从噪声数据学习偏微分方程的复合神经网络

A Compound Neural Network for Learning Partial Differential Equations from Noisy Data

提出一种名为NN-PDE(neural network-partial differential equations)的复合神经网络方法,用于噪声数据预处理和学习偏微分方程。NN-PDE用一套神经网络负责数据预处理,另一套网络耦合备选的方程信息,进而学习潜在的控制方程。两套网络复合为一套网络,可更加高效地处理噪声数据,有效减小噪声的影响。使用NN-PDE学习多种物理方程(如Burgers方程、Korteweg-de Vries方程、Kuramoto-Sivashinsky方程和Navier-Stokes方程)的噪声数据,均可获得准确的控制方程。

A compound neural network method,NN-PDE(neural network-partial differential equations),is proposed for data preprocessing and learning partial differential equation.NN-PDE uses one sub network to preprocess noisy data,and another one to couple information of the alternative equations to learn the underlying governing equation.These two sub networks are merged into one compound network so that it can process noisy data more efficiently and effectively to reduce the influence of noise.Noisy data generated from various physical equations(such as Burgers equation,Korteweg-de Vries(KdV)equation,Kuramoto-Sivashinsky(KS)equation and Navier-Stokes(NS)equation)are studied with NN-PDE,and accurate governing equations are obtained.