# Enhancing Physics-Informed Neural Networks with a Hybrid Parallel Kolmogorov-Arnold and MLP Architecture

arXiv: https://arxiv.org/abs/2503.23289 · HTML: https://mlsanity.com/paper/2503.23289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization](https://mlsanity.com/paper/1908.09375/) (2019)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)

## Abstract (arXiv)

Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid Parallel Kolmogorov-Arnold Network (KAN) and Multi-Layer Perceptron (MLP) Physics-Informed Neural Network (HPKM-PINN), a novel architecture that synergistically integrates parallelized KAN and MLP branches within a unified PINN framework. The HPKM-PINN introduces a scaling factor xi, to optimally balance the complementary strengths of KAN's interpretable function approximation and MLP's nonlinear feature learning, thereby enhancing predictive performance through a weighted fusion of their outputs. Through systematic numerical evaluations, we elucidate the impact of the scaling factor xi on the model's performance in both function approximation and partial differential equation (PDE) solving tasks. Benchmark experiments across canonical PDEs, such as the Poisson and Advection equations, demonstrate that HPKM-PINN achieves a marked decrease in loss values (reducing relative error by two orders of magnitude) compared to standalone KAN or MLP models. Furthermore, the framework exhibits numerical stability and robustness when applied to various physical systems. These findings highlight the HPKM-PINN's ability to leverage KAN's interpretability and MLP's expressivity, positioning it as a versatile and scalable tool for solving complex PDE-driven problems in computational science and engineering.