Physics-Informed with Power-Enhanced Residual Network for Interpolation
  and Inverse Problems
Amir Noorizadegan D. L. Young Y. C. Hon C. S. Chen
This paper introduces a novel neural network structure called the
Power-Enhancing residual network, designed to improve interpolation
capabilities for both smooth and non-smooth functions in 2D and 3D settings. By
adding power terms to residual elements, the architecture boosts the network's
expressive power. 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. The study also looks at the
impact of deeper network. 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. The codes implemented
are available at: \url{https://github.com/CMMAi/ResNet_for_PINN}.