Deep residual network for interpolation and inverse problems

In this paper, we introduce the Power-Enhancing Residual Network, a simplified version of the highway network. This novel neural network architecture aims to enhance interpolation capabilities. By incorporating power terms in residual elements, this architecture enhances the network's expressive capacity, leading to new possibilities in deep learning. We explore key design aspects such as network depth, width, and optimization techniques, showcasing its adaptability and performance advantages. Results highlight its precision and demonstrate superiority over conventional networks in accuracy, convergence speed, and computational efficiency. Additionally, we investigate deeper network configurations and apply the architecture to solve the inverse Burgers' equation, illustrating its effectiveness in real-world problems. Overall, the Power-Enhancing Residual Network represents a versatile and transformative solution, pushing the boundaries of machine learning. The codes implemented are available at: https://github.com/CMMAi/ResNet_for_PINN.