Runge-Kutta型多尺度神经网络求解非定常偏微分方程  

Multi-Scale Neural Networks Based on Runge-Kutta Method for Solving Unsteady Partial Differential Equations

作　　者：陈泽斌 冯新龙[1] CHEN Zebin;FENG Xinlong(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第2期142-149,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：Open Project of Key Laboratory of Xinjiang“Machine learning for incompressible magnetohydrodynamics models”(2020D04002)。

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.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.

关 键 词：非定常偏微分方程 q阶Runge-Kutta法 多尺度神经网络 m-缩放因子 高精度 

分 类 号：O175[理学—数学]