Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）

陈泽斌; 冯新龙

doi:10.13568/j.cnki.651094.651316.2022.06.25.0001

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Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）

数理科学 | 更新时间：2026-01-21

- Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）
- Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）
- 新疆大学学报（自然科学版中英文） 2023年40卷第2期页码：142-149
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  supported by Open Project of Key Laboratory of Xinjiang “Machine learning for incompressible magnetohydrodynamics models”(2020D04002)
- DOI：10.13568/j.cnki.651094.651316.2022.06.25.0001
  中图分类号： TP183;O241.82
- 纸质出版：2023
- 稿件说明：
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[1]陈泽斌,冯新龙.Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）[J].新疆大学学报(自然科学版)(中英文),2023,40(02):142-149.
[1]陈泽斌,冯新龙.Runge-Kutta型多尺度神经网络求解非定常偏微分方程（英文）[J].新疆大学学报(自然科学版)(中英文),2023,40(02):142-149. DOI： 10.13568/j.cnki.651094.651316.2022.06.25.0001.

DOI：10.13568/j.cnki.651094.651316.2022.06.25.0001.

摘要

提出了基于Runge-Kutta的多尺度神经网络方法求解非定常偏微分方程.利用q阶Runge-Kutta构造时间迭代格式

通过建立多时间步的总损失函数

实现多时间步的神经网络参数共享

并预测时域内任意时刻的函数值.同时采用m-缩放因子加快损失函数收敛

提高数值解精度.最后

给出了若干数值实验验证所提方法的有效性．

Abstract

This paper proposes the multi-scale neural networks method based on Runge-Kutta to solve unsteady partial differential equations. The method uses q-order Runge-Kutta to construct the time iteratione scheme

and further establishes the total loss function of multiple time steps

which is to realize the parameter sharing of neural networks with multiple time steps

and to predict the function value at any moment in the time domain. Besides

the m-scaling factor is adopted to speed up the convergence of the loss function and improve the accuracy of the numerical solution. Finally

several numerical experiments are presented to demonstrate the effectiveness of the proposed method.

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references

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