Power-enhanced residual network for function approximation and physics-informed inverse problems
Journal
Applied Mathematics and Computation
Journal Volume
480
Start Page
128910
ISSN
0096-3003
Date Issued
2024-11-01
Author(s)
DOI
10.1016/j.amc.2024.128910
Abstract
In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network, particularly the multi-layer perceptrons (MLPs). This paper introduces a novel neural network structure called the Power-Enhancing residual network, inspired by highway network and residual network, designed to improve the network's capabilities for both smooth and non-smooth functions approximation in 2D and 3D settings. By incorporating power terms into residual elements, the architecture enhances the stability of weight updating, thereby facilitating better convergence and accuracy. The study explores network depth, width, and optimization methods, showing the architecture's adaptability and performance advantages. Consistently, the results emphasize the exceptional accuracy of the proposed Power-Enhancing residual network, particularly for non-smooth functions. Real-world examples also confirm its superiority over plain neural network in terms of accuracy, convergence, and efficiency. Moreover, the proposed architecture is also applied to solving the inverse Burgers' equation, demonstrating superior performance. In conclusion, the Power-Enhancing residual network offers a versatile solution that significantly enhances neural network capabilities by emphasizing the importance of stable weight updates for effective training in deep neural networks. The codes implemented are available at: https://github.com/CMMAi/ResNet_for_PINN.
Subjects
Function approximation
Highway network for PINN
Interpolation
Inverse problem
Neural networks
Partial differential equations
Residual network
Publisher
Elsevier BV
Type
journal article