Imperial College London
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DR HUI XU

Faculty of Engineering, Department of Aeronautics

Honorary Research Fellow
 
 
 
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Contact

 

hui.xu

 
 
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Location

 

363Roderic Hill BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Wu:2022:10.1007/s10915-022-01980-y,
author = {Wu, W and Feng, X and Xu, H},
doi = {10.1007/s10915-022-01980-y},
journal = {Journal of Scientific Computing},
title = {Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations},
url = {http://dx.doi.org/10.1007/s10915-022-01980-y},
volume = {93},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - An improved neural networks method based on domain decomposition is proposed to solve partial differential equations, which is an extension of the physics informed neural networks (PINNs). Although recent research has shown that PINNs perform effectively in solving partial differential equations, they still have difficulties in solving large-scale complex problems, due to using a single neural network and gradient pathology. In this paper, the proposed approach aims at implementing calculations on sub-domains and improving the expressiveness of neural networks to mitigate gradient pathology. By investigations, it is shown that, although the neural networks structure and the loss function are complicated, the proposed method outperforms the classical PINNs with respect to training effectiveness, computational accuracy, and computational cost.
AU  - Wu,W
AU  - Feng,X
AU  - Xu,H
DO  - 10.1007/s10915-022-01980-y
PY  - 2022///
SN  - 0885-7474
TI  - Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations
T2  - Journal of Scientific Computing
UR  - http://dx.doi.org/10.1007/s10915-022-01980-y
VL  - 93
ER  -
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