Coarse-Gridded Simulation of the Nonlinear Schrödinger Equation with Machine Learning

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Benjamin F. Akers, Kristina O. F. Williams
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引用次数: 0

Abstract

A numerical method for evolving the nonlinear Schrödinger equation on a coarse spatial grid is developed. This trains a neural network to generate the optimal stencil weights to discretize the second derivative of solutions to the nonlinear Schrödinger equation. The neural network is embedded in a symmetric matrix to control the scheme’s eigenvalues, ensuring stability. The machine-learned method can outperform both its parent finite difference method and a Fourier spectral method. The trained scheme has the same asymptotic operation cost as its parent finite difference method after training. Unlike traditional methods, the performance depends on how close the initial data are to the training set.
利用机器学习对非线性薛定谔方程进行粗网格模拟
本研究开发了一种在粗空间网格上演化非线性薛定谔方程的数值方法。该方法训练神经网络生成最佳模版权重,以离散化非线性薛定谔方程解的二次导数。神经网络被嵌入到一个对称矩阵中,以控制该方案的特征值,从而确保稳定性。机器学习方法的性能优于其母有限差分法和傅立叶谱法。训练后的方案与其母有限差分法具有相同的渐近运算成本。与传统方法不同的是,其性能取决于初始数据与训练集的接近程度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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