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

Abstract 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.