๐ Legend-KINN: A Legendre Polynomial-Based Kolmogorov-Arnold-Informed Neural Network for Efficient PDE Solving
Summary & Overview
This paper presents a key component of my Ph.D. research: a significant study aimed at overcoming critical limitations in Physics-Informed Neural Networks (PINNs). This work, recently accepted by the journal Expert Systems With Applications, introduces a novel architecture to solve common problems of interpretability and training instability. ๏ปฟ We developed a unique Legendre Polynomial-Based Kolmogorov-Arnold-Informed Neural Network (Legend-KINN). A key innovation of our model is using Legendre polynomials to explicitly enhance the physical consistency and interpretability of the network. We also integrate a pseudo-time stepping method to stabilize the backpropagation path, which ensures faster and more robust convergence with significantly fewer parameters.
