation of PINNs does not yield satisfactory results. We investigate the convergence of PINN and propose a novel scaling transformation for the zeroth-order dispersion coefficient that allows PINN to account for all important physical effects. Our calculations show good agreement with the Split-Step Fourier (SSF) method for fiber lengths of up to several hundred meters.

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来源期刊
Doklady Mathematics
Doklady Mathematics 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
39
审稿时长
3-6 weeks
期刊介绍: Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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