The codes are implemented in tensorflow--1.14 or 1.15 under the interpreter python3.6 or python3.7. Additionally, if the codes are runned on a Server, one should use the miniconda3 for python 3.7 or 3.6. However, if you dowmload the latest version of miniconda3 from https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh, you will get a miniconda3 based on python 3.8. Hence, you should redirect to the https://docs.conda.io/en/latest/miniconda.html, then download the miniconda3 based on python3.7.
Based on the class of Python, we have reconstructed the all codes for MscaleDNN architecture and submitted them in url https://github.com/Blue-Giant/MscaleDNN_tf1Class
By means of the package of Pytorch, the corresponding codes of MscaleDNN can be found in url https://github.com/Blue-Giant/MscaleDNN_torch
It is need to point that the performance of class-based MscaleDNN is inferior to that of nonclass-based MscaleDNN. This is an open question.
created by Xi-An Li, Zhi-Qin John, Xu and Lei Zhang
This work exploited the technique of shifting the input data in narrow-range into large-range, then fed the transformed data into the DNN pipline.
Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse of dimensionality. In this work, we utilize the multi-scale DNN-based algorithm (MscaleDNN) proposed by Liu, Cai and Xu (2020) to solve multi-scale elliptic problems with possible nonlinearity, for example, the p-Laplacian problem. We improve the MscaleDNN algorithm by a smooth and localized activation function. Several numerical examples of multi-scale elliptic problems with separable or non-separable scales in low-dimensional and high-dimensional Euclidean spaces are used to demonstrate the effectiveness and accuracy of the MscaleDNN numerical scheme.
The matlab codes in 2D辅助matlab代码/p=2 are useful for E1,E2,E3 and E4.
The matlab codes in 2D辅助matlab代码/p=3Forier_scale are useful for E5.
The matlab codes in 2D辅助matlab代码/p=3Subspace are useful for E6.
Based on the above codes(DNN frameworks), we further designed a new algorithm to solve multi-scale PDEs, one can refer to https://github.com/Blue-Giant/SubspaceDNN_tf1