# Power-Enhanced Residual Network for Function Approximation and Physics-Informed Inverse Problems

arXiv: https://arxiv.org/abs/2310.15690 · HTML: https://mlsanity.com/paper/2310.15690/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [Residual Connections Encourage Iterative Inference](https://mlsanity.com/paper/1710.04773/) (2017)
- [Highway and Residual Networks learn Unrolled Iterative Estimation](https://mlsanity.com/paper/1612.07771/) (2016)

## Built on by (most cited first, 5 of 5)

- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning](https://mlsanity.com/paper/2407.07375/) (2024)
- [Partition-of-Unity Gaussian Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.23599/) (2026)
- [Highway Networks for Improved Surface Reconstruction: The Role of Residuals and Weight Updates](https://mlsanity.com/paper/2407.08134/) (2024)
- [Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2605.21534/) (2026)

## Abstract (arXiv)

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: urlhttps://github.com/CMMAi/ResNetforPINN.