Journal Article

Accurately Models the Relationship Between Physical Response and Structure Using Kolmogorov–Arnold Network

Wang, Yang, Gao, Zhibin, Li, Baowen, Shen, Xiangying, Sun, Jun, Zhu, Guimei, Zhu, Changliang, Ding, Xiangdong, Xiang, Changsheng, Zhang, Shuzhe

2025

Overview

Artificial intelligence (AI) in science is a key area of modern research. However, many current machine learning methods lack interpretability, making it difficult to grasp the physical mechanisms behind various phenomena, which hampers progress in related fields. This study focuses on the Poisson's ratio of a hexagonal lattice elastic network as it varies with structural deformation. By employing the Kolmogorov–Arnold Network (KAN), the transition of the network's Poisson's ratio from positive to negative as the hexagonal structural element shifts from a convex polygon to a concave polygon was accurately predicted. The KAN provides a clear mathematical framework that describes this transition, revealing the connection between the Poisson's ratio and the geometric properties of the hexagonal element, and accurately identifying the geometric parameters at which the Poisson's ratio equals zero. This work demonstrates the significant potential of the KAN network to clarify the mathematical relationships that underpin physical responses and structural behaviors. The present study underscores the remarkable capabilities of the Kolmogorov‐Arnold Network (KAN) in formula fitting for physical systems. KAN predicts the relationship between the Poisson's ratio of a metamaterial structure and its geometric parameters, demonstrating the transition of Poisson's ratio from positive to negative as the hexagonal component changes shape, illustrating its adaptability in analyzing complex systems.

• Publisher: John Wiley & Sons, Inc,John Wiley and Sons Inc,Wiley
• Subject: Accuracy / Artificial intelligence / Deep learning / Kolmogorov‐Arnold Network / Mechanical property / Neural networks / Poisson's ratio